Optimal Wentzell Boundary Control of Parabolic Equations
Energy Technology Data Exchange (ETDEWEB)
Luo, Yousong, E-mail: yousong.luo@rmit.edu.au [RMIT University, School of Mathematical and Geospatial Sciences (Australia)
2017-04-15
This paper deals with a class of optimal control problems governed by an initial-boundary value problem of a parabolic equation. The case of semi-linear boundary control is studied where the control is applied to the system via the Wentzell boundary condition. The differentiability of the state variable with respect to the control is established and hence a necessary condition is derived for the optimal solution in the case of both unconstrained and constrained problems. The condition is also sufficient for the unconstrained convex problems. A second order condition is also derived.
Optimal boundary control and boundary stabilization of hyperbolic systems
Gugat, Martin
2015-01-01
This brief considers recent results on optimal control and stabilization of systems governed by hyperbolic partial differential equations, specifically those in which the control action takes place at the boundary. The wave equation is used as a typical example of a linear system, through which the author explores initial boundary value problems, concepts of exact controllability, optimal exact control, and boundary stabilization. Nonlinear systems are also covered, with the Korteweg-de Vries and Burgers Equations serving as standard examples. To keep the presentation as accessible as possible, the author uses the case of a system with a state that is defined on a finite space interval, so that there are only two boundary points where the system can be controlled. Graduate and post-graduate students as well as researchers in the field will find this to be an accessible introduction to problems of optimal control and stabilization.
Optimal control problems for impulsive systems with integral boundary conditions
Directory of Open Access Journals (Sweden)
Allaberen Ashyralyev
2013-03-01
Full Text Available In this article, the optimal control problem is considered when the state of the system is described by the impulsive differential equations with integral boundary conditions. Applying the Banach contraction principle the existence and uniqueness of the solution is proved for the corresponding boundary problem by the fixed admissible control. The first and second variation of the functional is calculated. Various necessary conditions of optimality of the first and second order are obtained by the help of the variation of the controls.
Optimal control of wind turbines in a turbulent boundary layer
Yilmaz, Ali Emre; Meyers, Johan
2016-11-01
In recent years, optimal control theory was combined with large-eddy simulations to study the optimal control of wind farms and their interaction with the atmospheric boundary layer. The individual turbine's induction factors were dynamically controlled in time with the aim of increasing overall power extraction. In these studies, wind turbines were represented using an actuator disk method. In the current work, we focus on optimal control on a much finer mesh (and a smaller computational domain), representing turbines with an actuator line method. Similar to Refs., optimization is performed using a gradient-based method, and gradients are obtained employing an adjoint formulation. Different cases are investigated, that include a single and a double turbine case both with uniform inflow, and with turbulent-boundary-layer inflow. The authors acknowledge support from the European Research Council (FP7-Ideas, Grant No. 306471).
Optimal Control of a Parabolic Equation with Dynamic Boundary Condition
Energy Technology Data Exchange (ETDEWEB)
Hoemberg, D., E-mail: hoemberg@wias-berlin.de; Krumbiegel, K., E-mail: krumbieg@wias-berlin.de [Weierstrass Institute for Applied Mathematics and Stochastics, Nonlinear Optimization and Inverse Problems (Germany); Rehberg, J., E-mail: rehberg@wias-berlin.de [Weierstrass Institute for Applied Mathematics and Stochastics, Partial Differential Equations (Germany)
2013-02-15
We investigate a control problem for the heat equation. The goal is to find an optimal heat transfer coefficient in the dynamic boundary condition such that a desired temperature distribution at the boundary is adhered. To this end we consider a function space setting in which the heat flux across the boundary is forced to be an L{sup p} function with respect to the surface measure, which in turn implies higher regularity for the time derivative of temperature. We show that the corresponding elliptic operator generates a strongly continuous semigroup of contractions and apply the concept of maximal parabolic regularity. This allows to show the existence of an optimal control and the derivation of necessary and sufficient optimality conditions.
Directory of Open Access Journals (Sweden)
Weifeng Wang
2014-01-01
Full Text Available We study an optimal control problem governed by a semilinear parabolic equation, whose control variable is contained only in the boundary condition. An existence theorem for the optimal control is obtained.
Benincasa, T.; Donado Escobar, L. D.; Moroşanu, C.
2016-08-01
This paper is concerned with an optimal control problem (P) (both distributed control as well as boundary control) for the nonlinear phase-field (Allen-Cahn) equation, involving a regular potential and dynamic boundary condition. A family of approximate optimal control problems (Pɛ) is introduced and results for the existence of an optimal control for problems (P) and (Pɛ) are proven. Furthermore, the convergence result of the optimal solution of problem (Pɛ) to the optimal solution of problem (P) is proved. Besides the existence of an optimal control in problem (Pɛ), necessary optimality conditions (Pontryagin's principle) as well as a conceptual gradient-type algorithm to approximate the optimal control, were established in the end.
Optimal boundary control of parabolic system on doubly connected region in new space
Institute of Scientific and Technical Information of China (English)
陈任昭
1995-01-01
The optimal boundary control of the system governed by parabolic partial differential equations on a doubly connected region in the new space advanced by Lions is discussed. It proves the necessary and sufficient conditions for a control to be optimal and obtains the optimality system consisting of partial differential equations and variational inequalities. And the application of penalty shifting method to the approximate solution of control problems for the system is researched.
Construction of asymptotically optimal control for crisscross network from a free boundary problem
Directory of Open Access Journals (Sweden)
Amarjit Budhiraja
2016-12-01
Full Text Available An asymptotic framework for optimal control of multiclass stochastic processing networks, using formal diffusion approximations under suitable temporal and spatial scaling, by Brownian control problems (BCP and their equivalent workload formulations (EWF, has been developed by Harrison (1988. This framework has been implemented in many works for constructing asymptotically optimal control policies for a broad range of stochastic network models. To date all asymptotic optimality results for such networks correspond to settings where the solution of the EWF is a reflected Brownian motion in $\\mathbb{R} _{+}$ or a wedge in $\\mathbb{R} _{+}^{2}$. In this work we consider a well studied stochastic network which is perhaps the simplest example of a model with more than one dimensional workload process. In the regime considered here, the singular control problem corresponding to the EWF does not have a simple form explicit solution. However, by considering an associated free boundary problem one can give a representation for an optimal controlled process as a two dimensional reflected Brownian motion in a Lipschitz domain whose boundary is determined by the solution of the free boundary problem. Using the form of the optimal solution we propose a sequence of control policies, given in terms of suitable thresholds, for the scaled stochastic network control problems and prove that this sequence of policies is asymptotically optimal. As suggested by the solution of the EWF, the policy we propose requires a server to idle under certain conditions which are specified in terms of thresholds determined from the free boundary.
Solvability for a Class of Abstract Two-Point Boundary Value Problems Derived from Optimal Control
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Wang Lianwen
2007-01-01
Full Text Available The solvability for a class of abstract two-point boundary value problems derived from optimal control is discussed. By homotopy technique existence and uniqueness results are established under some monotonic conditions. Several examples are given to illustrate the application of the obtained results.
Solvability for a Class of Abstract Two-Point Boundary Value Problems Derived from Optimal Control
Directory of Open Access Journals (Sweden)
Lianwen Wang
2008-01-01
Full Text Available The solvability for a class of abstract two-point boundary value problems derived from optimal control is discussed. By homotopy technique existence and uniqueness results are established under some monotonic conditions. Several examples are given to illustrate the application of the obtained results.
Directory of Open Access Journals (Sweden)
Russel J Stonier
2003-08-01
Full Text Available In this paper we examine the application of evolutionary algorithms to find open-loop control solutions of the optimal control problem arising from the semidiscretisation of a linear parabolic tracking problem with boundary control. The solution is compared with the solutions obtained by methods based upon the variational equations of the Minimum Principle and the finite element method.
Park, Chandeok
This dissertation presents a general methodology for solving the optimal feedback control problem in the context of Hamiltonian system theory. It is first formulated as a two point boundary value problem for a standard Hamiltonian system, and the associated phase flow is viewed as a canonical transformation. Then relying on the Hamilton-Jacobi theory, we employ generating functions to develop a unified methodology for solving a variety of optimal feedback control formulations with general types of boundary conditions. The major accomplishment is to establish a theoretical connection between the optimal cost function and a special kind of generating function. Guided by this recognition, we are ultimately led to a new flexible representation of the optimal feedback control law for a given system, which is adjustable to various types of boundary conditions by algebraic conversions and partial differentiations. This adaptive property provides a substantial advantage over the classical dynamic programming method in the sense that we do not need to solve the Hamilton-Jacobi-Bellman equation repetitively for varying types of boundary conditions. Furthermore for a special type of boundary condition, it also enables us to work around an inherent singularity of the Hamilton-Jacobi-Bellman equation by a special algebraic transformation. Taking full advantage of these theoretical insights, we develop a systematic algorithm for solving a class of optimal feedback control problems represented by smooth analytic Hamiltonians, and apply it to problems with different characteristics. Then, broadening the practical utility of generating functions for problems where the relevant Hamiltonian is non-smooth, we construct a pair of Cauchy problems from the associated Hamilton-Jacobi equations. This alternative formulation is justified by solving problems with control constraints which usually feature non-smoothness in the control logic. The main result of this research establishes that
Faggian, Silvia
2007-01-01
The paper concerns the study of the Pontryagin Maximum Principle for an infinite dimensional and infinite horizon boundary control problem for linear partial differential equations. The optimal control model has already been studied both in finite and infinite horizon with Dynamic Programming methods in a series of papers by the same author, or by Faggian and Gozzi. Necessary and sufficient optimality conditions for open loop controls are established. Moreover the co-state variable is shown to coincide with the spatial gradient of the value function evaluated along the trajectory of the system, creating a parallel between Maximum Principle and Dynamic Programming. The abstract model applies, as recalled in one of the first sections, to optimal investment with vintage capital.
Directory of Open Access Journals (Sweden)
Т. Horsin
2014-01-01
Full Text Available We consider an optimal control problem associated to Dirichlet boundary valueproblem for linear elliptic equations on a bounded domain Ω. We take the matrixvalued coecients A(x of such system as a control in L1(Ω;RN RN. One of the important features of the admissible controls is the fact that the coecient matrices A(x are non-symmetric, unbounded on Ω, and eigenvalues of the symmetric part Asym = (A + At=2 may vanish in Ω.
Nguyen, Nhan T.
This thesis develops a new optimal control theory for a class of distributed-parameter systems governed by first-order quasilinear hyperbolic partial differential equations that arise in many physical applications such as fluid dynamics problems. These systems are controlled at their boundaries via boundary controls that are subject to dynamic constraints imposed by lumped-parameter systems governed by ordinary differential equations. A Mach number control problem for a closed-circuit wind tunnel is investigated. The flow is modeled using the Euler equations and is controlled by a compressor performance model defined as two-point boundary conditions. The boundary control inputs to the compressor are in turn controlled by two first-order lumped-parameter systems that represent dynamics of a drive motor system and an inlet guide vane system. Necessary conditions of optimality are developed by the minimum principle using the adjoint formulation of calculus of variations for a dual Hamiltonian system for the distributed and lumped-parameter systems. The theory is applied to analyze two problems of Mach number control in a wind tunnel: a nonlinear Mach number transition and a linear perturbation predictive feedforward optimal control in the presence of disturbance. Computational methods for general two-point boundary value problems involving coupled partial and ordinary differential equations are developed using a wave-splitting, finite difference upwind method with an explicit scheme for the state equations, and an implicit scheme and a quasi-steady state method for the adjoint equations. These computational methods are implemented to solve a two-point boundary value problem. Using a second-order gradient method, the optimal Mach number transition is computed. A linear-quadratic optimal control theory is developed for designing a Mach number control in the presence of a test model undergoing a continuous pitch motion. A feedback control is shown to not be able to
Optimal control of wind-farm boundary layers: effect of turbine response time
Munters, Wim; Meyers, Johan
2016-11-01
Complex turbine wake interactions play an important role in overall energy extraction in large wind farms. Current control strategies optimize individual turbine power, and lead to significant energy losses in wind farms compared to lone-standing turbines. In recent work, an optimal control framework for dynamic induction control of wind farms and their interaction with the atmospheric boundary layer (ABL) was introduced, with the aim of mitigating such losses. The framework applies a receding horizon methodology, in which the ABL state is modeled through large-eddy simulations. Previously, the framework was applied to both fully-developed and spatially developing wind farms, for which respective energy gains of 16% and 7% were obtained, albeit at the cost of additional turbine loading variability. Here, we quantify the trade-off between increased power extraction and smoothed turbine dynamics by varying the turbine response time in the control framework. We consider simulation cases restricted to underinduction compared to Betz-optimal induction, as well as cases that also allow overinduction. In addition, efforts on replicating optimized power gains with practical controllers are presented. The authors are supported by the ERC (ActiveWindFarms, Grant No.: 306471).
Nonlinear optimal control of bypass transition in a boundary layer flow
Xiao, Dandan; Papadakis, George
2016-11-01
Bypass transition is observed in a flat-plate boundary-layer flow when high levels of free stream turbulence are present. This scenario is characterized by the formation of streamwise elongated streaks inside the boundary layer, their break down into turbulent spots and eventually fully turbulent flow. In the current work, we perform DNS simulations of control of bypass transition in a zero-pressure-gradient boundary layer. A non-linear optimal control algorithm is developed that employs the direct-adjoint approach to minimise a quadratic cost function based on the deviation from the Blasius velocity profile. Using the Lagrange variational approach, the distribution of the blowing/suction control velocity is found by solving iteratively the non-linear Navier-Stokes and its adjoint equations in a forward/backward loop. The optimisation is performed over a finite time horizon during which the Lagrange functional is to be minimised. Large values of optimisation horizon result in instability of the adjoint equations. The results show that the controller is able to reduce the turbulent kinetic energy of the flow in the region where the objective function is defined and the velocity profile is seen to approach the Blasius solution. Significant drag reduction is also achieved.
Optimal decay rate of vibrating beam equations controlled by combined boundary feedback forces
Institute of Scientific and Technical Information of China (English)
于景元; 李胜家; 王耀庭; 粱展东
1999-01-01
The optimal decay rate problem is considered for boundary control system modeling by a flexible structure consisting of a Eular-Bernoulli beam. Controls are a bending moment in proportion to angular velocity and a shear force in proportion to velocity. A sensitivity asymptotic analysis of the system’ s eigenvalues and eigenfunctions is set up. It is proved that, for every 0
Nonlinear optimal control of bypass transition in a boundary layer flow
Xiao, Dandan; Papadakis, George
2017-05-01
The central aim of the paper is to apply and assess a nonlinear optimal control strategy to suppress bypass transition, due to bimodal interactions [T. A. Zaki and P. A. Durbin, "Mode interaction and the bypass route to transition," J. Fluid Mech. 531, 85 (2005)] in a zero-pressure-gradient boundary layer. To this end, a Lagrange variational formulation is employed that results in a set of adjoint equations. The optimal wall actuation (blowing and suction from a control slot) is found by solving iteratively the nonlinear Navier-Stokes and the adjoint equations in a forward/backward loop using direct numerical simulation. The optimization is performed in a finite time horizon. Large values of optimization horizon result in the instability of the adjoint equations. The control slot is located exactly in the region of transition. The results show that the control is able to significantly reduce the objective function, which is defined as the spatial and temporal integral of the quadratic deviation from the Blasius profile plus a term that quantifies the control cost. The physical mechanism with which the actuation interacts with the flow field is investigated and analysed in relation to the objective function employed. Examination of the joint probability density function shows that the control velocity is correlated with the streamwise velocity in the near wall region but this correlation is reduced as time elapses. The spanwise averaged velocity is distorted by the control action, resulting in a significant reduction of the skin friction coefficient. Results are presented with and without zero-net mass flow constraint of the actuation velocity. The skin friction coefficient drops below the laminar value if there is no mass constraint; it remains however larger than laminar when this constraint is imposed. Results are also compared with uniform blowing using the same time-average velocity obtained from the nonlinear optimal algorithm.
Optimal control oriented to therapy for a free-boundary tumor growth model.
Calzada, M Carmen; Fernández-Cara, Enrique; Marín, Mercedes
2013-05-21
This paper is devoted to present and solve some optimal control problems, oriented to therapy, for a particular model of tumor growth. In the considered systems, the state is given by one or several functions that provide information on the cell population and also the tumor shape evolution and the control is a time dependent function associated to the therapy strategy (in practice, a cytotoxic drug). We first present and analyze the model (based on PDEs) and the related optimal control problems. The solutions are expected to provide the best therapy strategies for a given set of constraints (here, the cost or objective function is a measure of the number of cells at a given final time T). We also recall some mathematical techniques for solving the related optimization problems and we illustrate the behavior of the methods and the validity of the models with several numerical experiments. In view of the results, we are able to design appropriate strategies that, at least to some extent, are confirmed by real data. Finally, we present some conclusions and indications on future work. Copyright © 2013 Elsevier Ltd. All rights reserved.
Directory of Open Access Journals (Sweden)
L. I. Rozonoer
1999-01-01
Full Text Available Necessary and sufficient conditions for existence of optimal control for all initial data are proved for LQ-optimization problem. If these conditions are fulfilled, necessary and sufficient conditions of optimality are formulated. Basing on the results, some general hypotheses on optimal control in terms of Pontryagin's maximum condition and Bellman's equation are proposed.
Allan, Brian G.; Owens, Lewis R., Jr.; Lin, John C.
2006-01-01
This research will investigate the use of Design-of-Experiments (DOE) in the development of an optimal passive flow control vane design for a boundary-layer-ingesting (BLI) offset inlet in transonic flow. This inlet flow control is designed to minimize the engine fan face distortion levels and first five Fourier harmonic half amplitudes while maximizing the inlet pressure recovery. Numerical simulations of the BLI inlet are computed using the Reynolds-averaged Navier-Stokes (RANS) flow solver, OVERFLOW, developed at NASA. These simulations are used to generate the numerical experiments for the DOE response surface model. In this investigation, two DOE optimizations were performed using a D-Optimal Response Surface model. The first DOE optimization was performed using four design factors which were vane height and angles-of-attack for two groups of vanes. One group of vanes was placed at the bottom of the inlet and a second group symmetrically on the sides. The DOE design was performed for a BLI inlet with a free-stream Mach number of 0.85 and a Reynolds number of 2 million, based on the length of the fan face diameter, matching an experimental wind tunnel BLI inlet test. The first DOE optimization required a fifth order model having 173 numerical simulation experiments and was able to reduce the DC60 baseline distortion from 64% down to 4.4%, while holding the pressure recovery constant. A second DOE optimization was performed holding the vanes heights at a constant value from the first DOE optimization with the two vane angles-of-attack as design factors. This DOE only required a second order model fit with 15 numerical simulation experiments and reduced DC60 to 3.5% with small decreases in the fourth and fifth harmonic amplitudes. The second optimal vane design was tested at the NASA Langley 0.3-Meter Transonic Cryogenic Tunnel in a BLI inlet experiment. The experimental results showed a 80% reduction of DPCPavg, the circumferential distortion level at the engine
Energy Technology Data Exchange (ETDEWEB)
Colli, Pierluigi, E-mail: pierluigi.colli@unipv.it [Università di Pavia, Dipartimento di Matematica “F. Casorati” (Italy); Farshbaf-Shaker, M. Hassan, E-mail: hassan.farshbaf-shaker@wias-berlin.de; Sprekels, Jürgen, E-mail: juergen.sprekels@wias-berlin.de [Weierstrass Institute (Germany)
2015-02-15
In this paper, we investigate optimal control problems for Allen-Cahn variational inequalities with a dynamic boundary condition involving double obstacle potentials and the Laplace-Beltrami operator. The approach covers both the cases of distributed controls and of boundary controls. The cost functional is of standard tracking type, and box constraints for the controls are prescribed. We prove existence of optimal controls and derive first-order necessary conditions of optimality. The general strategy is the following: we use the results that were recently established by two of the authors for the case of (differentiable) logarithmic potentials and perform a so-called “deep quench limit”. Using compactness and monotonicity arguments, it is shown that this strategy leads to the desired first-order necessary optimality conditions for the case of (non-differentiable) double obstacle potentials.
Optimization and Optimal Control
Chinchuluun, Altannar; Enkhbat, Rentsen; Tseveendorj, Ider
2010-01-01
During the last four decades there has been a remarkable development in optimization and optimal control. Due to its wide variety of applications, many scientists and researchers have paid attention to fields of optimization and optimal control. A huge number of new theoretical, algorithmic, and computational results have been observed in the last few years. This book gives the latest advances, and due to the rapid development of these fields, there are no other recent publications on the same topics. Key features: Provides a collection of selected contributions giving a state-of-the-art accou
LQG/LTR Optimal Attitude Control of Small Flexible Spacecraft Using Free-Free Boundary Conditions
2006-08-03
engine vibrating . A high recovery force from an SMA can be compared to the stretching or com- pression of a spring, such as one found in a mattress or a...Singer. “ Vibration Reduction Using Multi-Hump Extra-Insensitive Input Shapers.” 1995 American Control Confer- ence. 3830–3834. Evanston, IL: American...13 1.12 AEC-Able Engineering’s CoilAble Boom [49] . . . . . . . . . . . . . . . 14 2.1 Rotational- Vibrational Constraint
Aschepkov, Leonid T; Kim, Taekyun; Agarwal, Ravi P
2016-01-01
This book is based on lectures from a one-year course at the Far Eastern Federal University (Vladivostok, Russia) as well as on workshops on optimal control offered to students at various mathematical departments at the university level. The main themes of the theory of linear and nonlinear systems are considered, including the basic problem of establishing the necessary and sufficient conditions of optimal processes. In the first part of the course, the theory of linear control systems is constructed on the basis of the separation theorem and the concept of a reachability set. The authors prove the closure of a reachability set in the class of piecewise continuous controls, and the problems of controllability, observability, identification, performance and terminal control are also considered. The second part of the course is devoted to nonlinear control systems. Using the method of variations and the Lagrange multipliers rule of nonlinear problems, the authors prove the Pontryagin maximum principle for prob...
A Boundary Control Problem for the Viscous Cahn–Hilliard Equation with Dynamic Boundary Conditions
Energy Technology Data Exchange (ETDEWEB)
Colli, Pierluigi, E-mail: pierluigi.colli@unipv.it; Gilardi, Gianni, E-mail: gianni.gilardi@unipv.it [Universitá di Pavia and Research Associate at the IMATI – C.N.R. PAVIA, Dipartimento di Matematica “F. Casorati” (Italy); Sprekels, Jürgen, E-mail: juergen.sprekels@wias-berlin.de [Weierstrass Institute (Germany)
2016-04-15
A boundary control problem for the viscous Cahn–Hilliard equations with possibly singular potentials and dynamic boundary conditions is studied and first order necessary conditions for optimality are proved.
On filter boundary conditions in topology optimization
DEFF Research Database (Denmark)
Clausen, Anders; Andreassen, Erik
2017-01-01
we define three requirements that boundary conditions must fulfill in order to eliminate boundary effects. Previously suggested approaches are briefly reviewed in the light of these requirements. A new approach referred to as the “domain extension approach” is suggested. It effectively eliminates......Most research papers on topology optimization involve filters for regularization. Typically, boundary effects from the filters are ignored. Despite significant drawbacks the inappropriate homogeneous Neumann boundary conditions are used, probably because they are trivial to implement. In this paper...
Optimal Boundary Conditions for ORCA-2 Model
Kazantsev, Eugene
2012-01-01
A 4D-Var data assimilation technique is applied to a ORCA-2 configuration of the NEMO in order to identify the optimal parametrization of the boundary conditions on the lateral boundaries as well as on the bottom and on the surface of the ocean. The influence of the boundary conditions on the solution is analyzed as in the assimilation window and beyond the window. It is shown that optimal conditions for vertical operators allows to get stronger and finer jet streams (Gulf Stream, Kuroshio) in the solution. Analyzing the reasons of the jets reinforcement, we see that the major impact of the data assimilation is made on the parametrization of the bottom boundary conditions for lateral velocities u and v. Automatic generation of the tangent and adjoint codes is also discussed. Tapenade software is shown to be able to produce the adjoint code that can be used after a memory usage optimization.
Optimal Control of Mechanical Systems
Vadim Azhmyakov
2007-01-01
In the present work, we consider a class of nonlinear optimal control problems, which can be called “optimal control problems in mechanics.” We deal with control systems whose dynamics can be described by a system of Euler-Lagrange or Hamilton equations. Using the variational structure of the solution of the corresponding boundary-value problems, we reduce the initial optimal control problem to an auxiliary problem of multiobjective programming. This technique makes it possible to apply some ...
Optimal Control of Mechanical Systems
Directory of Open Access Journals (Sweden)
Vadim Azhmyakov
2007-01-01
Full Text Available In the present work, we consider a class of nonlinear optimal control problems, which can be called “optimal control problems in mechanics.” We deal with control systems whose dynamics can be described by a system of Euler-Lagrange or Hamilton equations. Using the variational structure of the solution of the corresponding boundary-value problems, we reduce the initial optimal control problem to an auxiliary problem of multiobjective programming. This technique makes it possible to apply some consistent numerical approximations of a multiobjective optimization problem to the initial optimal control problem. For solving the auxiliary problem, we propose an implementable numerical algorithm.
Boundary layer control for airships
Pake, F. A.; Pipitone, S. J.
1975-01-01
An investigation is summarized of the aerodynamic principle of boundary layer control for nonrigid LTA craft. The project included a wind tunnel test on a BLC body of revolution at zero angle of attack. Theoretical analysis is shown to be in excellent agreement with the test data. Methods are evolved for predicting the boundary layer development on a body of revolution and the suction pumping and propulsive power requirements. These methods are used to predict the performance characteristics of a full-scale airship. The analysis indicates that propulsive power reductions of 15 to 25 percent and endurance improvements of 20 to 40 percent may be realized in employing boundary-layer control to nonrigid airships.
Optimal control problem for the extended Fisher–Kolmogorov equation
Indian Academy of Sciences (India)
Ning Duan
2016-02-01
In this paper, the optimal control problem for the extended Fisher–Kolmogorov equation is studied. The optimal control under boundary condition is given, the existence of optimal solution to the equation is proved and the optimality system is established.
Boundary control of parabolic systems - Finite-element approximation
Lasiecka, I.
1980-01-01
The finite element approximation of a Dirichlet type boundary control problem for parabolic systems is considered. An approach based on the direct approximation of an input-output semigroup formula is applied. Error estimates are derived for optimal state and optimal control, and it is noted that these estimates are actually optimal with respect to the approximation theoretic properties.
Exact boundary controllability for a series of membranes elastically connected
Directory of Open Access Journals (Sweden)
Waldemar D. Bastos
2017-01-01
Full Text Available In this article we study the exact controllability with Neumann boundary controls for a system of linear wave equations coupled in parallel by lower order terms on piecewise smooth domains of the plane. We obtain square integrable controls for initial state with finite energy and time of controllability near the optimal value.
Optimal obstacle control problem
Institute of Scientific and Technical Information of China (English)
ZHU Li; LI Xiu-hua; GUO Xing-ming
2008-01-01
In the paper we discuss some properties of the state operators of the optimal obstacle control problem for elliptic variational inequality. Existence, uniqueness and regularity of the optimal control problem are established. In addition, the approximation of the optimal obstacle problem is also studied.
Optimal boundary conditions at the staircase-shaped coastlines
Kazantsev, Eugene
2014-01-01
A 4D-Var data assimilation technique is applied to the rectangular-box configuration of the NEMO in order to identify the optimal parametrization of boundary conditions at lateral boundaries. The case of the staircase-shaped coastlines is studied by rotating the model grid around the center of the box. It is shown that, in some cases, the formulation of the boundary conditions at the exact boundary leads to appearance of exponentially growing modes while optimal boundary conditions allow to correct the errors induced by the staircase-like appriximation of the coastline.
Bulgakov, V. K.; Strigunov, V. V.
2009-05-01
The Pontryagin maximum principle is used to prove a theorem concerning optimal control in regional macroeconomics. A boundary value problem for optimal trajectories of the state and adjoint variables is formulated, and optimal curves are analyzed. An algorithm is proposed for solving the boundary value problem of optimal control. The performance of the algorithm is demonstrated by computing an optimal control and the corresponding optimal trajectories.
Control and optimization system
Xinsheng, Lou
2013-02-12
A system for optimizing a power plant includes a chemical loop having an input for receiving an input parameter (270) and an output for outputting an output parameter (280), a control system operably connected to the chemical loop and having a multiple controller part (230) comprising a model-free controller. The control system receives the output parameter (280), optimizes the input parameter (270) based on the received output parameter (280), and outputs an optimized input parameter (270) to the input of the chemical loop to control a process of the chemical loop in an optimized manner.
Shornikov, Andrey; Starinova, Olga
2017-01-01
There is a problem to control spacecraft's motion near objects with irregular gravitational fields as asteroids. In this paper we present a mathematical model of spacecraft motion with an electric propulsion engine in an irregular non-spherical gravitational field of the asteroid Eros 433. We propose to use the model of single gravity points for simulation of the motion of a spacecraft in the irregular gravitational field. The equations of spacecraft motion are corresponding equations of the n-body problem. A boundary task of the control spacecraft's transfer between circular orbits from 200 km to 100 km is considered. Authors propose a combination of the Pontryagin's maximum principle and the Newton's step by step approximation as solutions methods for the boundary problem.
Schaft, A.J. van der
1987-01-01
It is argued that the existence of symmetries may simplify, as in classical mechanics, the solution of optimal control problems. A procedure for obtaining symmetries for the optimal Hamiltonian resulting from the Maximum Principle is given; this avoids the actual calculation of the optimal
Exact and Optimal Quantum Mechanics/Molecular Mechanics Boundaries.
Sun, Qiming; Chan, Garnet Kin-Lic
2014-09-09
Motivated by recent work in density matrix embedding theory, we define exact link orbitals that capture all quantum mechanical (QM) effects across arbitrary quantum mechanics/molecular mechanics (QM/MM) boundaries. Exact link orbitals are rigorously defined from the full QM solution, and their number is equal to the number of orbitals in the primary QM region. Truncating the exact set yields a smaller set of link orbitals optimal with respect to reproducing the primary region density matrix. We use the optimal link orbitals to obtain insight into the limits of QM/MM boundary treatments. We further analyze the popular general hybrid orbital (GHO) QM/MM boundary across a test suite of molecules. We find that GHOs are often good proxies for the most important optimal link orbital, although there is little detailed correlation between the detailed GHO composition and optimal link orbital valence weights. The optimal theory shows that anions and cations cannot be described by a single link orbital. However, expanding to include the second most important optimal link orbital in the boundary recovers an accurate description. The second optimal link orbital takes the chemically intuitive form of a donor or acceptor orbital for charge redistribution, suggesting that optimal link orbitals can be used as interpretative tools for electron transfer. We further find that two optimal link orbitals are also sufficient for boundaries that cut across double bonds. Finally, we suggest how to construct "approximately" optimal link orbitals for practical QM/MM calculations.
Optimal control computer programs
Kuo, F.
1992-01-01
The solution of the optimal control problem, even with low order dynamical systems, can usually strain the analytical ability of most engineers. The understanding of this subject matter, therefore, would be greatly enhanced if a software package existed that could simulate simple generic problems. Surprisingly, despite a great abundance of commercially available control software, few, if any, address the part of optimal control in its most generic form. The purpose of this paper is, therefore, to present a simple computer program that will perform simulations of optimal control problems that arise from the first necessary condition and the Pontryagin's maximum principle.
Integrated controls design optimization
Lou, Xinsheng; Neuschaefer, Carl H.
2015-09-01
A control system (207) for optimizing a chemical looping process of a power plant includes an optimizer (420), an income algorithm (230) and a cost algorithm (225) and a chemical looping process models. The process models are used to predict the process outputs from process input variables. Some of the process in puts and output variables are related to the income of the plant; and some others are related to the cost of the plant operations. The income algorithm (230) provides an income input to the optimizer (420) based on a plurality of input parameters (215) of the power plant. The cost algorithm (225) provides a cost input to the optimizer (420) based on a plurality of output parameters (220) of the power plant. The optimizer (420) determines an optimized operating parameter solution based on at least one of the income input and the cost input, and supplies the optimized operating parameter solution to the power plant.
Variational Data Assimilation for Optimizing Boundary Conditions in Ocean Models
Kazantsev, Christine; Tolstykh, Mikhail
2016-01-01
The review describes the development of ideas Gury Ivanovich Marchuk in the field of variational data assimilation for ocean models applied in particular in coupled models for long-range weather forecasts. Particular attention is paid to the optimization of boundary conditions on rigid boundaries. As idealized and realistic model configurations are considered. It is shown that the optimization allows us to determine the most sensitive model operators and bring the model solution closer to the assimilated data.
Topology and boundary shape optimization as an integrated design tool
Bendsoe, Martin Philip; Rodrigues, Helder Carrico
1990-01-01
The optimal topology of a two dimensional linear elastic body can be computed by regarding the body as a domain of the plane with a high density of material. Such an optimal topology can then be used as the basis for a shape optimization method that computes the optimal form of the boundary curves of the body. This results in an efficient and reliable design tool, which can be implemented via common FEM mesh generator and CAD type input-output facilities.
Colonius, Fritz
1988-01-01
This research monograph deals with optimal periodic control problems for systems governed by ordinary and functional differential equations of retarded type. Particular attention is given to the problem of local properness, i.e. whether system performance can be improved by introducing periodic motions. Using either Ekeland's Variational Principle or optimization theory in Banach spaces, necessary optimality conditions are proved. In particular, complete proofs of second-order conditions are included and the result is used for various versions of the optimal periodic control problem. Furthermore a scenario for local properness (related to Hopf bifurcation) is drawn up, giving hints as to where to look for optimal periodic solutions. The book provides mathematically rigorous proofs for results which are potentially of importance in chemical engineering and aerospace engineering.
Discrete Variational Optimal Control
Jimenez, Fernando; de Diego, David Martin
2012-01-01
This paper develops numerical methods for optimal control of mechanical systems in the Lagrangian setting. It extends the theory of discrete mechanics to enable the solutions of optimal control problems through the discretization of variational principles. The key point is to solve the optimal control problem as a variational integrator of a specially constructed higher-dimensional system. The developed framework applies to systems on tangent bundles, Lie groups, underactuated and nonholonomic systems with symmetries, and can approximate either smooth or discontinuous control inputs. The resulting methods inherit the preservation properties of variational integrators and result in numerically robust and easily implementable algorithms. Several theoretical and a practical examples, e.g. the control of an underwater vehicle, will illustrate the application of the proposed approach.
Discrete Variational Optimal Control
Jiménez, Fernando; Kobilarov, Marin; Martín de Diego, David
2013-06-01
This paper develops numerical methods for optimal control of mechanical systems in the Lagrangian setting. It extends the theory of discrete mechanics to enable the solutions of optimal control problems through the discretization of variational principles. The key point is to solve the optimal control problem as a variational integrator of a specially constructed higher dimensional system. The developed framework applies to systems on tangent bundles, Lie groups, and underactuated and nonholonomic systems with symmetries, and can approximate either smooth or discontinuous control inputs. The resulting methods inherit the preservation properties of variational integrators and result in numerically robust and easily implementable algorithms. Several theoretical examples and a practical one, the control of an underwater vehicle, illustrate the application of the proposed approach.
Boundary Controllability of Nonlinear Fractional Integrodifferential Systems
Directory of Open Access Journals (Sweden)
Ahmed HamdyM
2010-01-01
Full Text Available Sufficient conditions for boundary controllability of nonlinear fractional integrodifferential systems in Banach space are established. The results are obtained by using fixed point theorems. We also give an application for integropartial differential equations of fractional order.
Faugeras, Blaise; Blum, Jacques; Heumann, Holger; Boulbe, Cédric
2017-08-01
The modelization of polarimetry Faraday rotation measurements commonly used in tokamak plasma equilibrium reconstruction codes is an approximation to the Stokes model. This approximation is not valid for the foreseen ITER scenarios where high current and electron density plasma regimes are expected. In this work a method enabling the consistent resolution of the inverse equilibrium reconstruction problem in the framework of non-linear free-boundary equilibrium coupled to the Stokes model equation for polarimetry is provided. Using optimal control theory we derive the optimality system for this inverse problem. A sequential quadratic programming (SQP) method is proposed for its numerical resolution. Numerical experiments with noisy synthetic measurements in the ITER tokamak configuration for two test cases, the second of which is an H-mode plasma, show that the method is efficient and that the accuracy of the identification of the unknown profile functions is improved compared to the use of classical Faraday measurements.
Boundary conditions control for a Shallow-Water model
Kazantsev, Eugene
2012-01-01
A variational data assimilation technique was used to estimate optimal discretization of interpolation operators and derivatives in the nodes adjacent to the rigid boundary. Assimilation of artificially generated observational data in the shallow-water model in a square box and assimilation of real observations in the model of the Black sea are discussed. It is shown in both experiments that controlling the discretization of operators near a rigid boundary can bring the model solution closer to observations as in the assimilation window and beyond the window. This type of control allows also to improve climatic variability of the model.
On Symmetries in Optimal Control
van der Schaft, A. J.
1986-01-01
We discuss the use of symmetries in solving optimal control problems. In particular a procedure for obtaining symmetries is given which can be performed before the actual calculation of the optimal control and optimal Hamiltonian.
On Symmetries in Optimal Control
Schaft, A.J. van der
1986-01-01
We discuss the use of symmetries in solving optimal control problems. In particular a procedure for obtaining symmetries is given which can be performed before the actual calculation of the optimal control and optimal Hamiltonian.
Optimized joystick controller.
Ding, D; Cooper, R A; Spaeth, D
2004-01-01
The purpose of the study was to develop an optimized joystick control interface for electric powered wheelchairs and thus provide safe and effective control of electric powered wheelchairs to people with severe physical disabilities. The interface enables clinicians to tune joystick parameters for each individual subject through selecting templates, dead zones, and bias axes. In terms of hand tremor usually associated with people with traumatic brain injury, cerebral palsy, and multiple sclerosis, fuzzy logic rules were applied to suppress erratic hand movements and extract the intended motion from the joystick. Simulation results were presented to show the graphical tuning interface as well as the performance of the fuzzy logic controller.
Quality Tetrahedral Mesh Smoothing via Boundary-Optimized Delaunay Triangulation.
Gao, Zhanheng; Yu, Zeyun; Holst, Michael
2012-12-01
Despite its great success in improving the quality of a tetrahedral mesh, the original optimal Delaunay triangulation (ODT) is designed to move only inner vertices and thus cannot handle input meshes containing "bad" triangles on boundaries. In the current work, we present an integrated approach called boundary-optimized Delaunay triangulation (B-ODT) to smooth (improve) a tetrahedral mesh. In our method, both inner and boundary vertices are repositioned by analytically minimizing the error between a paraboloid function and its piecewise linear interpolation over the neighborhood of each vertex. In addition to the guaranteed volume-preserving property, the proposed algorithm can be readily adapted to preserve sharp features in the original mesh. A number of experiments are included to demonstrate the performance of our method.
Active control of ionized boundary layers
Mendes, R V
1997-01-01
The challenging problems, in the field of control of chaos or of transition to chaos, lie in the domain of infinite-dimensional systems. Access to all variables being impossible in this case and the controlling action being limited to a few collective variables, it will not in general be possible to drive the whole system to the desired behaviour. A paradigmatic problem of this type is the control of the transition to turbulence in the boundary layer of fluid motion. By analysing a boundary layer flow for an ionized fluid near an airfoil, one concludes that active control of the transition amounts to the resolution of an generalized integro-differential eigenvalue problem. To cope with the required response times and phase accuracy, electromagnetic control, whenever possible, seems more appropriate than mechanical control by microactuators.
Guibout, Vincent M.
This dissertation has been motivated by the need for new methods to address complex problems that arise in spacecraft formation design. As a direct result of this motivation, a general methodology for solving two-point boundary value problems for Hamiltonian systems has been found. Using the Hamilton-Jacobi theory in conjunction with the canonical transformation induced by the phase flow, it is shown that generating functions solve two-point boundary value problems. Traditional techniques for addressing these problems are iterative and require an initial guess. The method presented in this dissertation solves boundary value problems at the cost of a single function evaluation, although it requires knowledge of at least one generating function. Properties of this method are presented. Specifically, we show that it includes perturbation theory and generalizes it to nonlinear systems. Most importantly, it predicts the existence of multiple solutions and allows one to recover all of these solutions. To demonstrate the efficiency of this approach, an algorithm for computing the generating functions is proposed and its convergence properties are studied. As the method developed in this work is based on the Hamiltonian structure of the problem, particular attention must be paid to the numerics of the algorithm. To address this, a general framework for studying the discretization of certain dynamical systems is developed. This framework generalizes earlier work on discretization of Lagrangian and Hamiltonian systems on tangent and cotangent bundles respectively. In addition, it provides new insights into some symplectic integrators and leads to a new discrete Hamilton-Jacobi theory. Most importantly, it allows one to discretize optimal control problems. In particular, a discrete maximum principle is presented. This dissertation also investigates applications of the proposed method to solve two-point boundary value problems. In particular, new techniques for designing
Boundary layer control device for duct silencers
Schmitz, Fredric H. (Inventor); Soderman, Paul T. (Inventor)
1993-01-01
A boundary layer control device includes a porous cover plate, an acoustic absorber disposed under the porous cover plate, and a porous flow resistive membrane interposed between the porous cover plate and the acoustic absorber. The porous flow resistive membrane has a flow resistance low enough to permit sound to enter the acoustic absorber and high enough to damp unsteady flow oscillations.
Optimal control for chemical engineers
Upreti, Simant Ranjan
2013-01-01
Optimal Control for Chemical Engineers gives a detailed treatment of optimal control theory that enables readers to formulate and solve optimal control problems. With a strong emphasis on problem solving, the book provides all the necessary mathematical analyses and derivations of important results, including multiplier theorems and Pontryagin's principle.The text begins by introducing various examples of optimal control, such as batch distillation and chemotherapy, and the basic concepts of optimal control, including functionals and differentials. It then analyzes the notion of optimality, de
A free boundary approach to shape optimization problems.
Bucur, D; Velichkov, B
2015-09-13
The analysis of shape optimization problems involving the spectrum of the Laplace operator, such as isoperimetric inequalities, has known in recent years a series of interesting developments essentially as a consequence of the infusion of free boundary techniques. The main focus of this paper is to show how the analysis of a general shape optimization problem of spectral type can be reduced to the analysis of particular free boundary problems. In this survey article, we give an overview of some very recent technical tools, the so-called shape sub- and supersolutions, and show how to use them for the minimization of spectral functionals involving the eigenvalues of the Dirichlet Laplacian, under a volume constraint.
Power, control and optimization
Vasant, Pandian; Barsoum, Nader
2013-01-01
The book consists of chapters based on selected papers of international conference „Power, Control and Optimization 2012”, held in Las Vegas, USA. Readers can find interesting chapters discussing various topics from the field of power control, its distribution and related fields. Book discusses topics like energy consumption impacted by climate, mathematical modeling of the influence of thermal power plant on the aquatic environment, investigation of cost reduction in residential electricity bill using electric vehicle at peak times or allocation and size evaluation of distributed generation using ANN model and others. Chapter authors are to the best of our knowledge the originators or closely related to the originators of presented ideas and its applications. Hence, this book certainly is one of the few books discussing the benefit from intersection of those modern and fruitful scientific fields of research with very tight and deep impact on real life and industry. This book is devoted to the studies o...
Oil Reservoir Production Optimization using Optimal Control
DEFF Research Database (Denmark)
Völcker, Carsten; Jørgensen, John Bagterp; Stenby, Erling Halfdan
2011-01-01
Practical oil reservoir management involves solution of large-scale constrained optimal control problems. In this paper we present a numerical method for solution of large-scale constrained optimal control problems. The method is a single-shooting method that computes the gradients using the adjo......Practical oil reservoir management involves solution of large-scale constrained optimal control problems. In this paper we present a numerical method for solution of large-scale constrained optimal control problems. The method is a single-shooting method that computes the gradients using...... the adjoint method. We use an Explicit Singly Diagonally Implicit Runge-Kutta (ESDIRK) method for the integration and a quasi-Newton Sequential Quadratic Programming (SQP) algorithm for the constrained optimization. We use this algorithm in a numerical case study to optimize the production of oil from an oil...... reservoir using water ooding and smart well technology. Compared to the uncontrolled case, the optimal operation increases the Net Present Value of the oil field by 10%....
LOCAL EXACT BOUNDARY CONTROLLABILITY FOR A CLASS OFQUASILINEAR HYPERBOLIC SYSTEMS
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
For a class of mixed initial-boundary value problem for general quasilinear hyperbolic systems, this paper establishes the local exact boundary controllability with boundary controls only acting on one end. As an application, the authors show the local exact boundary controllability for a kind of nonlinear vibrating string problem.
Linear Controllers for Turbulent Boundary Layers
Lim, Junwoo; Kim, John; Kang, Sung-Moon; Speyer, Jason
2000-11-01
Several recent studies have shown that controllers based on a linear system theory work surprisingly well in turbulent flows, suggesting that a linear mechanism may play an important role even in turbulent flows. It has been also shown that non-normality of the linearized Navier-Stokes equations is an essential characteristic in the regeneration of near-wall turbulence structures in turbulent boundary layers. A few controllers designed to reduce the role of different linear mechanisms, including that to minimize the non-normality of the linearized Navier-Stokes equations, have been developed and applied to a low Reynolds nubmer turbulent channel flow. A reduced-order model containing the most controllable and observables modes is derived for each system. Other existing control schemes, such as Choi et al's opposition control, have been examined from the point of a linear system control. Further discussion on controller design, such as choice of cost function and other control parameters, will be presented.
Boundary layer control of rotating convection systems.
King, Eric M; Stellmach, Stephan; Noir, Jerome; Hansen, Ulrich; Aurnou, Jonathan M
2009-01-15
Turbulent rotating convection controls many observed features of stars and planets, such as magnetic fields, atmospheric jets and emitted heat flux patterns. It has long been argued that the influence of rotation on turbulent convection dynamics is governed by the ratio of the relevant global-scale forces: the Coriolis force and the buoyancy force. Here, however, we present results from laboratory and numerical experiments which exhibit transitions between rotationally dominated and non-rotating behaviour that are not determined by this global force balance. Instead, the transition is controlled by the relative thicknesses of the thermal (non-rotating) and Ekman (rotating) boundary layers. We formulate a predictive description of the transition between the two regimes on the basis of the competition between these two boundary layers. This transition scaling theory unifies the disparate results of an extensive array of previous experiments, and is broadly applicable to natural convection systems.
Boundary control of fluid flow through porous media
DEFF Research Database (Denmark)
Hasan, Agus; Foss, Bjarne; Sagatun, Svein Ivar
2010-01-01
The flow of fluids through porous media can be described by the Boussinesq’s equation with mixed boundary conditions; a Neumann’s boundary condition and a nonlinear boundary condition. The nonlinear boundary condition provides a means to control the fluid flow through porous media. In this paper,......, some stabilizing controllers are constructed for various cases using Lyapunov design....
Optimal control, optimization and asymptotic analysis of Purcell's microswimmer model
Wiezel, Oren; Or, Yizhar
2016-11-01
Purcell's swimmer (1977) is a classic model of a three-link microswimmer that moves by performing periodic shape changes. Becker et al. (2003) showed that the swimmer's direction of net motion is reversed upon increasing the stroke amplitude of joint angles. Tam and Hosoi (2007) used numerical optimization in order to find optimal gaits for maximizing either net displacement or Lighthill's energetic efficiency. In our work, we analytically derive leading-order expressions as well as next-order corrections for both net displacement and energetic efficiency of Purcell's microswimmer. Using these expressions enables us to explicitly show the reversal in direction of motion, as well as obtaining an estimate for the optimal stroke amplitude. We also find the optimal swimmer's geometry for maximizing either displacement or energetic efficiency. Additionally, the gait optimization problem is revisited and analytically formulated as an optimal control system with only two state variables, which can be solved using Pontryagin's maximum principle. It can be shown that the optimal solution must follow a "singular arc". Numerical solution of the boundary value problem is obtained, which exactly reproduces Tam and Hosoi's optimal gait.
Temporally optimized spanwise vorticity sensor measurements in turbulent boundary layers
Morrill-Winter, C.; Klewicki, J.; Baidya, R.; Marusic, I.
2015-12-01
Multi-element hot-wire anemometry was used to measure spanwise vorticity fluctuations in turbulent boundary layers. Smooth wall boundary layer profiles, with very good spatial and temporal resolution, were acquired over a Kármán number range of 2000-12,700 at the Melbourne Wind Tunnel at the University of Melbourne and the University of New Hampshire's Flow Physics Facility. A custom hot-wire probe was necessary to simultaneously obtain velocity and spanwise vorticity measurements centered at a fixed point in space. A custom calibration/processing scheme was developed to utilize single-wall-parallel wires to optimize the accuracy of the measured wall-normal velocity fluctuations derived from the sensor's ×-array.
Optimal Control of Evolutionary Dynamics
Chakrabarti, Raj; McLendon, George
2008-01-01
Elucidating the fitness measures optimized during the evolution of complex biological systems is a major challenge in evolutionary theory. We present experimental evidence and an analytical framework demonstrating how biochemical networks exploit optimal control strategies in their evolutionary dynamics. Optimal control theory explains a striking pattern of extremization in the redox potentials of electron transport proteins, assuming only that their fitness measure is a control objective functional with bounded controls.
Optimal control of nonsmooth distributed parameter systems
Tiba, Dan
1990-01-01
The book is devoted to the study of distributed control problems governed by various nonsmooth state systems. The main questions investigated include: existence of optimal pairs, first order optimality conditions, state-constrained systems, approximation and discretization, bang-bang and regularity properties for optimal control. In order to give the reader a better overview of the domain, several sections deal with topics that do not enter directly into the announced subject: boundary control, delay differential equations. In a subject still actively developing, the methods can be more important than the results and these include: adapted penalization techniques, the singular control systems approach, the variational inequality method, the Ekeland variational principle. Some prerequisites relating to convex analysis, nonlinear operators and partial differential equations are collected in the first chapter or are supplied appropriately in the text. The monograph is intended for graduate students and for resea...
Optimal control problems with switching points
Seywald, Hans
1991-09-01
An overview is presented of the problems and difficulties that arise in solving optimal control problems with switching points. A brief discussion of existing optimality conditions is given and a numerical approach for solving the multipoint boundary value problems associated with the first-order necessary conditions of optimal control is presented. Two real-life aerospace optimization problems are treated explicitly. These are altitude maximization for a sounding rocket (Goddard Problem) in the presence of a dynamic pressure limit, and range maximization for a supersonic aircraft flying in the vertical, also in the presence of a dynamic pressure limit. In the second problem singular control appears along arcs with active dynamic pressure limit, which in the context of optimal control, represents a first-order state inequality constraint. An extension of the Generalized Legendre-Clebsch Condition to the case of singular control along state/control constrained arcs is presented and is applied to the aircraft range maximization problem stated above. A contribution to the field of Jacobi Necessary Conditions is made by giving a new proof for the non-optimality of conjugate paths in the Accessory Minimum Problem. Because of its simple and explicit character, the new proof may provide the basis for an extension of Jacobi's Necessary Condition to the case of the trajectories with interior point constraints. Finally, the result that touch points cannot occur for first-order state inequality constraints is extended to the case of vector valued control functions.
On the regularity of optimal control for a parabolic system of order 2m
Directory of Open Access Journals (Sweden)
Ornella Fiodo
1992-05-01
Full Text Available An optimal control problem for a parabolic operator of order 2m with the boundary conditions containing the control is considered. A regularity theorem for the parabolic problem and the regularity of the optimal control is proved.
Multimodel methods for optimal control of aeroacoustics.
Energy Technology Data Exchange (ETDEWEB)
Chen, Guoquan (Rice University, Houston, TX); Collis, Samuel Scott
2005-01-01
A new multidomain/multiphysics computational framework for optimal control of aeroacoustic noise has been developed based on a near-field compressible Navier-Stokes solver coupled with a far-field linearized Euler solver both based on a discontinuous Galerkin formulation. In this approach, the coupling of near- and far-field domains is achieved by weakly enforcing continuity of normal fluxes across a coupling surface that encloses all nonlinearities and noise sources. For optimal control, gradient information is obtained by the solution of an appropriate adjoint problem that involves the propagation of adjoint information from the far-field to the near-field. This computational framework has been successfully applied to study optimal boundary-control of blade-vortex interaction, which is a significant noise source for helicopters on approach to landing. In the model-problem presented here, the noise propagated toward the ground is reduced by 12dB.
Control of the Transitional Boundary Layer
Belson, Brandt A.
This work makes advances in the delay of boundary layer transition from laminar to turbulent flow via feedback control. The applications include the reduction of drag over streamline bodies (e.g., airplane wings) and the decrease of mixing and heat transfer (e.g., over turbine blades in jet engines). A difficulty in many fields is designing feedback controllers for high-dimensional systems, be they experiments or high-fidelity simulations, because the required time and resources are too large. A cheaper alternative is to approximate the high-dimensional system with a reduced-order model and design a controller for the model. We implement several model reduction algorithms in "modred", an open source and publicly available library that is applicable to a wide range of problems. We use this library to study the role of sensors and actuators in feedback control of transition in the 2D boundary layer. Previous work uses a feedforward configuration in which the sensor is upstream of the actuator, but we show that the actuator-sensor pair is unsuitable for feedback control due to an inability to sense the exponentially-growing Tollmien-Schlichting waves. A new actuator-sensor pair is chosen that more directly affects and measures the TS waves, and as a result it is effective in a feedback configuration. Lastly, the feedback controller is shown to outperform feedforward controllers in the presence of unmodeled disturbances. Next, we focus on a specific type of actuator, the single dielectric barrier discharge (SDBD) plasma actuator. An array of these plasma actuators is oriented to produce stream-wise vorticity and thus directly cancel the structures with the largest transient growth (so-called stream-wise streaks). We design a feedback controller using only experimental data by first developing an empirical input-output quasi-steady model. Then, we design feedback controllers for the model such that the controllers perform well when applied to the experiment. Lastly, we
Predicting Loss-of-Control Boundaries Toward a Piloting Aid
Barlow, Jonathan; Stepanyan, Vahram; Krishnakumar, Kalmanje
2012-01-01
This work presents an approach to predicting loss-of-control with the goal of providing the pilot a decision aid focused on maintaining the pilot's control action within predicted loss-of-control boundaries. The predictive architecture combines quantitative loss-of-control boundaries, a data-based predictive control boundary estimation algorithm and an adaptive prediction method to estimate Markov model parameters in real-time. The data-based loss-of-control boundary estimation algorithm estimates the boundary of a safe set of control inputs that will keep the aircraft within the loss-of-control boundaries for a specified time horizon. The adaptive prediction model generates estimates of the system Markov Parameters, which are used by the data-based loss-of-control boundary estimation algorithm. The combined algorithm is applied to a nonlinear generic transport aircraft to illustrate the features of the architecture.
Parameter estimation for chaotic systems based on improved boundary chicken swarm optimization
Chen, Shaolong; Yan, Renhuan
2016-10-01
Estimating unknown parameters for chaotic system is a key problem in the field of chaos control and synchronization. Through constructing an appropriate fitness function, parameter estimation of chaotic system could be converted to a multidimensional parameter optimization problem. In this paper, a new method base on improved boundary chicken swarm optimization (IBCSO) algorithm is proposed for solving the problem of parameter estimation in chaotic system. However, to the best of our knowledge, there is no published research work on chicken swarm optimization for parameters estimation of chaotic system. Computer simulation based on Lorenz system and comparisons with chicken swarm optimization, particle swarm optimization, and genetic algorithm shows the effectiveness and feasibility of the proposed method.
Peters, J; Ecabert, O; Meyer, C; Kneser, R; Weese, J
2010-02-01
Segmentation of medical images can be achieved with the help of model-based algorithms. Reliable boundary detection is a crucial component to obtain robust and accurate segmentation results and to enable full automation. This is especially important if the anatomy being segmented is too variable to initialize a mean shape model such that all surface regions are close to the desired contours. Several boundary detection algorithms are widely used in the literature. Most use some trained image appearance model to characterize and detect the desired boundaries. Although parameters of the boundary detection can vary over the model surface and are trained on images, their performance (i.e., accuracy and reliability of boundary detection) can only be assessed as an integral part of the entire segmentation algorithm. In particular, assessment of boundary detection cannot be done locally and independently on model parameterization and internal energies controlling geometric model properties. In this paper, we propose a new method for the local assessment of boundary detection called Simulated Search. This method takes any boundary detection function and evaluates its performance for a single model landmark in terms of an estimated geometric boundary detection error. In consequence, boundary detection can be optimized per landmark during model training. We demonstrate the success of the method for cardiac image segmentation. In particular we show that the Simulated Search improves the capture range and the accuracy of the boundary detection compared to a traditional training scheme. We also illustrate how the Simulated Search can be used to identify suitable classes of features when addressing a new segmentation task. Finally, we show that the Simulated Search enables multi-modal heart segmentation using a single algorithmic framework. On computed tomography and magnetic resonance images, average segmentation errors (surface-to-surface distances) for the four chambers and
Optimal performance of constrained control systems
Harvey, P. Scott, Jr.; Gavin, Henri P.; Scruggs, Jeffrey T.
2012-08-01
This paper presents a method to compute optimal open-loop trajectories for systems subject to state and control inequality constraints in which the cost function is quadratic and the state dynamics are linear. For the case in which inequality constraints are decentralized with respect to the controls, optimal Lagrange multipliers enforcing the inequality constraints may be found at any time through Pontryagin’s minimum principle. In so doing, the set of differential algebraic Euler-Lagrange equations is transformed into a nonlinear two-point boundary-value problem for states and costates whose solution meets the necessary conditions for optimality. The optimal performance of inequality constrained control systems is calculable, allowing for comparison to previous, sub-optimal solutions. The method is applied to the control of damping forces in a vibration isolation system subjected to constraints imposed by the physical implementation of a particular controllable damper. An outcome of this study is the best performance achievable given a particular objective, isolation system, and semi-active damper constraints.
Optimizing EDMF parameterization for stratocumulus-topped boundary layer
Jones, C. R.; Bretherton, C. S.; Witek, M. L.; Suselj, K.
2014-12-01
We present progress in the development of an Eddy Diffusion / Mass Flux (EDMF) turbulence parameterization, with the goal of improving the representation of the cloudy boundary layer in NCEP's Global Forecast System (GFS), as part of a multi-institution Climate Process Team (CPT). Current GFS versions substantially under-predict cloud amount and cloud radiative impact over much of the globe, leading to large biases in the surface and top of atmosphere energy budgets. As part of the effort to correct these biases, the CPT is developing a new EDMF turbulence scheme for GFS, in which local turbulent mixing is represented by an eddy diffusion term while nonlocal shallow convection is represented by a mass flux term. The sum of both contributions provides the total turbulent flux. Our goal is for this scheme to more skillfully simulate cloud radiative properties without negatively impacting other measures of weather forecast skill. One particular challenge faced by an EDMF parameterization is to be able to handle stratocumulus regimes as well as shallow cumulus regimes. In order to isolate the behavior of the proposed EDMF parameterization and aid in its further development, we have implemented the scheme in a portable MATLAB single column model (SCM). We use this SCM framework to optimize the simulation of stratocumulus cloud top entrainment and boundary layer decoupling.
Chen, G.; Zheng, Q.; Coleman, M.; Weerakoon, S.
1983-01-01
This paper briefly reviews convergent finite difference schemes for hyperbolic initial boundary value problems and their applications to boundary control systems of hyperbolic type which arise in the modelling of vibrations. These difference schemes are combined with the primal and the dual approaches to compute the optimal control in the unconstrained case, as well as the case when the control is subject to inequality constraints. Some of the preliminary numerical results are also presented.
Optimal magnetic attitude control
DEFF Research Database (Denmark)
Wisniewski, Rafal; Markley, F.L.
1999-01-01
because control torques can only be generated perpendicular to the local geomagnetic field vector. This has been a serious obstacle for using magnetorquer based control for three-axis stabilization of a low earth orbit satellite. The problem of controlling the spacecraft attitude using only magnetic...
Optimal control studies for steamflooding
Energy Technology Data Exchange (ETDEWEB)
Liu, Wei.
1992-01-01
A system science approach using optimal control theory of distributed parameter systems has been developed to determine operating strategies that maximize the economic attractiveness of the steamflooding Enhanced Oil Recovery (EOR) process. Necessary conditions for optimization are established by using the calculus of variations and Pontryagin's Maximum Principle. The objective criterion is to maximize the difference between oil revenue and injected steam cost. A stable and efficient numerical algorithm, based on an iterative gradient method, is developed. The optimal control model is based on a three-dimensional, three-phase (oil, steam and water) steam injection numerical simulator. A discrete form of the model is formulated. The optimized operating variables are the optimal bottom-hole pressure, the optimal injection rate of steam and water, and the optimal steam quality policies. Another optimal control study is also conducted on a simplified one-dimensional model (the extended Neuman model) to provide quick and reliable preliminary information on the economic feasibility of steamflooding processes. The simplified control model only considers the injection rate of steam as the control variable. The performance of this system science approach is investigated through various one-, two- and three-dimensional steamflooding problems. The effects of reservoir properties and heterogeneity on optimal policies as well as the sensitivity of the control variables are also studied. Results show this approach yields significant insight into the steamflooding EOR process. Improvement of the economic objective is significant under optimal operation conditions. These optimization results are quite important in a successful application of the steamflooding EOR method.
1979-12-01
with Uncertain Components 44 13 Component Uncertainty Representation of Uncertain Pole-Zero Locations 46 12 A Feedback Control System 60 i 1 I vii €in...OF FEEDBACK SYSTEM ROBUSTNESS A feedback control system design is said to be robust if it is able to meet design specifications despite differences... feedback control system design problems, the design specifications usually demand that the system be "robust" against the effects of deviations within
Optimal control in thermal engineering
Badescu, Viorel
2017-01-01
This book is the first major work covering applications in thermal engineering and offering a comprehensive introduction to optimal control theory, which has applications in mechanical engineering, particularly aircraft and missile trajectory optimization. The book is organized in three parts: The first part includes a brief presentation of function optimization and variational calculus, while the second part presents a summary of the optimal control theory. Lastly, the third part describes several applications of optimal control theory in solving various thermal engineering problems. These applications are grouped in four sections: heat transfer and thermal energy storage, solar thermal engineering, heat engines and lubrication.Clearly presented and easy-to-use, it is a valuable resource for thermal engineers and thermal-system designers as well as postgraduate students.
Optimally growing boundary layer disturbances in a convergent nozzle preceded by a circular pipe
Uzun, Ali; Davis, Timothy B.; Alvi, Farrukh S.; Hussaini, M. Yousuff
2017-06-01
We report the findings from a theoretical analysis of optimally growing disturbances in an initially turbulent boundary layer. The motivation behind this study originates from the desire to generate organized structures in an initially turbulent boundary layer via excitation by disturbances that are tailored to be preferentially amplified. Such optimally growing disturbances are of interest for implementation in an active flow control strategy that is investigated for effective jet noise control. Details of the optimal perturbation theory implemented in this study are discussed. The relevant stability equations are derived using both the standard decomposition and the triple decomposition. The chosen test case geometry contains a convergent nozzle, which generates a Mach 0.9 round jet, preceded by a circular pipe. Optimally growing disturbances are introduced at various stations within the circular pipe section to facilitate disturbance energy amplification upstream of the favorable pressure gradient zone within the convergent nozzle, which has a stabilizing effect on disturbance growth. Effects of temporal frequency, disturbance input and output plane locations as well as separation distance between output and input planes are investigated. The results indicate that optimally growing disturbances appear in the form of longitudinal counter-rotating vortex pairs, whose size can be on the order of several times the input plane mean boundary layer thickness. The azimuthal wavenumber, which represents the number of counter-rotating vortex pairs, is found to generally decrease with increasing separation distance. Compared to the standard decomposition, the triple decomposition analysis generally predicts relatively lower azimuthal wavenumbers and significantly reduced energy amplification ratios for the optimal disturbances.
Symposium on Optimal Control Theory
1987-01-01
Control theory can be roughly classified as deterministic or stochastic. Each of these can further be subdivided into game theory and optimal control theory. The central problem of control theory is the so called constrained maximization (which- with slight modifications--is equivalent to minimization). One can then say, heuristically, that the major problem of control theory is to find the maximum of some performance criterion (or criteria), given a set of constraints. The starting point is, of course, a mathematical representation of the performance criterion (or criteria)- sometimes called the objective functional--along with the constraints. When the objective functional is single valued (Le. , when there is only one objective to be maximized), then one is dealing with optimal control theory. When more than one objective is involved, and the objectives are generally incompatible, then one is dealing with game theory. The first paper deals with stochastic optimal control, using the dynamic programming ...
Optimal control theory an introduction
Kirk, Donald E
2004-01-01
Optimal control theory is the science of maximizing the returns from and minimizing the costs of the operation of physical, social, and economic processes. Geared toward upper-level undergraduates, this text introduces three aspects of optimal control theory: dynamic programming, Pontryagin's minimum principle, and numerical techniques for trajectory optimization.Chapters 1 and 2 focus on describing systems and evaluating their performances. Chapter 3 deals with dynamic programming. The calculus of variations and Pontryagin's minimum principle are the subjects of chapters 4 and 5, and chapter
Optimality principles in sensorimotor control.
Todorov, Emanuel
2004-09-01
The sensorimotor system is a product of evolution, development, learning and adaptation-which work on different time scales to improve behavioral performance. Consequently, many theories of motor function are based on 'optimal performance': they quantify task goals as cost functions, and apply the sophisticated tools of optimal control theory to obtain detailed behavioral predictions. The resulting models, although not without limitations, have explained more empirical phenomena than any other class. Traditional emphasis has been on optimizing desired movement trajectories while ignoring sensory feedback. Recent work has redefined optimality in terms of feedback control laws, and focused on the mechanisms that generate behavior online. This approach has allowed researchers to fit previously unrelated concepts and observations into what may become a unified theoretical framework for interpreting motor function. At the heart of the framework is the relationship between high-level goals, and the real-time sensorimotor control strategies most suitable for accomplishing those goals.
Albu, A. F.
2016-05-01
The problem of controlling the phase boundary evolution in the course of solidification of metals with different thermodynamic properties is studied. The underlying mathematical model of the process is based on a three-dimensional nonstationary two-phase initial-boundary value problem of the Stefan type. The control functions are determined by optimal control problems, which are solved numerically with the help of gradient optimization methods. The gradient of the cost function is exactly computed by applying the fast automatic differentiation technique. The research results are described and analyzed. Some of them are illustrated.
Optimal actuation in vibration control
Guzzardo, C. A.; Pang, S. S.; Ram, Y. M.
2013-02-01
The paper addresses the problem of finding the optimal location of actuators and their relative gain so that the control effort in an actively controlled vibrating system is minimized. In technical terms the problem is finding the optimal input vector of unit norm that minimizes the norm of the control gain vector. This problem is addressed in the context of the active natural frequency modification problem associated with resonance avoidance in undamped systems, and in the context of the single-input-multi-output pole assignment problem for second order systems.
Optimal Control of Teaching Process
Institute of Scientific and Technical Information of China (English)
BAO Man; ZHANG Guo-zhi
2002-01-01
The authors first put forward quadratic form performance index as a criterion of measuringmerits and demerits of teaching process. On this base, we got a low of optimal control after the quantificationof the teacher's functions. It must play a leading role on how the teacher fully controls the whole teachingprocess.
Optimal control of quantum measurement
Energy Technology Data Exchange (ETDEWEB)
Egger, Daniel; Wilhelm, Frank [Theoretical Physics, Saarland University, 66123 Saarbruecken (Germany)
2015-07-01
Pulses to steer the time evolution of quantum systems can be designed with optimal control theory. In most cases it is the coherent processes that can be controlled and one optimizes the time evolution towards a target unitary process, sometimes also in the presence of non-controllable incoherent processes. Here we show how to extend the GRAPE algorithm in the case where the incoherent processes are controllable and the target time evolution is a non-unitary quantum channel. We perform a gradient search on a fidelity measure based on Choi matrices. We illustrate our algorithm by optimizing a measurement pulse for superconducting phase qubits. We show how this technique can lead to large measurement contrast close to 99%. We also show, within the validity of our model, that this algorithm can produce short 1.4 ns pulses with 98.2% contrast.
Optimality Conditions for Inventory Control
Feinberg, Eugene A.
2016-01-01
This tutorial describes recently developed general optimality conditions for Markov Decision Processes that have significant applications to inventory control. In particular, these conditions imply the validity of optimality equations and inequalities. They also imply the convergence of value iteration algorithms. For total discounted-cost problems only two mild conditions on the continuity of transition probabilities and lower semi-continuity of one-step costs are needed. For average-cost pr...
Boundary control of nonlinear coupled heat systems using backstepping
Bendevis, Paul
2016-10-20
A state feedback boundary controller is designed for a 2D coupled PDE system modelling heat transfer in a membrane distillation system for water desalination. Fluid is separated into two compartments with nonlinear coupling at a membrane boundary. The controller sets the temperature on one boundary in order to track a temperature difference across the membrane boundary. The control objective is achieved by an extension of backstepping methods to these coupled equations. Stability of the target system via Lyapunov like methods, and the invertibility of the integral transformation are used to show the stability of the tracking error.
Directory of Open Access Journals (Sweden)
Shaolong Chen
2016-01-01
Full Text Available Parameter estimation is an important problem in nonlinear system modeling and control. Through constructing an appropriate fitness function, parameter estimation of system could be converted to a multidimensional parameter optimization problem. As a novel swarm intelligence algorithm, chicken swarm optimization (CSO has attracted much attention owing to its good global convergence and robustness. In this paper, a method based on improved boundary chicken swarm optimization (IBCSO is proposed for parameter estimation of nonlinear systems, demonstrated and tested by Lorenz system and a coupling motor system. Furthermore, we have analyzed the influence of time series on the estimation accuracy. Computer simulation results show it is feasible and with desirable performance for parameter estimation of nonlinear systems.
Boundary-controlled spin chains for robust quantum state transfer
Zwick, Analia; Stolze, Joachim; Osenda, Omar
2011-01-01
Quantum state transfer in the presence of noise is one of the main challenges for building quantum computers. We compare the quantum state transfer properties for two classes of qubit chains under the influence of static randomness. In fully engineered chains all nearest-neighbor couplings are tuned in such a way that a single-qubit state can be transferred perfectly between the ends of the chain, while in boundary-controlled chains only the two couplings between the transmitting and receiving qubits and the remainder of the chain can be optimized. We study how the noise in the couplings affects the state transfer fidelity depending on the noise model and strength as well as the chain type and length. We show that the desired level of fidelity and transfer time are important factors in designing a chain. In particular we demonstrate that transfer efficiency comparable or better than that of the most robust engineered systems can also be reached in boundary-controlled chains without the demanding engineering o...
Optimal control linear quadratic methods
Anderson, Brian D O
2007-01-01
This augmented edition of a respected text teaches the reader how to use linear quadratic Gaussian methods effectively for the design of control systems. It explores linear optimal control theory from an engineering viewpoint, with step-by-step explanations that show clearly how to make practical use of the material.The three-part treatment begins with the basic theory of the linear regulator/tracker for time-invariant and time-varying systems. The Hamilton-Jacobi equation is introduced using the Principle of Optimality, and the infinite-time problem is considered. The second part outlines the
A STABILITY THEOREM FOR CONSTRAINED OPTIMAL CONTROL PROBLEMS
Institute of Scientific and Technical Information of China (English)
M.H. Farag
2004-01-01
This paper presents the stability of difference approximations of an optimal control problem for a quasilinear parabolic equation with controls in the coefficients, boundary conditions and additional restrictions. The optimal control problem has been convered to one of the optimization problem using a penalty function technique. The difference approximations problem for the considered problem is obtained. The estimations of stability of the solution of difference approximations problem are proved. The stability estimation of the solution of difference approximations problem by the controls is obtained.
Optimal control of motorsport differentials
Tremlett, A. J.; Massaro, M.; Purdy, D. J.; Velenis, E.; Assadian, F.; Moore, A. P.; Halley, M.
2015-12-01
Modern motorsport limited slip differentials (LSD) have evolved to become highly adjustable, allowing the torque bias that they generate to be tuned in the corner entry, apex and corner exit phases of typical on-track manoeuvres. The task of finding the optimal torque bias profile under such varied vehicle conditions is complex. This paper presents a nonlinear optimal control method which is used to find the minimum time optimal torque bias profile through a lane change manoeuvre. The results are compared to traditional open and fully locked differential strategies, in addition to considering related vehicle stability and agility metrics. An investigation into how the optimal torque bias profile changes with reduced track-tyre friction is also included in the analysis. The optimal LSD profile was shown to give a performance gain over its locked differential counterpart in key areas of the manoeuvre where a quick direction change is required. The methodology proposed can be used to find both optimal passive LSD characteristics and as the basis of a semi-active LSD control algorithm.
Optimal trajectory generation for generalization of discrete movements with boundary condition
DEFF Research Database (Denmark)
Herzog, Sebastian; Wörgötter, Florentin; Kulvicius, Tomas
2016-01-01
with zero error. Moreover, it has most of the properties of the state-of-the-art trajectory generation methods such as robustness to perturbations and generalisation to new boundary position and velocity conditions. We believe that, due to these features, our method has great potential for various robotic......Trajectory generation methods play an important role in robotics since they are essential for the execution of actions. In this paper we present a novel trajectory generation method for generalization of accurate movements with boundary conditions. Our approach originates from optimal control...... theory and is based on a second order dynamic system. We evaluate our method and compare it to state-of-the-art movement generation methods in both simulations and a real robot experiment. We show that the new method is very compact in its representation and can reproduce demonstrated trajectories...
The effects of aging on the speed-accuracy compromise: Boundary optimality in the diffusion model.
Starns, Jeffrey J; Ratcliff, Roger
2010-06-01
We evaluated age-related differences in the optimality of decision boundary settings in a diffusion model analysis. In the model, the width of the decision boundary represents the amount of evidence that must accumulate in favor of a response alternative before a decision is made. Wide boundaries lead to slow but accurate responding, and narrow boundaries lead to fast but inaccurate responding. There is a single value of boundary separation that produces the most correct answers in a given period of time, and we refer to this value as the reward rate optimal boundary (RROB). We consistently found across a variety of decision tasks that older adults used boundaries that were much wider than the RROB value. Young adults used boundaries that were closer to the RROB value, although age differences in optimality were smaller with instructions emphasizing speed than with instructions emphasizing accuracy. Young adults adjusted their boundary settings to more closely approach the RROB value when they were provided with accuracy feedback and extensive practice. Older participants showed no evidence of making boundary adjustments in response to feedback or task practice, and they consistently used boundary separation values that produced accuracy levels that were near asymptote. Our results suggest that young adults attempt to balance speed and accuracy to achieve the most correct answers per unit time, whereas older adultts attempt to minimize errors even if they must respond quite slowly to do so.
Control and optimal control theories with applications
Burghes, D N
2004-01-01
This sound introduction to classical and modern control theory concentrates on fundamental concepts. Employing the minimum of mathematical elaboration, it investigates the many applications of control theory to varied and important present-day problems, e.g. economic growth, resource depletion, disease epidemics, exploited population, and rocket trajectories. An original feature is the amount of space devoted to the important and fascinating subject of optimal control. The work is divided into two parts. Part one deals with the control of linear time-continuous systems, using both transfer fun
Optimal control with aerospace applications
Longuski, James M; Prussing, John E
2014-01-01
Want to know not just what makes rockets go up but how to do it optimally? Optimal control theory has become such an important field in aerospace engineering that no graduate student or practicing engineer can afford to be without a working knowledge of it. This is the first book that begins from scratch to teach the reader the basic principles of the calculus of variations, develop the necessary conditions step-by-step, and introduce the elementary computational techniques of optimal control. This book, with problems and an online solution manual, provides the graduate-level reader with enough introductory knowledge so that he or she can not only read the literature and study the next level textbook but can also apply the theory to find optimal solutions in practice. No more is needed than the usual background of an undergraduate engineering, science, or mathematics program: namely calculus, differential equations, and numerical integration. Although finding optimal solutions for these problems is a...
Phase modulated solitary waves controlled by bottom boundary condition
Mukherjee, Abhik
2014-01-01
A forced KdV equation is derived to describe weakly nonlinear, shallow water surface wave propagation over non trivial bottom boundary condition. We show that different functional forms of bottom boundary conditions self-consistently produce different forced kdV equations as the evolution equations for the free surface. Solitary wave solutions have been analytically obtained where phase gets modulated controlled by bottom boundary condition whereas amplitude remains constant.
Controls on boundary layer ventilation: Boundary layer processes and large-scale dynamics
Sinclair, V. A.; Gray, S. L.; Belcher, S. E.
2010-06-01
Midlatitude cyclones are important contributors to boundary layer ventilation. However, it is uncertain how efficient such systems are at transporting pollutants out of the boundary layer, and variations between cyclones are unexplained. In this study 15 idealized baroclinic life cycles, with a passive tracer included, are simulated to identify the relative importance of two transport processes: horizontal divergence and convergence within the boundary layer and large-scale advection by the warm conveyor belt. Results show that the amount of ventilation is insensitive to surface drag over a realistic range of values. This indicates that although boundary layer processes are necessary for ventilation they do not control the magnitude of ventilation. A diagnostic for the mass flux out of the boundary layer has been developed to identify the synoptic-scale variables controlling the strength of ascent in the warm conveyor belt. A very high level of correlation (R2 values exceeding 0.98) is found between the diagnostic and the actual mass flux computed from the simulations. This demonstrates that the large-scale dynamics control the amount of ventilation, and the efficiency of midlatitude cyclones to ventilate the boundary layer can be estimated using the new mass flux diagnostic. We conclude that meteorological analyses, such as ERA-40, are sufficient to quantify boundary layer ventilation by the large-scale dynamics.
Optimal control of hybrid vehicles
Jager, Bram; Kessels, John
2013-01-01
Optimal Control of Hybrid Vehicles provides a description of power train control for hybrid vehicles. The background, environmental motivation and control challenges associated with hybrid vehicles are introduced. The text includes mathematical models for all relevant components in the hybrid power train. The power split problem in hybrid power trains is formally described and several numerical solutions detailed, including dynamic programming and a novel solution for state-constrained optimal control problems based on Pontryagin’s maximum principle. Real-time-implementable strategies that can approximate the optimal solution closely are dealt with in depth. Several approaches are discussed and compared, including a state-of-the-art strategy which is adaptive for vehicle conditions like velocity and mass. Two case studies are included in the book: · a control strategy for a micro-hybrid power train; and · experimental results obtained with a real-time strategy implemented in...
Optimization and optimal control in automotive systems
Kolmanovsky, Ilya; Steinbuch, Maarten; Re, Luigi
2014-01-01
This book demonstrates the use of the optimization techniques that are becoming essential to meet the increasing stringency and variety of requirements for automotive systems. It shows the reader how to move away from earlier approaches, based on some degree of heuristics, to the use of more and more common systematic methods. Even systematic methods can be developed and applied in a large number of forms so the text collects contributions from across the theory, methods and real-world automotive applications of optimization. Greater fuel economy, significant reductions in permissible emissions, new drivability requirements and the generally increasing complexity of automotive systems are among the criteria that the contributing authors set themselves to meet. In many cases multiple and often conflicting requirements give rise to multi-objective constrained optimization problems which are also considered. Some of these problems fall into the domain of the traditional multi-disciplinary optimization applie...
Optimal control of hydroelectric facilities
Zhao, Guangzhi
This thesis considers a simple yet realistic model of pump-assisted hydroelectric facilities operating in a market with time-varying but deterministic power prices. Both deterministic and stochastic water inflows are considered. The fluid mechanical and engineering details of the facility are described by a model containing several parameters. We present a dynamic programming algorithm for optimizing either the total energy produced or the total cash generated by these plants. The algorithm allows us to give the optimal control strategy as a function of time and to see how this strategy, and the associated plant value, varies with water inflow and electricity price. We investigate various cases. For a single pumped storage facility experiencing deterministic power prices and water inflows, we investigate the varying behaviour for an oversimplified constant turbine- and pump-efficiency model with simple reservoir geometries. We then generalize this simple model to include more realistic turbine efficiencies, situations with more complicated reservoir geometry, and the introduction of dissipative switching costs between various control states. We find many results which reinforce our physical intuition about this complicated system as well as results which initially challenge, though later deepen, this intuition. One major lesson of this work is that the optimal control strategy does not differ much between two differing objectives of maximizing energy production and maximizing its cash value. We then turn our attention to the case of stochastic water inflows. We present a stochastic dynamic programming algorithm which can find an on-average optimal control in the face of this randomness. As the operator of a facility must be more cautious when inflows are random, the randomness destroys facility value. Following this insight we quantify exactly how much a perfect hydrological inflow forecast would be worth to a dam operator. In our final chapter we discuss the
Optimal Control Theory on almost-Lie Algebroids
Jozwikowski, Michal
2011-01-01
We extend the Pontryagin Maximum Principle (PMP) to the geometric setting of almost-Lie (AL) algebroids -- objects which generalize Lie algebroids. The result may be understood as a very general reduction scheme for optimal control problems (OCPs). It covers the standard PMP, as well as gives necessary optimality conditions for symmetric OCPs on Lie groups, principal bundles, and Lie groupoids. We do not assume the symmetry of boundary conditions. The ideas are based on a very general concept of homotopy of admissible paths on AL algebroids. Our framework works for OCPs with fixed-end-points and general boundary conditions.
Pan, Qing; Wang, Ruofan; Reglin, Bettina; Fang, Luping; Pries, Axel R; Ning, Gangmin
2014-01-01
Estimation of the boundary condition is a critical problem in simulating hemodynamics in microvascular networks. This paper proposed a boundary estimation strategy based on a particle swarm optimization (PSO) algorithm, which aims to minimize the number of vessels with inverted flow direction in comparison to the experimental observation. The algorithm took boundary values as the particle swarm and updated the position of the particles iteratively to approach the optimization target. The method was tested in a real rat mesenteric network. With random initial boundary values, the method achieved a minimized 9 segments with an inverted flow direction in the network with 546 vessels. Compared with reported literature, the current work has the advantage of a better fit with experimental observations and is more suitable for the boundary estimation problem in pulsatile hemodynamic models due to the experiment-based optimization target selection.
Feedback Control and Estimation Applied to Boundary Layers Subject to Free-Stream Turbulence
2006-11-01
R. G. Jacobs and P. A. Durbin , “Simulations of bypass transition,” J. Fluid Mech., vol. 428, pp. 185–212, 2001. [10] R. S. Rogallo, “Numerical...vol. 404, pp. 289–309, 2000. [20] P. Cathalifaud and P. Luchini, “ Algebraic growth in boundary layers: Optimal control by blowing and suction at the
Optimal Control of Electrodynamic Tethers
2008-06-01
left with ( ) ( ) 1 2 1 2 23 3 3 32 1 2 1 2 3 3 ˆ ˆ 2 2 2 ˆ ˆ 6 6 t t t t t t m m m m m T m L m L M M m LM M M MLm M M... Contract RH4-394049, March 1985, p 31. 9 Pelaez, J. and Lorenzini, E. C., “Libration Control of Electrodynamic Tethers in Inclined Orbit,” Journal of...COVERED (From – To) Aug 2006 – Jul 2008 4. TITLE AND SUBTITLE Optimal Control of Electrodynamic Tethers 5a. CONTRACT NUMBER 5b
Free Boundary Control of the Markov Process.
1988-01-04
used for the optimal selection and matching problems (such as matching army recruits to the jobs needed to be performed, cf. Rachev and Taksar [1987...Avail and/or Dist Special 2j .... anal" Rachev , S. and Taksar, M. I., 1987, "Kantorovich Functionals in Space of Probability Measures and Their
Directory of Open Access Journals (Sweden)
Ruisheng Sun
2016-01-01
Full Text Available This paper presents a new parametric optimization approach based on a modified particle swarm optimization (PSO to design a class of impulsive-correction projectiles with discrete, flexible-time interval, and finite-energy control. In terms of optimal control theory, the task is described as the formulation of minimum working number of impulses and minimum control error, which involves reference model linearization, boundary conditions, and discontinuous objective function. These result in difficulties in finding the global optimum solution by directly utilizing any other optimization approaches, for example, Hp-adaptive pseudospectral method. Consequently, PSO mechanism is employed for optimal setting of impulsive control by considering the time intervals between two neighboring lateral impulses as design variables, which makes the briefness of the optimization process. A modification on basic PSO algorithm is developed to improve the convergence speed of this optimization through linearly decreasing the inertial weight. In addition, a suboptimal control and guidance law based on PSO technique are put forward for the real-time consideration of the online design in practice. Finally, a simulation case coupled with a nonlinear flight dynamic model is applied to validate the modified PSO control algorithm. The results of comparative study illustrate that the proposed optimal control algorithm has a good performance in obtaining the optimal control efficiently and accurately and provides a reference approach to handling such impulsive-correction problem.
Boundary Controllability of Integrodifferential Systems in Banach Spaces
Indian Academy of Sciences (India)
K Balachandran; E R Anandhi
2001-02-01
Sufficient conditions for boundary controllability of integrodifferential systems in Banach spaces are established. The results are obtained by using the strongly continuous semigroup theory and the Banach contraction principle. Examples are provided to illustrate the theory.
Vortex Generators to Control Boundary Layer Interactions
Babinsky, Holger (Inventor); Loth, Eric (Inventor); Lee, Sang (Inventor)
2014-01-01
Devices for generating streamwise vorticity in a boundary includes various forms of vortex generators. One form of a split-ramp vortex generator includes a first ramp element and a second ramp element with front ends and back ends, ramp surfaces extending between the front ends and the back ends, and vertical surfaces extending between the front ends and the back ends adjacent the ramp surfaces. A flow channel is between the first ramp element and the second ramp element. The back ends of the ramp elements have a height greater than a height of the front ends, and the front ends of the ramp elements have a width greater than a width of the back ends.
Zhengnan Li; Tao Yang; Zhiwei Feng
2016-01-01
To solve the multiobjective optimization problem on hypersonic glider vehicle trajectory design subjected to complex constraints, this paper proposes a multiobjective trajectory optimization method that combines the boundary intersection method and pseudospectral method. The multiobjective trajectory optimization problem (MTOP) is established based on the analysis of the feature of hypersonic glider vehicle trajectory. The MTOP is translated into a set of general optimization subproblems by u...
Bristled shark skin: a microgeometry for boundary layer control?
Energy Technology Data Exchange (ETDEWEB)
Lang, A W; Hidalgo, P; Westcott, M [Aerospace Engineering and Mechanics Department, University of Alabama, Box 870280, Tuscaloosa, AL 35487 (United States); Motta, P [Biology Department, University of South Florida, 4202 East Fowler Avenue, Tampa, FL 33620 (United States)], E-mail: alang@eng.ua.edu
2008-12-01
There exists evidence that some fast-swimming shark species may have the ability to bristle their scales during fast swimming. Experimental work using a water tunnel facility has been performed to investigate the flow field over and within a bristled shark skin model submerged within a boundary layer to deduce the possible boundary layer control mechanisms being used by these fast-swimming sharks. Fluorescent dye flow visualization provides evidence of the formation of embedded cavity vortices within the scales. Digital particle image velocimetry (DPIV) data, used to evaluate the cavity vortex formation and boundary layer characteristics close to the surface, indicate increased momentum in the slip layer forming above the scales. This increase in flow velocity close to the shark's skin is indicative of boundary layer control mechanisms leading to separation control and possibly transition delay for the bristled shark skin microgeometry.
Boundary controllability for a nonlinear beam equation
Directory of Open Access Journals (Sweden)
Xiao-Min Cao
2015-09-01
Full Text Available This article concerns a nonlinear system modeling the bending vibrations of a nonlinear beam of length $L>0$. First, we derive the existence of long time solutions near an equilibrium. Then we prove that the nonlinear beam is locally exact controllable around the equilibrium in $H^4(0,L$ and with control functions in $H^2(0,T$. The approach we used are open mapping theorem, local controllability established by linearization, and the induction.
Exact boundary controllability of nodal profile for quasilinear hyperbolic systems
Li, Tatsien; Gu, Qilong
2016-01-01
This book provides a comprehensive overview of the exact boundary controllability of nodal profile, a new kind of exact boundary controllability stimulated by some practical applications. This kind of controllability is useful in practice as it does not require any precisely given final state to be attained at a suitable time t=T by means of boundary controls, instead it requires the state to exactly fit any given demand (profile) on one or more nodes after a suitable time t=T by means of boundary controls. In this book we present a general discussion of this kind of controllability for general 1-D first order quasilinear hyperbolic systems and for general 1-D quasilinear wave equations on an interval as well as on a tree-like network using a modular-structure construtive method, suggested in LI Tatsien's monograph "Controllability and Observability for Quasilinear Hyperbolic Systems"(2010), and we establish a complete theory on the local exact boundary controllability of nodal profile for 1-D quasilinear hyp...
Galerkin approximations of nonlinear optimal control problems in Hilbert spaces
Directory of Open Access Journals (Sweden)
Mickael D. Chekroun
2017-07-01
Full Text Available Nonlinear optimal control problems in Hilbert spaces are considered for which we derive approximation theorems for Galerkin approximations. Approximation theorems are available in the literature. The originality of our approach relies on the identification of a set of natural assumptions that allows us to deal with a broad class of nonlinear evolution equations and cost functionals for which we derive convergence of the value functions associated with the optimal control problem of the Galerkin approximations. This convergence result holds for a broad class of nonlinear control strategies as well. In particular, we show that the framework applies to the optimal control of semilinear heat equations posed on a general compact manifold without boundary. The framework is then shown to apply to geoengineering and mitigation of greenhouse gas emissions formulated here in terms of optimal control of energy balance climate models posed on the sphere $\\mathbb{S}^2$.
Yan, Yan
2015-01-01
We study a new optimization scheme that generates smooth and robust solutions for Dirichlet velocity boundary control (DVBC) of conjugate heat transfer (CHT) processes. The solutions to the DVBC of the incompressible Navier-Stokes equations are typically nonsmooth, due to the regularity degradation of the boundary stress in the adjoint Navier-Stokes equations. This nonsmoothness is inherited by the solutions to the DVBC of CHT processes, since the CHT process couples the Navier-Stokes equations of fluid motion with the convection-diffusion equations of fluid-solid thermal interaction. Our objective in the CHT boundary control problem is to select optimally the fluid inflow profile that minimizes an objective function that involves the sum of the mismatch between the temperature distribution in the fluid system and a prescribed temperature profile and the cost of the control.Our strategy to resolve the nonsmoothness of the boundary control solution is based on two features, namely, the objective function with a regularization term on the gradient of the control profile on both the continuous and the discrete levels, and the optimization scheme with either explicit or implicit smoothing effects, such as the smoothed Steepest Descent and the Limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) methods. Our strategy to achieve the robustness of the solution process is based on combining the smoothed optimization scheme with the numerical continuation technique on the regularization parameters in the objective function. In the section of numerical studies, we present two suites of experiments. In the first one, we demonstrate the feasibility and effectiveness of our numerical schemes in recovering the boundary control profile of the standard case of a Poiseuille flow. In the second one, we illustrate the robustness of our optimization schemes via solving more challenging DVBC problems for both the channel flow and the flow past a square cylinder, which use initial
Boundary Shape Control of the Navier-Stokes Equations and Applications
Institute of Scientific and Technical Information of China (English)
Kaitai LI; Jian SU; Aixiang HUANG
2010-01-01
In this paper,the geometrical design for the blade's surface(s)in an impeller or for the profile of an aircraft,is modeled from the mathematical point of view by a boundary shape control problem for the Navier-Stokes equations.The objective function is the sum of a global dissipative function and the power of the fluid.The control variables are the geometry of the boundary and the state equations are the Navier-Stokes equations.The Euler-Lagrange equations of the optimal control problem are derived,which are an elliptic boundary value system of fourth order,coupled with the Navier-Stokes equations.The authors also prove the existence of the solution of the optimal control problem,the existence of the solution of the Navier-Stokes equations with mixed boundary conditions,the weak continuity of the solution of the Navier-Stokes equations with respect to the geometry shape of the blade's surface and the existence of solutions of the equations for the G(a)teaux derivative of the solution of the Navier-Stokes equations with respect to the geometry of the boundary.
HCCI Engine Optimization and Control
Energy Technology Data Exchange (ETDEWEB)
Rolf D. Reitz
2005-09-30
The goal of this project was to develop methods to optimize and control Homogeneous-Charge Compression Ignition (HCCI) engines, with emphasis on diesel-fueled engines. HCCI offers the potential of nearly eliminating IC engine NOx and particulate emissions at reduced cost over Compression Ignition Direct Injection engines (CIDI) by controlling pollutant emissions in-cylinder. The project was initiated in January, 2002, and the present report is the final report for work conducted on the project through December 31, 2004. Periodic progress has also been reported at bi-annual working group meetings held at USCAR, Detroit, MI, and at the Sandia National Laboratories. Copies of these presentation materials are available on CD-ROM, as distributed by the Sandia National Labs. In addition, progress has been documented in DOE Advanced Combustion Engine R&D Annual Progress Reports for FY 2002, 2003 and 2004. These reports are included as the Appendices in this Final report.
Power optimized programmable embedded controller
Kamaraju, M; Tilak, A V N; 10.5121/ijcnc.2010.2409
2010-01-01
Now a days, power has become a primary consideration in hardware design, and is critical in computer systems especially for portable devices with high performance and more functionality. Clock-gating is the most common technique used for reducing processor's power. In this work clock gating technique is applied to optimize the power of fully programmable Embedded Controller (PEC) employing RISC architecture. The CPU designed supports i) smart instruction set, ii) I/O port, UART iii) on-chip clocking to provide a range of frequencies , iv) RISC as well as controller concepts. The whole design is captured using VHDL and is implemented on FPGA chip using Xilinx .The architecture and clock gating technique together is found to reduce the power consumption by 33.33% of total power consumed by this chip.
Directory of Open Access Journals (Sweden)
Zhengnan Li
2016-01-01
Full Text Available To solve the multiobjective optimization problem on hypersonic glider vehicle trajectory design subjected to complex constraints, this paper proposes a multiobjective trajectory optimization method that combines the boundary intersection method and pseudospectral method. The multiobjective trajectory optimization problem (MTOP is established based on the analysis of the feature of hypersonic glider vehicle trajectory. The MTOP is translated into a set of general optimization subproblems by using the boundary intersection method and pseudospectral method. The subproblems are solved by nonlinear programming algorithm. In this method, the solution that has been solved is employed as the initial guess for the next subproblem so that the time consumption of the entire multiobjective trajectory optimization problem shortens. The maximal range and minimal peak heat problem is solved by the proposed method. The numerical results demonstrate that the proposed method can obtain the Pareto front of the optimal trajectory, which can provide the reference for the trajectory design of hypersonic glider vehicle.
Optimal control of induction heating processes
Rapoport, Edgar
2006-01-01
This book introduces new approaches to solving optimal control problems in induction heating process applications. Optimal Control of Induction Heating Processes demonstrates how to apply and use new optimization techniques for different types of induction heating installations. Focusing on practical methods for solving real engineering optimization problems, the text features a variety of specific optimization examples for induction heater modes and designs, particularly those used in industrial applications. The book describes basic physical phenomena in induction heating and induction
Boundary-layer control by electric fields A feasibility study
Mendes, R V
1998-01-01
A problem of great concern in aviation and submarine propulsion is the control of the boundary layer and, in particular, the methods to extend the laminar region as a means to decrease noise and fuel consumption. In this paper we study the flow of air along an airfoil when a layer of ionized gas and a longitudinal electric field are created in the boundary layer region. By deriving scaling solutions and more accurate numerical solutions we discuss the possibility of achieving significant boundary layer control for realistic physical parameters. Practical design formulas and criteria are obtained. We also discuss the perspectives for active control of the laminar-to-turbulent transition fluctuations by electromagnetic field modulation.
Optimal control of sun tracking solar concentrators
Hughes, R. O.
1979-01-01
Application of the modern control theory to derive an optimal sun tracking control for a point focusing solar concentrator is presented. A standard tracking problem converted to regulator problem using a sun rate input achieves an almost zero steady state tracking error with the optimal control formulation. However, these control techniques are costly because optimal type algorithms require large computing systems, thus they will be used mainly as comparison standards for other types of control algorithms and help in their development.
Temperature controller optimization by computational intelligence
Directory of Open Access Journals (Sweden)
Ćojbašić Žarko M.
2016-01-01
Full Text Available In this paper a temperature control system for an automated educational classroom is optimized with several advanced computationally intelligent methods. Controller development and optimization has been based on developed and extensively tested mathematical and simulation model of the observed object. For the observed object cascade P-PI temperature controller has been designed and conventionally tuned. To improve performance and energy efficiency of the system, several metaheuristic optimizations of the controller have been attempted, namely genetic algorithm optimization, simulated annealing optimization, particle swarm optimization and ant colony optimization. Efficiency of the best results obtained with proposed computationally intelligent optimization methods has been compared with conventional controller tuning. Results presented in this paper demonstrate that heuristic optimization of advanced temperature controller can provide improved energy efficiency along with other performance improvements and improvements regarding equipment wear. Not only that presented methodology provides for determination and tuning of the core controller, but it also allows that advanced control concepts such as anti-windup controller gain are optimized simultaneously, which is of significant importance since interrelation of all control system parameters has important influence on the stability and performance of the system as a whole. Based on the results obtained, general conclusions are presented indicating that meta-heuristic computationally intelligent optimization of heating, ventilation, and air conditioning control systems is a feasible concept with strong potential in providing improved performance, comfort and energy efficiency. [Projekat Ministarstva nauke Republike Srbije, br. TR 33047 i br. TR 35016
Optimal traffic control in highway transportation networks using linear programming
Li, Yanning
2014-06-01
This article presents a framework for the optimal control of boundary flows on transportation networks. The state of the system is modeled by a first order scalar conservation law (Lighthill-Whitham-Richards PDE). Based on an equivalent formulation of the Hamilton-Jacobi PDE, the problem of controlling the state of the system on a network link in a finite horizon can be posed as a Linear Program. Assuming all intersections in the network are controllable, we show that the optimization approach can be extended to an arbitrary transportation network, preserving linear constraints. Unlike previously investigated transportation network control schemes, this framework leverages the intrinsic properties of the Halmilton-Jacobi equation, and does not require any discretization or boolean variables on the link. Hence this framework is very computational efficient and provides the globally optimal solution. The feasibility of this framework is illustrated by an on-ramp metering control example.
Constrained Optimization and Optimal Control for Partial Differential Equations
Leugering, Günter; Griewank, Andreas
2012-01-01
This special volume focuses on optimization and control of processes governed by partial differential equations. The contributors are mostly participants of the DFG-priority program 1253: Optimization with PDE-constraints which is active since 2006. The book is organized in sections which cover almost the entire spectrum of modern research in this emerging field. Indeed, even though the field of optimal control and optimization for PDE-constrained problems has undergone a dramatic increase of interest during the last four decades, a full theory for nonlinear problems is still lacking. The cont
Fuzzy logic control and optimization system
Lou, Xinsheng [West Hartford, CT
2012-04-17
A control system (300) for optimizing a power plant includes a chemical loop having an input for receiving an input signal (369) and an output for outputting an output signal (367), and a hierarchical fuzzy control system (400) operably connected to the chemical loop. The hierarchical fuzzy control system (400) includes a plurality of fuzzy controllers (330). The hierarchical fuzzy control system (400) receives the output signal (367), optimizes the input signal (369) based on the received output signal (367), and outputs an optimized input signal (369) to the input of the chemical loop to control a process of the chemical loop in an optimized manner.
AN APPLICATION OF OPTIMAL CONTROL THEORY.
The purpose of this article is to show that optimal control theory can be used to develop a control strategy for a practical system, namely a distillation column. The approach will be to model the complex system with a simple model, use optimal control theory to determine a control strategy for the simple model, and then apply the results to the original system. (Author)
Boundary Control of Linear Evolution PDEs - Continuous and Discrete
DEFF Research Database (Denmark)
Rasmussen, Jan Marthedal
2004-01-01
Consider a partial di erential equation (PDE) of evolution type, such as the wave equation or the heat equation. Assume now that you can influence the behavior of the solution by setting the boundary conditions as you please. This is boundary control in a broad sense. A substantial amount...... erential equations. This field has mostly concerned engineers and others with practical applications in mind. This thesis makes an attempt to bridge the two research areas. More specifically, we make finite dimensional approximations to certain evolution PDEs, and analyze how properties of the discrete...... systems resemble the properties of the continuous system. A common framework in which the continuous systems are formulated will be provided. The treatment includes many types of linear evolution PDEs and boundary conditions. We also consider di erent types of controllability, such as approximate, null...
A Quasi Time Optimal Receding Horizon Control
Bania, Piotr
2007-01-01
This paper presents a quasi time optimal receding horizon control algorithm. The proposed algorithm generates near time optimal control when the state of the system is far from the target. When the state attains a certain neighbourhood of the aim, it begins the adaptation of the cost function. The purpose of this adaptation is to move from the time optimal control to the stabilizing control. Sufficient conditions for the stability of the closed loop system and the manner of the adaptation of ...
Model-based dynamic control and optimization of gas networks
Energy Technology Data Exchange (ETDEWEB)
Hofsten, Kai
2001-07-01
by a structured sequential quadratic programming algorithm of Newton type. Each open loop problem is specified using a nonlinear prediction model. For each iteration of the quadratic programming procedure, a linear time variant prediction model is formulated. The suggested controller also handles time varying source capacity. Potential problems such as infeasibility and the security of the supply when facing a change in the status of the infrastructure of the transmission system under a transient customer load are treated. Comments on the infeasibility due to errors such as load forecast error, model error and state estimation error are also discussed. A simplified nonlinear model called the creep flow model is used to describe the fluid dynamics inside a natural gas transmission line. Different assumptions and reformulations of this model yield the different control, simulation and optimization models used in this thesis. The control of a single gas transmission line is investigated using linear model predictive control based on instant linearization of the nonlinear model. Model predictive control using a bi quadratic optimization model formulated from the creep flow model is also investigated. A distributed parameter control model of the gas dynamics for a transmission line is formulated. An analytic solution of this model is given with both Neuman boundary conditions and distributed supplies and loads. A transfer function model is developed expressing the dynamics between the defined output and the control and disturbance inputs of the transmission line. Based on the qualitative behaviour observed from the step responses of the solutions of the distributed parameter model formulated in this thesis, simplified transfer function models were developed. These control models expresses the dynamics of a natural gas transmission line with Neuman boundary control and load. Further, these models were used to design a control law, which is a combination of a Smith
CT image segmentation using FEM with optimized boundary condition.
Directory of Open Access Journals (Sweden)
Hiroyuki Hishida
Full Text Available The authors propose a CT image segmentation method using structural analysis that is useful for objects with structural dynamic characteristics. Motivation of our research is from the area of genetic activity. In order to reveal the roles of genes, it is necessary to create mutant mice and measure differences among them by scanning their skeletons with an X-ray CT scanner. The CT image needs to be manually segmented into pieces of the bones. It is a very time consuming to manually segment many mutant mouse models in order to reveal the roles of genes. It is desirable to make this segmentation procedure automatic. Although numerous papers in the past have proposed segmentation techniques, no general segmentation method for skeletons of living creatures has been established. Against this background, the authors propose a segmentation method based on the concept of destruction analogy. To realize this concept, structural analysis is performed using the finite element method (FEM, as structurally weak areas can be expected to break under conditions of stress. The contribution of the method is its novelty, as no studies have so far used structural analysis for image segmentation. The method's implementation involves three steps. First, finite elements are created directly from the pixels of a CT image, and then candidates are also selected in areas where segmentation is thought to be appropriate. The second step involves destruction analogy to find a single candidate with high strain chosen as the segmentation target. The boundary conditions for FEM are also set automatically. Then, destruction analogy is implemented by replacing pixels with high strain as background ones, and this process is iterated until object is decomposed into two parts. Here, CT image segmentation is demonstrated using various types of CT imagery.
Directory of Open Access Journals (Sweden)
Liaqat Ali
2016-09-01
Full Text Available In this research work a new version of Optimal Homotopy Asymptotic Method is applied to solve nonlinear boundary value problems (BVPs in finite and infinite intervals. It comprises of initial guess, auxiliary functions (containing unknown convergence controlling parameters and a homotopy. The said method is applied to solve nonlinear Riccati equations and nonlinear BVP of order two for thin film flow of a third grade fluid on a moving belt. It is also used to solve nonlinear BVP of order three achieved by Mostafa et al. for Hydro-magnetic boundary layer and micro-polar fluid flow over a stretching surface embedded in a non-Darcian porous medium with radiation. The obtained results are compared with the existing results of Runge-Kutta (RK-4 and Optimal Homotopy Asymptotic Method (OHAM-1. The outcomes achieved by this method are in excellent concurrence with the exact solution and hence it is proved that this method is easy and effective.
Performance investigation of multigrid optimization for DNS-based optimal control problems
Nita, Cornelia; Vandewalle, Stefan; Meyers, Johan
2016-11-01
Optimal control theory in Direct Numerical Simulation (DNS) or Large-Eddy Simulation (LES) of turbulent flow involves large computational cost and memory overhead for the optimization of the controls. In this context, the minimization of the cost functional is typically achieved by employing gradient-based iterative methods such as quasi-Newton, truncated Newton or non-linear conjugate gradient. In the current work, we investigate the multigrid optimization strategy (MGOpt) in order to speed up the convergence of the damped L-BFGS algorithm for DNS-based optimal control problems. The method consists in a hierarchy of optimization problems defined on different representation levels aiming to reduce the computational resources associated with the cost functional improvement on the finest level. We examine the MGOpt efficiency for the optimization of an internal volume force distribution with the goal of reducing the turbulent kinetic energy or increasing the energy extraction in a turbulent wall-bounded flow; problems that are respectively related to drag reduction in boundary layers, or energy extraction in large wind farms. Results indicate that in some cases the multigrid optimization method requires up to a factor two less DNS and adjoint DNS than single-grid damped L-BFGS. The authors acknowledge support from OPTEC (OPTimization in Engineering Center of Excellence, KU Leuven, Grant No PFV/10/002).
Controlling near shore nonlinear surging waves through bottom boundary conditions
Mukherjee, Abhik; Kundu, Anjan
2016-01-01
Instead of taking the usual passive view for warning of near shore surging waves including extreme waves like tsunamis, we aim to study the possibility of intervening and controlling nonlinear surface waves through the feedback boundary effect at the bottom. It has been shown through analytic result that the controlled leakage at the bottom may regulate the surface solitary wave amplitude opposing the hazardous variable depth effect. The theoretical results are applied to a real coastal bathymetry in India.
Boundary control for a class of pseudoparabolic differential equations
DEFF Research Database (Denmark)
Hasan, Agus; Aamo, Ole Morten; Foss, Bjarne
2013-01-01
The boundary stabilization problem for a class of linear and nonlinear pseudo-parabolic differential equations is considered. The proposed control laws are used to achieve global exponential stability for the linear system and semi-global exponential stability for the nonlinear system in the H1H1......-sense. An H2H2 bound of the solution for the nonlinear system is also derived. A numerical example is included to illustrate the application of the proposed control laws....
A Controlled Particle Filter for Global Optimization
Zhang, Chi; Taghvaei, Amirhossein; Mehta, Prashant G.
2017-01-01
A particle filter is introduced to numerically approximate a solution of the global optimization problem. The theoretical significance of this work comes from its variational aspects: (i) the proposed particle filter is a controlled interacting particle system where the control input represents the solution of a mean-field type optimal control problem; and (ii) the associated density transport is shown to be a gradient flow (steepest descent) for the optimal value function, with respect to th...
Solution of the boundary value problem for optimal escape in continuous stochastic systems and maps.
S; Beri; Mannella, R.; Luchinsky, Dmitry G.; Silchenko, A. N.; McClintock, Peter V. E.
2005-01-01
Topologies of invariant manifolds and optimal trajectories are investigated in stochastic continuous systems and maps. A topological method is introduced that simplifies the solution of boundary value problems: The activation energy is calculated as a function of a set of parameters characterizing the initial conditions of the escape path. The method is applied explicitly to compute the optimal escape path and the activation energy for a variety of dynamical systems and maps.
Optimizing Dynamical Network Structure for Pinning Control
Orouskhani, Yasin; Jalili, Mahdi; Yu, Xinghuo
2016-04-01
Controlling dynamics of a network from any initial state to a final desired state has many applications in different disciplines from engineering to biology and social sciences. In this work, we optimize the network structure for pinning control. The problem is formulated as four optimization tasks: i) optimizing the locations of driver nodes, ii) optimizing the feedback gains, iii) optimizing simultaneously the locations of driver nodes and feedback gains, and iv) optimizing the connection weights. A newly developed population-based optimization technique (cat swarm optimization) is used as the optimization method. In order to verify the methods, we use both real-world networks, and model scale-free and small-world networks. Extensive simulation results show that the optimal placement of driver nodes significantly outperforms heuristic methods including placing drivers based on various centrality measures (degree, betweenness, closeness and clustering coefficient). The pinning controllability is further improved by optimizing the feedback gains. We also show that one can significantly improve the controllability by optimizing the connection weights.
Time-optimal control of infinite order distributed parabolic systems involving time lags
Directory of Open Access Journals (Sweden)
G.M. Bahaa
2014-06-01
Full Text Available A time-optimal control problem for linear infinite order distributed parabolic systems involving constant time lags appear both in the state equation and in the boundary condition is presented. Some particular properties of the optimal control are discussed.
Adaptive optimization and control using neural networks
Energy Technology Data Exchange (ETDEWEB)
Mead, W.C.; Brown, S.K.; Jones, R.D.; Bowling, P.S.; Barnes, C.W.
1993-10-22
Recent work has demonstrated the ability of neural-network-based controllers to optimize and control machines with complex, non-linear, relatively unknown control spaces. We present a brief overview of neural networks via a taxonomy illustrating some capabilities of different kinds of neural networks. We present some successful control examples, particularly the optimization and control of a small-angle negative ion source.
Optimal Control of Switched Systems based on Bezier Control Points
FatemeGhomanjani; Mohammad HadiFarahi
2012-01-01
This paper presents a new approach for solving optimal control problems for switched systems. We focus on problems in which a pre-specified sequence of active subsystems is given. For such problems, we need to seek both the optimal switching instants and the optimal continuous inputs. A Bezier control points method is applied for solving an optimal control problem which is supervised by a switched dynamic system. Two steps of approximation exist here. First, the time interval is divided into ...
Optimal Control and Optimization of Stochastic Supply Chain Systems
Song, Dong-Ping
2013-01-01
Optimal Control and Optimization of Stochastic Supply Chain Systems examines its subject in the context of the presence of a variety of uncertainties. Numerous examples with intuitive illustrations and tables are provided, to demonstrate the structural characteristics of the optimal control policies in various stochastic supply chains and to show how to make use of these characteristics to construct easy-to-operate sub-optimal policies. In Part I, a general introduction to stochastic supply chain systems is provided. Analytical models for various stochastic supply chain systems are formulated and analysed in Part II. In Part III the structural knowledge of the optimal control policies obtained in Part II is utilized to construct easy-to-operate sub-optimal control policies for various stochastic supply chain systems accordingly. Finally, Part IV discusses the optimisation of threshold-type control policies and their robustness. A key feature of the book is its tying together of ...
An iterative method for controlling reactive power flow in boundary transformers
Energy Technology Data Exchange (ETDEWEB)
Trigo, Angel L.; Martinez, Jose L.; Riquelme, Jesus; Romero, Esther [Department of Electrical Engineering, University of Seville (Spain)
2011-02-15
This paper presents an operational tool designed to help the system operator to control the reactive power flow in transmission-subtransmission boundary transformers. The main objective is to determine the minimum number of control actions necessary to ensure that reactive power flows in transmission/subtransmission transformers remain within limits. The proposed iterative procedure combines the use of a linear programming problem and a load flow tool. The linear programming assumes a linear behaviour between dependent and control variables around an operating point, modelled with sensitivities. Experimental results regarding IEEE systems are provided comparing the performance of the proposed approach with that of a conventional optimal power flow. (author)
Exact controllability for a semilinear wave equation with both interior and boundary controls
Directory of Open Access Journals (Sweden)
Bui An Ton
2005-01-01
Full Text Available The exact controllability of a semilinear wave equation in a bounded open domain of Rn, with controls on a part of the boundary and in the interior, is shown. Feedback laws are established.
Solving Optimal Control Problems by Exploiting Inherent Dynamical Systems Structures
Flaßkamp, Kathrin; Ober-Blöbaum, Sina; Kobilarov, Marin
2012-08-01
Computing globally efficient solutions is a major challenge in optimal control of nonlinear dynamical systems. This work proposes a method combining local optimization and motion planning techniques based on exploiting inherent dynamical systems structures, such as symmetries and invariant manifolds. Prior to the optimal control, the dynamical system is analyzed for structural properties that can be used to compute pieces of trajectories that are stored in a motion planning library. In the context of mechanical systems, these motion planning candidates, termed primitives, are given by relative equilibria induced by symmetries and motions on stable or unstable manifolds of e.g. fixed points in the natural dynamics. The existence of controlled relative equilibria is studied through Lagrangian mechanics and symmetry reduction techniques. The proposed framework can be used to solve boundary value problems by performing a search in the space of sequences of motion primitives connected using optimized maneuvers. The optimal sequence can be used as an admissible initial guess for a post-optimization. The approach is illustrated by two numerical examples, the single and the double spherical pendula, which demonstrates its benefit compared to standard local optimization techniques.
DEFF Research Database (Denmark)
Yoon, Gil Ho; Park, Y.K.; Kim, Y.Y.
2007-01-01
A new topology optimization scheme, called the element stacking method, is developed to better handle design optimization involving material-dependent boundary conditions and selection of elements of different types. If these problems are solved by existing standard approaches, complicated finite...... element models or topology optimization reformulation may be necessary. The key idea of the proposed method is to stack multiple elements on the same discretization pixel and select a single or no element. In this method, stacked elements on the same pixel have the same coordinates but may have...
Optimization of Temperature Controller for Electric Furnace
Institute of Scientific and Technical Information of China (English)
2000-01-01
Genetic algorithms are based on the principle of natural selection and the optimization of natural generation. We can select the number of the bit strings and mutation rate reasonably, the global optimal solution can be obtained. GAs adopt the binary code as optimizing parameter and this binary code can be used in computer controller easily. This paper studies the application of the GAs to the electric furnace temperature control. When the electric furnace mathematics model varies with the working condition, the parameter of controller can be optimized on line. So the system performance can be improved effectively.
OPTIMAL CONTROL PROBLEM FOR PARABOLIC VARIATIONAL INEQUALITIES
Institute of Scientific and Technical Information of China (English)
汪更生
2001-01-01
This paper deals with the optimal control problems of systems governed by a parabolic variational inequality coupled with a semilinear parabolic differential equations.The maximum principle and some kind of approximate controllability are studied.
Fast Solvers of Fredholm Optimal Control Problems
Institute of Scientific and Technical Information of China (English)
Mario; Borzì
2010-01-01
The formulation of optimal control problems governed by Fredholm integral equations of second kind and an efficient computational framework for solving these control problems is presented. Existence and uniqueness of optimal solutions is proved.A collective Gauss-Seidel scheme and a multigrid scheme are discussed. Optimal computational performance of these iterative schemes is proved by local Fourier analysis and demonstrated by results of numerical experiments.
Almost optimal adaptive LQ control: SISO case
Polderman, Jan W.; Daams, Jasper
2002-01-01
In this paper an almost optimal indirect adaptive controller for input/output dynamical systems is proposed. The control part of the adaptive control scheme is based on a modified LQ control law: by adding a time-varying gain to the certainty equivalent control law the conflict between
Efficient evolutionary algorithms for optimal control
López Cruz, I.L.
2002-01-01
If optimal control problems are solved by means of gradient based local search methods, convergence to local solutions is likely. Recently, there has been an increasing interest in the use of global optimisation algorithms to solve optimal control problems, wh
Connections Between Singular Control and Optimal Switching
Guo, Xin; Tomecek, Pascal
2007-01-01
This paper builds a new theoretical connection between singular control of finite variation and optimal switching problems. This correspondence provides a novel method for solving high-dimensional singular control problems, and enables us to extend the theory of reversible investment: sufficient conditions are derived for the existence of optimal controls and for the regularity of value functions. Consequently, our regularity result links singular controls and Dynkin games through sequential ...
Tracking control of a flexible beam by nonlinear boundary feedback
Directory of Open Access Journals (Sweden)
Bao-Zhu Guo
1995-01-01
Full Text Available This paper is concerned with tracking control of a dynamic model consisting of a flexible beam rotated by a motor in a horizontal plane at the one end and a tip body rigidly attached at the free end. The well-posedness of the closed loop systems considering the dissipative nonlinear boundary feedback is discussed and the asymptotic stability about difference energy of the hybrid system is also investigated.
Neural Networks for Optimal Control
DEFF Research Database (Denmark)
Sørensen, O.
1995-01-01
Two neural networks are trained to act as an observer and a controller, respectively, to control a non-linear, multi-variable process.......Two neural networks are trained to act as an observer and a controller, respectively, to control a non-linear, multi-variable process....
Neural Networks for Optimal Control
DEFF Research Database (Denmark)
Sørensen, O.
1995-01-01
Two neural networks are trained to act as an observer and a controller, respectively, to control a non-linear, multi-variable process.......Two neural networks are trained to act as an observer and a controller, respectively, to control a non-linear, multi-variable process....
Optimal switching using coherent control
DEFF Research Database (Denmark)
Kristensen, Philip Trøst; Heuck, Mikkel; Mørk, Jesper
2013-01-01
that the switching time, in general, is not limited by the cavity lifetime. Therefore, the total energy required for switching is a more relevant figure of merit than the switching speed, and for a particular two-pulse switching scheme we use calculus of variations to optimize the switching in terms of input energy....
Energy Technology Data Exchange (ETDEWEB)
Watanabe, Tadao; Tsurekawa, Sadahiro
1999-11-12
Grain boundaries can be effectively controlled to produce or enhance their beneficial effects and also to diminish or reduce their detrimental effects on bulk properties in polycrystalline materials. Particular attention has been paid to the control of intergranular brittleness which remains a serious problem of material processing and development. Recent studies are presented and discussed, which have been successfully performed to control intergranular brittleness of intrinsically brittle materials such as the refractory metal molybdenum and the ordered intermetallic alloy Ni{sub 3}Al and to produce superplasticity in an Al-Li alloy, by grain boundary engineering through controlling a new microstructural factor termed the grain boundary character distribution (GBCD). The optimization of GBCD and the grain boundary connectivity has been found to be a key to produce desirable bulk mechanical properties in both structural and functional polycrystalline materials.
USING OPTIMAL FEEDBACK CONTROL FOR CHAOS TARGETING
Institute of Scientific and Technical Information of China (English)
PENG ZHAO-WANG; ZHONG TING-XIU
2000-01-01
Since the conventional open-loop optimal targeting of chaos is very sensitive to noise, a close-loop optimal targeting method is proposed to improve the targeting performance under noise. The present optimal targeting model takes into consideration both precision and speed of the targeting procedure. The parameters, rather than the output, of the targeting controller, are directly optimized to obtain optimal chaos targeting. Analysis regarding the mechanism is given from physics aspect and numerical experiment on the Hénon map is carried out to compare the targeting performance under noise between the close-loop and the open-loop methods.
Model-based dynamic control and optimization of gas networks
Energy Technology Data Exchange (ETDEWEB)
Hofsten, Kai
2001-07-01
by a structured sequential quadratic programming algorithm of Newton type. Each open loop problem is specified using a nonlinear prediction model. For each iteration of the quadratic programming procedure, a linear time variant prediction model is formulated. The suggested controller also handles time varying source capacity. Potential problems such as infeasibility and the security of the supply when facing a change in the status of the infrastructure of the transmission system under a transient customer load are treated. Comments on the infeasibility due to errors such as load forecast error, model error and state estimation error are also discussed. A simplified nonlinear model called the creep flow model is used to describe the fluid dynamics inside a natural gas transmission line. Different assumptions and reformulations of this model yield the different control, simulation and optimization models used in this thesis. The control of a single gas transmission line is investigated using linear model predictive control based on instant linearization of the nonlinear model. Model predictive control using a bi quadratic optimization model formulated from the creep flow model is also investigated. A distributed parameter control model of the gas dynamics for a transmission line is formulated. An analytic solution of this model is given with both Neuman boundary conditions and distributed supplies and loads. A transfer function model is developed expressing the dynamics between the defined output and the control and disturbance inputs of the transmission line. Based on the qualitative behaviour observed from the step responses of the solutions of the distributed parameter model formulated in this thesis, simplified transfer function models were developed. These control models expresses the dynamics of a natural gas transmission line with Neuman boundary control and load. Further, these models were used to design a control law, which is a combination of a Smith
Linear optimal control of tokamak fusion devices
Energy Technology Data Exchange (ETDEWEB)
Kessel, C.E.; Firestone, M.A.; Conn, R.W.
1989-05-01
The control of plasma position, shape and current in a tokamak fusion reactor is examined using linear optimal control. These advanced tokamaks are characterized by non up-down symmetric coils and structure, thick structure surrounding the plasma, eddy currents, shaped plasmas, superconducting coils, vertically unstable plasmas, and hybrid function coils providing ohmic heating, vertical field, radial field, and shaping field. Models of the electromagnetic environment in a tokamak are derived and used to construct control gains that are tested in nonlinear simulations with initial perturbations. The issues of applying linear optimal control to advanced tokamaks are addressed, including complex equilibrium control, choice of cost functional weights, the coil voltage limit, discrete control, and order reduction. Results indicate that the linear optimal control is a feasible technique for controlling advanced tokamaks where the more common classical control will be severely strained or will not work. 28 refs., 13 figs.
Optimal Control of Switched Systems based on Bezier Control Points
Directory of Open Access Journals (Sweden)
FatemeGhomanjani
2012-06-01
Full Text Available This paper presents a new approach for solving optimal control problems for switched systems. We focus on problems in which a pre-specified sequence of active subsystems is given. For such problems, we need to seek both the optimal switching instants and the optimal continuous inputs. A Bezier control points method is applied for solving an optimal control problem which is supervised by a switched dynamic system. Two steps of approximation exist here. First, the time interval is divided into k sub-intervals. Second, the trajectory and control functions are approximatedby Bezier curves in each subinterval. Bezier curves have been considered as piecewise polynomials of degree n, then they will be determined by n+1 control points on any subinterval. The optimal control problem is there by converted into a nonlinear programming problem (NLP, which can be solved by known algorithms. However in this paper the MATLAB optimization routine FMINCON is used for solving resulting NLP.
System Optimization by Periodic Control.
1979-09-30
extended re- sults are now contained in a single report [3] which will appear as a regular paper in the December, 1979 issue of the IEEE Transactions on Automatic Control . The...Test Revisited, " to appear in the IEEE Transactions on Automatic Control . 4. D. J. Lyons, "Improved Aircraft Cruise by Periodic Control," Ph. D
Stochastic boundary control design for Timoshenko beams with large motions
Do, K. D.
2017-08-01
This paper considers modeling and boundary control of Timoshenko beams with large motions under both deterministic and stochastic external loads. The original nonlinear partial differential equations governing motion of the beams are derived and used in the control design. The control design is based on the Lyapunov direct method. The proposed controllers guarantee globally practically K∞-exponentially p-stability of the beam motions at the reference state. Well-posedness and stability are analyzed based on a Lyapunov-type theorem developed to study well-posedness and stability for a class of stochastic evolution systems in Hilbert space. Simulation results are included to illustrate the effectiveness of the proposed control design.
Optimal Control Development System for Electrical Drives
Directory of Open Access Journals (Sweden)
Marian GAICEANU
2008-08-01
Full Text Available In this paper the optimal electrical drive development system is presented. It consists of both electrical drive types: DC and AC. In order to implement the optimal control for AC drive system an Altivar 71 inverter, a Frato magnetic particle brake (as load, three-phase induction machine, and dSpace 1104 controller have been used. The on-line solution of the matrix Riccati differential equation (MRDE is computed by dSpace 1104 controller, based on the corresponding feedback signals, generating the optimal speed reference for the AC drive system. The optimal speed reference is tracked by Altivar 71 inverter, conducting to energy reduction in AC drive. The classical control (consisting of rotor field oriented control with PI controllers and the optimal one have been implemented by designing an adequate ControlDesk interface. The three-phase induction machine (IM is controlled at constant flux. Therefore, the linear dynamic mathematical model of the IM has been obtained. The optimal control law provides transient regimes with minimal energy consumption. The obtained solution by integration of the MRDE is orientated towards the numerical implementation-by using a zero order hold. The development system is very useful for researchers, doctoral students or experts training in electrical drive. The experimental results are shown.
Dynamic optimization and adaptive controller design
Inamdar, S. R.
2010-10-01
In this work I present a new type of controller which is an adaptive tracking controller which employs dynamic optimization for optimizing current value of controller action for the temperature control of nonisothermal continuously stirred tank reactor (CSTR). We begin with a two-state model of nonisothermal CSTR which are mass and heat balance equations and then add cooling system dynamics to eliminate input multiplicity. The initial design value is obtained using local stability of steady states where approach temperature for cooling action is specified as a steady state and a design specification. Later we make a correction in the dynamics where material balance is manipulated to use feed concentration as a system parameter as an adaptive control measure in order to avoid actuator saturation for the main control loop. The analysis leading to design of dynamic optimization based parameter adaptive controller is presented. The important component of this mathematical framework is reference trajectory generation to form an adaptive control measure.
Optimal control of renewable economic resources
Energy Technology Data Exchange (ETDEWEB)
Adelani, L.A.
1987-01-01
Two main problems are studied: economic optimization, and determination of the optimal age of harvest for an initially immature population which follows a Bertalanffy-type growth law. Conditions are derived on the economic parameters that make maximization of economic rent biologically superior to maximization of sustainable yield. A general equation is derived for the optimal equilibrium biomass size when maximization of present value is the control objective. Also, it is shown that under perfectly elastic demand for the resource, a critical price level exists beyond which economic optimization has to be sacrificed in order to enhance conservation of the resource. An equation is derived whose solution represents the optimal age of harvest for an initially immature population stock. In certain circumstances, analytic forms are obtained for the optimal age of harvest. Some properties of the optimal age of harvest are also investigated.
Optimal Control of Isometric Muscle Dynamics
Directory of Open Access Journals (Sweden)
Robert Rockenfeller
2015-03-01
Full Text Available We use an indirect optimal control approach to calculate the optimal neural stimulation needed to obtain measured isometric muscle forces. The neural stimulation of the nerve system is hereby considered to be a control function (input of the system ’muscle’ that solely determines the muscle force (output. We use a well-established muscle model and experimental data of isometric contractions. The model consists of coupled activation and contraction dynamics described by ordinary differential equations. To validate our results, we perform a comparison with commercial optimal control software.
Optimal Control of Evolution Mixed Variational Inclusions
Energy Technology Data Exchange (ETDEWEB)
Alduncin, Gonzalo, E-mail: alduncin@geofisica.unam.mx [Universidad Nacional Autónoma de México, Departamento de Recursos Naturales, Instituto de Geofísica (Mexico)
2013-12-15
Optimal control problems of primal and dual evolution mixed variational inclusions, in reflexive Banach spaces, are studied. The solvability analysis of the mixed state systems is established via duality principles. The optimality analysis is performed in terms of perturbation conjugate duality methods, and proximation penalty-duality algorithms to mixed optimality conditions are further presented. Applications to nonlinear diffusion constrained problems as well as quasistatic elastoviscoplastic bilateral contact problems exemplify the theory.
MDP Optimal Control under Temporal Logic Constraints
Ding, Xu Chu; Belta, Calin; Rus, Daniela
2011-01-01
In this paper, we develop a method to automatically generate a control policy for a dynamical system modeled as a Markov Decision Process (MDP). The control specification is given as a Linear Temporal Logic (LTL) formula over a set of propositions defined on the states of the MDP. We synthesize a control policy such that the MDP satisfies the given specification almost surely, if such a policy exists. In addition, we designate an "optimizing proposition" to be repeatedly satisfied, and we formulate a novel optimization criterion in terms of minimizing the expected cost in between satisfactions of this proposition. We propose a sufficient condition for a policy to be optimal, and develop a dynamic programming algorithm that synthesizes a policy that is optimal under some conditions, and sub-optimal otherwise. This problem is motivated by robotic applications requiring persistent tasks, such as environmental monitoring or data gathering, to be performed.
Energy Optimal Control of Induction Motor Drives
DEFF Research Database (Denmark)
Abrahamsen, Flemming
This thesis deals with energy optimal control of small and medium-size variable speed induction motor drives for especially Heating, Ventilation and Air-Condition (HVAC) applications. Optimized efficiency is achieved by adapting the magnetization level in the motor to the load, and the basic...... purpose is demonstrate how this can be done for low-cost PWM-VSI drives without bringing the robustness of the drive below an acceptable level. Four drives are investigated with respect to energy optimal control: 2.2 kW standard and high-efficiency motor drives, 22 kW and 90 kW standard motor drives....... The method has been to make extensive efficiency measurements within the specified operating area with optimized efficiency and with constant air-gap flux, and to establish reliable converter and motor loss models based on those measurements. The loss models have been used to analyze energy optimal control...
Dynamic programming for infinite horizon boundary control problems of PDE's with age structure
Faggian, Silvia
2008-01-01
We develop the dynamic programming approach for a family of infinite horizon boundary control problems with linear state equation and convex cost. We prove that the value function of the problem is the unique regular solution of the associated stationary Hamilton--Jacobi--Bellman equation and use this to prove existence and uniqueness of feedback controls. The idea of studying this kind of problem comes from economic applications, in particular from models of optimal investment with vintage capital. Such family of problems has already been studied in the finite horizon case by Faggian. The infinite horizon case is more difficult to treat and it is more interesting from the point of view of economic applications, where what mainly matters is the behavior of optimal trajectories and controls in the long run. The study of infinite horizon is here performed through a nontrivial limiting procedure from the corresponding finite horizon problem.
Optimal Speed Control for Cruising
DEFF Research Database (Denmark)
Blanke, M.
1994-01-01
With small profit margins in merchant shipping and more than eighty percent of sailing time being cross ocean voyages, speed control is crucial for vessel profitability......With small profit margins in merchant shipping and more than eighty percent of sailing time being cross ocean voyages, speed control is crucial for vessel profitability...
Optimal Speed Control for Cruising
DEFF Research Database (Denmark)
Blanke, M.
1994-01-01
With small profit margins in merchant shipping and more than eighty percent of sailing time being cross ocean voyages, speed control is crucial for vessel profitability......With small profit margins in merchant shipping and more than eighty percent of sailing time being cross ocean voyages, speed control is crucial for vessel profitability...
Directory of Open Access Journals (Sweden)
Yuliang Wang
Full Text Available Cell image segmentation plays a central role in numerous biology studies and clinical applications. As a result, the development of cell image segmentation algorithms with high robustness and accuracy is attracting more and more attention. In this study, an automated cell image segmentation algorithm is developed to get improved cell image segmentation with respect to cell boundary detection and segmentation of the clustered cells for all cells in the field of view in negative phase contrast images. A new method which combines the thresholding method and edge based active contour method was proposed to optimize cell boundary detection. In order to segment clustered cells, the geographic peaks of cell light intensity were utilized to detect numbers and locations of the clustered cells. In this paper, the working principles of the algorithms are described. The influence of parameters in cell boundary detection and the selection of the threshold value on the final segmentation results are investigated. At last, the proposed algorithm is applied to the negative phase contrast images from different experiments. The performance of the proposed method is evaluated. Results show that the proposed method can achieve optimized cell boundary detection and highly accurate segmentation for clustered cells.
Wang, Yuliang; Zhang, Zaicheng; Wang, Huimin; Bi, Shusheng
2015-01-01
Cell image segmentation plays a central role in numerous biology studies and clinical applications. As a result, the development of cell image segmentation algorithms with high robustness and accuracy is attracting more and more attention. In this study, an automated cell image segmentation algorithm is developed to get improved cell image segmentation with respect to cell boundary detection and segmentation of the clustered cells for all cells in the field of view in negative phase contrast images. A new method which combines the thresholding method and edge based active contour method was proposed to optimize cell boundary detection. In order to segment clustered cells, the geographic peaks of cell light intensity were utilized to detect numbers and locations of the clustered cells. In this paper, the working principles of the algorithms are described. The influence of parameters in cell boundary detection and the selection of the threshold value on the final segmentation results are investigated. At last, the proposed algorithm is applied to the negative phase contrast images from different experiments. The performance of the proposed method is evaluated. Results show that the proposed method can achieve optimized cell boundary detection and highly accurate segmentation for clustered cells.
Controllability of a viscoelastic plate using one boundary control in displacement or bending
Pandolfi, L.
2016-01-01
In this paper we consider a viscoelastic plate (linear viscoelasticity of the Maxwell-Boltzmann type) and we compare its controllability properties with the (known) controllability of a purely elastic plate (the control acts on the boundary displacement or bending). By combining operator and moment methods, we prove that the viscoelastic plate inherits the controllability properties of the purely elastic plate.
Modeling, Optimization & Control of Hydraulic Networks
DEFF Research Database (Denmark)
Tahavori, Maryamsadat
2014-01-01
to check if the network is controllable. Afterward the pressure control problem in water supply systems is formulated as an optimal control problem. The goal is to minimize the power consumption in pumps and also to regulate the pressure drop at the end-users to a desired value. The formulated optimal...... in water network is pressure management. By reducing the pressure in the water network, the leakage can be reduced significantly. Also it reduces the amount of energy consumption in water networks. The primary purpose of this work is to develop control algorithms for pressure control in water supply...... systems. To have better understanding of water leakage, to control pressure and leakage effectively and for optimal design of water supply system, suitable modeling is an important prerequisite. Therefore a model with the main objective of pressure control and consequently leakage reduction is presented...
Talaei, Behzad; Jagannathan, Sarangapani; Singler, John
2017-03-06
In this paper, neurodynamic programming-based output feedback boundary control of distributed parameter systems governed by uncertain coupled semilinear parabolic partial differential equations (PDEs) under Neumann or Dirichlet boundary control conditions is introduced. First, Hamilton-Jacobi-Bellman (HJB) equation is formulated in the original PDE domain and the optimal control policy is derived using the value functional as the solution of the HJB equation. Subsequently, a novel observer is developed to estimate the system states given the uncertain nonlinearity in PDE dynamics and measured outputs. Consequently, the suboptimal boundary control policy is obtained by forward-in-time estimation of the value functional using a neural network (NN)-based online approximator and estimated state vector obtained from the NN observer. Novel adaptive tuning laws in continuous time are proposed for learning the value functional online to satisfy the HJB equation along system trajectories while ensuring the closed-loop stability. Local uniformly ultimate boundedness of the closed-loop system is verified by using Lyapunov theory. The performance of the proposed controller is verified via simulation on an unstable coupled diffusion reaction process.
Greenhouse climate management : an optimal control approach
Henten, van E.J.
1994-01-01
In this thesis a methodology is developed for the construction and analysis of an optimal greenhouse climate control system.
In chapter 1, the results of a literature survey are presented and the research objectives are defined. In the literature, optimal greenhouse climate
Optimal control and the calculus of variations
Pinch, Enid R
1993-01-01
This introduction to optimal control theory is intended for undergraduate mathematicians and for engineers and scientists with some knowledge of classical analysis. It includes sections on classical optimization and the calculus of variations. All the important theorems are carefully proved. There are many worked examples and exercises for the reader to attempt.
Optimization and control of metal forming processes
Havinga, Gosse Tjipke
2016-01-01
Inevitable variations in process and material properties limit the accuracy of metal forming processes. Robust optimization methods or control systems can be used to improve the production accuracy. Robust optimization methods are used to design production processes with low sensitivity to the distu
Greenhouse climate management: an optimal control approach.
Henten, van E.J.
1994-01-01
In this thesis a methodology is developed for the construction and analysis of an optimal greenhouse climate control system.In chapter 1, the results of a literature survey are presented and the research objectives are defined. In the literature, optimal greenhouse climate management systems have be
A Feedback Optimal Control Algorithm with Optimal Measurement Time Points
Directory of Open Access Journals (Sweden)
Felix Jost
2017-02-01
Full Text Available Nonlinear model predictive control has been established as a powerful methodology to provide feedback for dynamic processes over the last decades. In practice it is usually combined with parameter and state estimation techniques, which allows to cope with uncertainty on many levels. To reduce the uncertainty it has also been suggested to include optimal experimental design into the sequential process of estimation and control calculation. Most of the focus so far was on dual control approaches, i.e., on using the controls to simultaneously excite the system dynamics (learning as well as minimizing a given objective (performing. We propose a new algorithm, which sequentially solves robust optimal control, optimal experimental design, state and parameter estimation problems. Thus, we decouple the control and the experimental design problems. This has the advantages that we can analyze the impact of measurement timing (sampling independently, and is practically relevant for applications with either an ethical limitation on system excitation (e.g., chemotherapy treatment or the need for fast feedback. The algorithm shows promising results with a 36% reduction of parameter uncertainties for the Lotka-Volterra fishing benchmark example.
Optimized chaos control with simple limiters.
Wagner, C; Stoop, R
2001-01-01
We present an elementary derivation of chaos control with simple limiters using the logistic map and the Henon map as examples. This derivation provides conditions for optimal stabilization of unstable periodic orbits of a chaotic attractor.
The optimal control and its multiple applications
2009-01-01
In this work we refer to motivations, applications, and relations of control theory with other areas of mathematics. We present a brief historical review of optimal control theory, from its roots in the calculus of variations and the classical theory of control to the present time, giving particular emphasis to the Pontryagin maximum principle.
Multiple Objective Optimization and Optimal Control of Fermentation Processes
Directory of Open Access Journals (Sweden)
Mitko Petrov
2008-10-01
Full Text Available A multiple objective optimization is applied for finding an optimum policy of fed-batch processes of whey fermentation and L-lysine production. The multiple objective optimization problems are transformed to a standard problem of optimization with single objective function by a general utility function with weight coefficients for each single utility coefficient criteria. A combined algorithm is applied when solving the maximizing decision problem. The algorithm includes a method for random search of finding an initial point and a method based on the fuzzy sets theory, combined in order to find the best solution of the optimization problem. The application of the combined algorithm eliminates the main disadvantage of the used fuzzy optimization method, namely it decreases the number of discrete values of the control variables. Thus, the algorithm allows problems with larger scale to be solved. After this multiple optimization, the useful product quality rises and the residual substrate concentration at the end of the process decreases. In this way, the process productivity is increased.
Boundary control of long waves in nonlinear dispersive systems
DEFF Research Database (Denmark)
Hasan, Agus; Foss, Bjarne; Aamo, Ole Morten
2011-01-01
Unidirectional propagation of long waves in nonlinear dispersive systems may be modeled by the Benjamin-Bona-Mahony-Burgers equation, a third order partial differential equation incorporating linear dissipative and dispersive terms, as well as a term covering nonlinear wave phenomena. For higher...... orders of the nonlinearity, the equation may have unstable solitary wave solutions. Although it is a one dimensional problem, achieving a global result for this equation is not trivial due to the nonlinearity and the mixed partial derivative. In this paper, two sets of nonlinear boundary control laws...... that achieve global exponential stability and semi-global exponential stability are derived for both linear and nonlinear cases....
Optimal impulse control problems and linear programming.
Bauso, D.
2009-01-01
Optimal impulse control problems are, in general, difficult to solve. A current research goal is to isolate those problems that lead to tractable solutions. In this paper, we identify a special class of optimal impulse control problems which are easy to solve. Easy to solve means that solution algorithms are polynomial in time and therefore suitable to the on-line implementation in real-time problems. We do this by using a paradigm borrowed from the Operations Research field. As main result, ...
Neuro-optimal control of helicopter UAVs
Nodland, David; Ghosh, Arpita; Zargarzadeh, H.; Jagannathan, S.
2011-05-01
Helicopter UAVs can be extensively used for military missions as well as in civil operations, ranging from multirole combat support and search and rescue, to border surveillance and forest fire monitoring. Helicopter UAVs are underactuated nonlinear mechanical systems with correspondingly challenging controller designs. This paper presents an optimal controller design for the regulation and vertical tracking of an underactuated helicopter using an adaptive critic neural network framework. The online approximator-based controller learns the infinite-horizon continuous-time Hamilton-Jacobi-Bellman (HJB) equation and then calculates the corresponding optimal control input that minimizes the HJB equation forward-in-time. In the proposed technique, optimal regulation and vertical tracking is accomplished by a single neural network (NN) with a second NN necessary for the virtual controller. Both of the NNs are tuned online using novel weight update laws. Simulation results are included to demonstrate the effectiveness of the proposed control design in hovering applications.
The effects of redundant control inputs in optimal control
Institute of Scientific and Technical Information of China (English)
DUAN ZhiSheng; HUANG Lin; YANG Ying
2009-01-01
For a stabillzable system,the extension of the control inputs has no use for stabllizability,but it is important for optimal control.In this paper,a necessary and sufficient condition is presented to strictly decrease the quadratic optimal performance index after control input extensions.A similar result is also provided for H_2 optimal control problem.These results show an essential difference between single-input and multi-input control systems.Several examples are taken to illustrate related problems.
Hybrid optimization schemes for quantum control
Energy Technology Data Exchange (ETDEWEB)
Goerz, Michael H.; Koch, Christiane P. [Universitaet Kassel, Theoretische Physik, Kassel (Germany); Whaley, K. Birgitta [University of California, Department of Chemistry, Berkeley, CA (United States)
2015-12-15
Optimal control theory is a powerful tool for solving control problems in quantum mechanics, ranging from the control of chemical reactions to the implementation of gates in a quantum computer. Gradient-based optimization methods are able to find high fidelity controls, but require considerable numerical effort and often yield highly complex solutions. We propose here to employ a two-stage optimization scheme to significantly speed up convergence and achieve simpler controls. The control is initially parametrized using only a few free parameters, such that optimization in this pruned search space can be performed with a simplex method. The result, considered now simply as an arbitrary function on a time grid, is the starting point for further optimization with a gradient-based method that can quickly converge to high fidelities. We illustrate the success of this hybrid technique by optimizing a geometric phase gate for two superconducting transmon qubits coupled with a shared transmission line resonator, showing that a combination of Nelder-Mead simplex and Krotov's method yields considerably better results than either one of the two methods alone. (orig.)
Chemical optimization algorithm for fuzzy controller design
Astudillo, Leslie; Castillo, Oscar
2014-01-01
In this book, a novel optimization method inspired by a paradigm from nature is introduced. The chemical reactions are used as a paradigm to propose an optimization method that simulates these natural processes. The proposed algorithm is described in detail and then a set of typical complex benchmark functions is used to evaluate the performance of the algorithm. Simulation results show that the proposed optimization algorithm can outperform other methods in a set of benchmark functions. This chemical reaction optimization paradigm is also applied to solve the tracking problem for the dynamic model of a unicycle mobile robot by integrating a kinematic and a torque controller based on fuzzy logic theory. Computer simulations are presented confirming that this optimization paradigm is able to outperform other optimization techniques applied to this particular robot application
OPTIMAL OPERATIONAL CONTROL OF INTERCEPTOR SEWER SYSTEM
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
In this paper, a mathematical model was built up to solve the problem of optimal operational control by analysing the factors on an interceptor sewer system and a Fortran program was produced for this model. This paper shows that the optimal control states can be determined by working out the optimal flow rates by means of Linear Programming (LP). The result is very sensitive to interception points and the concentration weight coefficients over time. The result further highlights some practical applications for the existing sewer systems or the sewer systems under design.
Investigation on evolutionary optimization of chaos control
Energy Technology Data Exchange (ETDEWEB)
Zelinka, Ivan [Faculty of Applied Informatics, Tomas Bata University in Zli' n, Nad Stranemi 4511, 762 72 Zli' n (Czech Republic)], E-mail: zelinka@fai.utb.cz; Senkerik, Roman [Faculty of Applied Informatics, Tomas Bata University in Zli' n, Nad Stranemi 4511, 762 72 Zli' n (Czech Republic)], E-mail: senkerik@fai.utb.cz; Navratil, Eduard [Faculty of Applied Informatics, Tomas Bata University in Zli' n, Nad Stranemi 4511, 762 72 Zli' n (Czech Republic)], E-mail: enavratil@fai.utb.cz
2009-04-15
This work deals with an investigation on optimization of the feedback control of chaos based on the use of evolutionary algorithms. The main objective is to show that evolutionary algorithms are capable of optimization of chaos control. As models of deterministic chaotic systems, one-dimensional Logistic equation and two-dimensional Henon map were used. The optimizations were realized in several ways, each one for another set of parameters of evolution algorithms or separate cost functions. The evolutionary algorithm SOMA (self-organizing migrating algorithm) was used in four versions. For each version simulations were repeated several times to show and check for robustness of the applied method.
Free and moving boundaries analysis, simulation and control
Glowinski, Roland
2007-01-01
Optimal Tubes: Geodesic Metric, Euler Flow, Moving Domain J.P. Zolésio Numerical Simulation of Pattern Formation in a Rotating Suspension of Non-Brownian Settling Particles Tsorg-Whay Pan and Roland Glowinski On the Homogenization of Optimal Control Problems on Periodic Graphs P.I. Kogut and G. Leugering Lift and Sedimentation of Particles in the Flow of a Viscoelastic Liquid in a Channel G.P. Galdi and V. Heuveline Modeling and Simulation of Liquid-Gas Free Surface Flows A. Caboussat, M.
Directory of Open Access Journals (Sweden)
KOTSUR, M.
2015-05-01
Full Text Available We give a solution of optimal control problem for distributed parameter systems described by nonlinear partial differential equations with nonstandard boundary conditions. The variational method is used to obtain the general form of the necessary conditions of optimality. A suitable algorithm based on the numerical method of successive approximations has been constructed for computing the optimal control functions. The results are applied for optimization of transient thermoelectric cooling process. Optimal dependences of current on time have been calculated for thermoelectric cooler power supply with the purpose of minimizing the cooling temperature within a preset time interval.
Optimal control novel directions and applications
Aronna, Maria; Kalise, Dante
2017-01-01
Focusing on applications to science and engineering, this book presents the results of the ITN-FP7 SADCO network’s innovative research in optimization and control in the following interconnected topics: optimality conditions in optimal control, dynamic programming approaches to optimal feedback synthesis and reachability analysis, and computational developments in model predictive control. The novelty of the book resides in the fact that it has been developed by early career researchers, providing a good balance between clarity and scientific rigor. Each chapter features an introduction addressed to PhD students and some original contributions aimed at specialist researchers. Requiring only a graduate mathematical background, the book is self-contained. It will be of particular interest to graduate and advanced undergraduate students, industrial practitioners and to senior scientists wishing to update their knowledge.
OPTIMAL CONTROL FOR ELECTRIC VEHICLE STABILIZATION
Directory of Open Access Journals (Sweden)
MARIAN GAICEANU
2016-01-01
Full Text Available This main objective of the paper is to stabilize an electric vehicle in optimal manner to a step lane change maneuver. To define the mathematical model of the vehicle, the rigid body moving on a plane is taken into account. An optimal lane keeping controller delivers the adequate angles in order to stabilize the vehicle’s trajectory in an optimal way. Two degree of freedom linear bicycle model is adopted as vehicle model, consisting of lateral and yaw motion equations. The proposed control maintains the lateral stability by taking the feedback information from the vehicle transducers. In this way only the lateral vehicle’s dynamics are enough to considerate. Based on the obtained linear mathematical model the quadratic optimal control is designed in order to maintain the lateral stability of the electric vehicle. The numerical simulation results demonstrate the feasibility of the proposed solution.
Optimal control of a CSTR process
Directory of Open Access Journals (Sweden)
A. Soukkou
2008-12-01
Full Text Available Designing an effective criterion and learning algorithm for find the best structure is a major problem in the control design process. In this paper, the fuzzy optimal control methodology is applied to the design of the feedback loops of an Exothermic Continuous Stirred Tank Reactor system. The objective of design process is to find an optimal structure/gains of the Robust and Optimal Takagi Sugeno Fuzzy Controller (ROFLC. The control signal thus obtained will minimize a performance index, which is a function of the tracking/regulating errors, the quantity of the energy of the control signal applied to the system, and the number of fuzzy rules. The genetic learning is proposed for constructing the ROFLC. The chromosome genes are arranged into two parts, the binary-coded part contains the control genes and the real-coded part contains the genes parameters representing the fuzzy knowledge base. The effectiveness of this chromosome formulation enables the fuzzy sets and rules to be optimally reduced. The performances of the ROFLC are compared to these found by the traditional PD controller with Genetic Optimization (PD_GO. Simulations demonstrate that the proposed ROFLC and PD_GO has successfully met the design specifications.
Optimal Control of Active Recoil Mechanisms
1977-02-01
pressures in different chambers, rod pull are available and can be plotted. A linear state feedback control system is proposed to adapt this...desirable. A linear state feedback control system with variable gains is proposed in the report. A separate control law is designed for each...optimization algorithm to choose a feasible solution. 27 3.3 Results for M-37 Recoil Mechanism The linear state feedback control system and
Optimal control of radiator systems; Optimal reglering av radiatorsystem
Energy Technology Data Exchange (ETDEWEB)
Wollerstrand, J.; Ljunggren, P.; Johansson, P.O.
2007-07-01
This report presents results from a study aiming to considerably improve the development towards minimizing the primary return temperature from a district heating (DH) substation by optimizing the control algorithm for the space heating system. The investigation of this research field started about 20 years ago in Sweden when low flow operation of space heating systems was introduced. Following a couple of years of partly confused discussions, the method was accepted by many, but was rejected by others. Our thesis is that further improvement of cooling of DH water is possible when advanced, but robust, control algorithms are used for the space heating system. A space heating system is traditionally designed for a specific constant circulation flow combined with a suitable control curve for the space heating supply temperature as a function of the outdoor temperature. Optimal choice of the control curve varies from case to case and is an issue both we and others have dealt with in previous work. A large step was to derive theoretical control curves for optimal control of the space heating system, with an analysis of how temperature and circulation flow varies with heat load. The estimated gain varies strongly depending on the conditions, however, with realistic conditions it can be as much as 5 deg C decreased DH return temperature on yearly average. To be able to work properly under varying physical circumstances, a control algorithm must be able to combine variation of space heating supply temperature and circulation flow as a function of the heat load. By regulating the rotation speed of the circulation pump this can be achieved. Such regulation can be adjusted for each and every building by regulating a few parameters in a regulator. The results from this work are, that important theoretical knowledge has been completed, to show results systematically and to find support from practical experiments. A hands-on description of the method for optimizing DH water
Optimization problems for switched systems with impulsive control
Institute of Scientific and Technical Information of China (English)
Junhao HU; Huayou WANG; Xinzhi LIU; Bin LIU
2005-01-01
By using Impulsive Maximum Principal and three stage optimization method,this paper discusses optimization problems for linear impulsive switched systems with hybrid controls,which includes continuous control and impulsive control.The linear quadratic optimization problems without constraints such as optimal hybrid control,optimal stability and optimal switching instants are addressed in detail.These results are applicable to optimal control problems in economics,mechanics,and management.
Open-loop control of noise amplification in a separated boundary layer flow
Boujo, Edouard; Gallaire, François
2014-01-01
Linear optimal gains are computed for the subcritical two-dimensional separated boundary-layer flow past a bump. Very large optimal gain values are found, making it possible for small-amplitude noise to be strongly amplified and to destabilize the flow. The optimal forcing is located close to the summit of the bump, while the optimal response is the largest in the shear layer. The largest amplification occurs at frequencies corresponding to eigenvalues which first become unstable at higher Reynolds number. Nonlinear direct numerical simulations show that a low level of noise is indeed sufficient to trigger random flow unsteadiness, characterized here by large-scale vortex shedding. Next, a variational technique is used to compute efficiently the sensitivity of optimal gains to steady control (through source of momentum in the flow, or blowing/suction at the wall). A systematic analysis at several frequencies identifies the bump summit as the most sensitive region for control with wall actuation. Based on thes...
Institute of Scientific and Technical Information of China (English)
Min LIU; Keqi WU
2008-01-01
Based on the immersed boundary method (IBM) and the finite volume optimized pre-factored compact (FVOPC) scheme, a numerical simulation of noise propagation inside and outside the casing of a cross flow fan is estab-lished. The unsteady linearized Euler equations are solved to directly simulate the aero-acoustic field. In order to validate the FVOPC scheme, a simulation case: one dimensional linear wave propagation problem is carried out using FVOPC scheme, DRP scheme and HOC scheme. The result of FVOPC is in good agreement with the ana-lytic solution and it is better than the results of DRP and HOC schemes, the FVOPC is less dispersion and dissi-pation than DRP and HOC schemes. Then, numerical simulation of noise propagation problems is performed. The noise field of 36 compact rotating noise sources is obtained with the rotating velocity of 1000r/min. The PML absorbing boundary condition is applied to the sound far field boundary condition for depressing the numerical reflection. Wall boundary condition is applied to the casing. The results show that there are reflections on the casing wall and sound wave interference in the field. The FVOPC with the IBM is suitable for noise propagation problems under the complex geometries for depressing the dispersion and dissipation, and also keeping the high order precision.
Centralized Stochastic Optimal Control of Complex Systems
Energy Technology Data Exchange (ETDEWEB)
Malikopoulos, Andreas [ORNL
2015-01-01
In this paper we address the problem of online optimization of the supervisory power management control in parallel hybrid electric vehicles (HEVs). We model HEV operation as a controlled Markov chain using the long-run expected average cost per unit time criterion, and we show that the control policy yielding the Pareto optimal solution minimizes the average cost criterion online. The effectiveness of the proposed solution is validated through simulation and compared to the solution derived with dynamic programming using the average cost criterion.
Cyclic Control Optimization for a Smart Rotor
DEFF Research Database (Denmark)
Bergami, Leonardo; Henriksen, Lars Christian
2012-01-01
The paper presents a method to determine cyclic control trajectories for a smart rotor undergoing periodic-deterministic load variations. The control trajectories result from a constrained optimization problem, where the cost function to minimize is given by the variation of the blade root flapwise...... bending moment within a rotor revolution. The method is applied to a rotor equipped with trailing edge flaps, and capable of individual blade pitching. Results show that the optimized cyclic control significantly alleviates the load variations from periodic disturbances; the combination of both cyclic...
An example in linear quadratic optimal control
Weiss, George; Zwart, Heiko J.
1998-01-01
We construct a simple example of a quadratic optimal control problem for an infinite-dimensional linear system based on a shift semigroup. This system has an unbounded control operator. The cost is quadratic in the input and the state, and the weighting operators are bounded. Despite its extreme
An example in linear quadratic optimal control
Weiss, George; Zwart, Heiko J.
1998-01-01
We construct a simple example of a quadratic optimal control problem for an infinite-dimensional linear system based on a shift semigroup. This system has an unbounded control operator. The cost is quadratic in the input and the state, and the weighting operators are bounded. Despite its extreme sim
Micro vortex generator control of axisymmetric high-speed laminar boundary layer separation
Estruch-Samper, D.; Vanstone, L.; Hillier, R.; Ganapathisubramani, B.
2015-09-01
Interest in the development of micro vortex generators (MVGs) to control high-speed flow separation has grown in the last decade. In contrast to conventional vortex generators, MVGs are fully submerged in the boundary layer and have the potential of inducing surface flow mixing with marginal drag penalty when suitably designed. Also, they do not result in undesired reduced mass flow such as with suction methods. The flow mechanisms at the location of MVGs are not yet fully understood, and optimal designs are difficult to establish given that both numerical predictions and experiments are particularly challenged for short element heights, yet optimal MVGs are generally expected to be at least shorter than half the local boundary layer thickness. The present work aims at investigating experimentally the fundamental flow physics concerning an individual MVG element (of `canonical' or simplified geometry) at a range of near-wall heights. A fully laminar base flow is considered so as to isolate the effect of incoming turbulence as well as the more complex physics that may occur when specific and/or multiple elements are used. Tests were performed in a gun tunnel at a freestream Mach number of 8.9 and Reynolds number of /m, and the basic test model consisted of a blunt-nosed cylinder which produced an axisymmetric laminar boundary layer with an edge Mach number of 3.4 and Reynolds number of /m at the MVG location. A laminar shock-wave/boundary layer interaction with separation was induced by a flare located further downstream on the model. Measurements consisted of time-resolved surface heat transfer obtained in the axial direction immediately downstream of the MVG and along the interaction, together with simultaneous high-speed schlieren imaging. The height () of the MVG element used in a `diamond' configuration (square planform with one vertex facing the flow) was adjusted between tests ranging from = 0.03 to 0.58, where the local undisturbed boundary layer thickness
Energy Technology Data Exchange (ETDEWEB)
Kokawa, Hiroyuki; Shimada, Masayuki; Wang, Zhan Jie; Sato, Yutaka S. [Tohoku Univ., School of Engineering, Sendai, Miyagi (Japan); Sato, Yoshihiro [Osaka City Univ., Graduate School of Engineering, Osaka (Japan); Kiuchi, Kiyoshi [Japan Atomic Energy Research Inst., Tokai, Ibaraki (Japan). Tokai Research Establishment
2003-03-01
Grain boundary structure control of type 304 austenitic stainless steel and nickel base Inconel Alloy 600 used in reactor pipe materials was studied to inhibit intergranular corrosion (IGC) due to sensitization. A transmission electron microscopic study showed that low-energy grain boundaries, such as coincidence site lattice boundaries are highly resistant to sensitization, i.e., to intergranular precipitation, chromium depletion and corrosion, compared with ordinary high-angle (random) boundaries. A thermo-mechanical treatment was tried to control grain boundary structure of type 304 austenitic stainless steel for producing a highly intergranular corrosion-resistant material. The effects of process parameters in thermo-mechanical treatment such as pre-strain, annealing temperature, time, etc., on grain boundary characteristics and IGC resistance corrosion of type 304 austenitic stainless steels were examined. The excellent IGC resistance was obtained by slight pre-strain annealing at a relatively low temperature due to the optimized grain boundary character distribution. The uniform distribution of a high frequency of coincidence site lattice boundaries and consequent discontinuity of random boundary network were observed in the material. The optimum distribution can be formed by introducing low energy segments on migrating random boundaries during twin emission and boundary-boundary reactions in the grain growth without additional generation of random boundaries. (author)
Computational Methods for Design, Control and Optimization
2007-10-01
34scenario" that applies to channel flows ( Poiseuille flows , Couette flow ) and pipe flows . Over the past 75 years many complex "transition theories" have...other areas of flow control, optimization and aerodynamic design. approximate sensitivity calculations and optimization codes. The effort was built on a...for fluid flow problems. The improved robustness and computational efficiency of this approach makes it practical for a wide class of problems. The
Directory of Open Access Journals (Sweden)
Juan Carlos Ceballos V.
2005-10-01
Full Text Available The exact boundary controllability of the higher order nonlinear Schrodinger equation with constant coefficients on a bounded domain with various boundary conditions is studied. We derive the exact boundary controllability for this equation for sufficiently small initial and final states.
An Optimal Control of Bone Marrow in Cancer Chemotherapy by Artificial Neural Networks
Directory of Open Access Journals (Sweden)
H. Hosseinipour
2015-09-01
Full Text Available Although neural network models for cancer chemotherapy have been analyzed since the early seventies, less research has been done in actually formulating them as optimal control problems. In this paper an artificial neural networks-based method for optimal control of bone marrow in cell-cycle-specific chemotherapy is proposed. In this method, we use artificial neural networks for approximating the optimal control problem which maximizes both bone marrow mass and drug`s dose at the same time. The corresponding model be transfer to Hamiltonian function and using Pontryagin principle we create the boundary conditions. After defining boundary conditions, we use the approximating property of artificial networks and put the boundary conditions in error functions to satisfy the limitations..
Institute of Scientific and Technical Information of China (English)
李玉芳; 周丽丽
2012-01-01
According to the characteristics of pure EV power system, an optimization design method of brake force control algorithm of electro-hydraulic composite brake system with multi - boundary conditions was proposed. And based on the analysis of boundary conditions, including the braking strength requirements, ECE regulations, and motor/battery characteristics etc, a reasonable range of brake force distribution ratio was achieved. And braking force distribution approach between the front and rear axles was brought out by considering such factors as the braking strength of demand and using frequency of the various adhesion coefficient roads. And the simulation analysis verifies the rationality and effectiveness of the brake force distribution algorithm.%根据纯电动汽车动力系统的特点,提出电—液复合制动系统控制算法的多边界条件优化设计方法.基于对制动强度需求、ECE法规和电机/蓄电池特性等多边界条件的分析,得出制动力分配比例的合理取值范围,以此为基础,提出根据制动强度需求和不同附着系数路面的使用频率等因素确定前后轴制动力分配系数的方法.仿真分析验证了制动力分配算法的有效性和合理性.
Ma, Xu; Arce, Gonzalo R
2009-07-01
Recently, a set of generalized gradient-based optical proximity correction (OPC) optimization methods have been developed to solve for the forward and inverse lithography problems under the thin-mask assumption, where the mask is considered a thin 2D object. However, as the critical dimension printed on the wafer shrinks into the subwavelength regime, thick-mask effects become prevalent, and thus these effects must be taken into account in OPC optimization methods. OPC methods derived under the thin-mask assumption have inherent limitations and perform poorly in the subwavelength regime. This paper focuses on developing model-based forward binary mask optimization methods that account for the thick-mask effects of coherent imaging systems. The boundary layer (BL) model is exploited to simplify and characterize the thick-mask effects, leading to a model-based OPC method. The BL model is simpler than other thick-mask models, treating the near field of the mask as the superposition of the interior transmission areas and the boundary layers. The advantages and limitations of the proposed algorithm are discussed, and several illustrative simulations are presented.
Binary mask optimization for forward lithography based on boundary layer model in coherent systems
Ma, Xu; Arce, Gonzalo R.
2010-04-01
Recently, a set of generalized gradient-based optical proximity correction (OPC) optimization methods have been developed to solve for the forward and inverse lithography problem under the thin-mask assumption, where the mask is considered a thin 2-D object. However, as the critical dimension printed on the wafer shrinks into the subwavelength regime, thick-mask effects become prevalent and thus these effects must be taken into account in OPC optimization methods. OPC methods derived under the thin-mask assumption have inherent limitations and perform poorly in the subwavelength scenario. This paper focuses on developing model-based forward binary mask optimization methods which account for the thick-mask effects of coherent imaging systems. The boundary layer (BL) model is exploited to simplify and characterize the thick-mask effects, leading to a computationally efficient OPC method. The BL model is simpler than other thick-mask models, treating the near field of the mask as the superposition of the interior transmission areas and the boundary layers. The advantages and limitations of the proposed algorithm are discussed and several illustrative simulations are presented.
FEEDBACK CONTROL OPTIMIZATION FOR SEISMICALLY EXCITED BUILDINGS
Institute of Scientific and Technical Information of China (English)
Xueping Li; Zuguang Ying
2007-01-01
A feedback control optimization method of partially observable linear structures via stationary response is proposed and analyzed with linear building structures equipped with control devices and sensors. First, the partially observable control problem of the structure under horizontal ground acceleration excitation is converted into a completely observable control problem. Then the It(o) stochastic differential equations of the system are derived based on the stochastic averaging method for quasi-integrable Hamiltonian systems and the stationary solution to the Fokker-Plank-Kolmogorov (FPK) equation associated with the It(o) equations is obtained.The performance index in terms of the mean system energy and mean square control force is established and the optimal control force is obtained by minimizing the performance index. Finally, the numerical results for a three-story building structure model under El Centro, Hachinohe,Northridge and Kobe earthquake excitations are given to illustrate the application and the effectiveness of the proposed method.
Directory of Open Access Journals (Sweden)
Haibo Chen
2013-01-01
Full Text Available Based on an internal tidal model, the practical performances of the limited-memory BFGS (L-BFGS method and two gradient descent (GD methods (the normal one with Wolfe’s line search and the simplified one are investigated computationally through a series of ideal experiments in which the open boundary conditions (OBCs are inverted by assimilating the interior observations with the adjoint method. In the case that the observations closer to the unknown boundary are included for assimilation, the L-BFGS method performs the best. As compared with the simplified GD method, the normal one really uses less iteration to reach a satisfactory solution, but its advantage over the simplified one is much smaller than expected. In the case that only the observations that are further from the unknown boundary are assimilated, the simplified GD method performs the best instead, whereas the performances of the other two methods are not satisfactory. The advanced L-BFGS algorithm and Wolfe’s line search still need to be improved when applied to the practical cases. The simplified GD method, which is controllable and easy to implement, should be regarded seriously as a choice, especially when the classical advanced optimization techniques fail or perform poorly.
Optimal control applications in electric power systems
Christensen, G S; Soliman, S A
1987-01-01
Significant advances in the field of optimal control have been made over the past few decades. These advances have been well documented in numerous fine publications, and have motivated a number of innovations in electric power system engineering, but they have not yet been collected in book form. Our purpose in writing this book is to provide a description of some of the applications of optimal control techniques to practical power system problems. The book is designed for advanced undergraduate courses in electric power systems, as well as graduate courses in electrical engineering, applied mathematics, and industrial engineering. It is also intended as a self-study aid for practicing personnel involved in the planning and operation of electric power systems for utilities, manufacturers, and consulting and government regulatory agencies. The book consists of seven chapters. It begins with an introductory chapter that briefly reviews the history of optimal control and its power system applications and also p...
2016 Network Games, Control, and Optimization Conference
Jimenez, Tania; Solan, Eilon
2017-01-01
This contributed volume offers a collection of papers presented at the 2016 Network Games, Control, and Optimization conference (NETGCOOP), held at the University of Avignon in France, November 23-25, 2016. These papers highlight the increasing importance of network control and optimization in many networking application domains, such as mobile and fixed access networks, computer networks, social networks, transportation networks, and, more recently, electricity grids and biological networks. Covering a wide variety of both theoretical and applied topics in the areas listed above, the authors explore several conceptual and algorithmic tools that are needed for efficient and robust control operation, performance optimization, and better understanding the relationships between entities that may be acting cooperatively or selfishly in uncertain and possibly adversarial environments. As such, this volume will be of interest to applied mathematicians, computer scientists, engineers, and researchers in other relate...
Stochastic Optimal Control Models for Online Stores
Bradonjić, Milan
2011-01-01
We present a model for the optimal design of an online auction/store by a seller. The framework we use is a stochastic optimal control problem. In our setting, the seller wishes to maximize her average wealth level, where she can control her price per unit via her reputation level. The corresponding Hamilton-Jacobi-Bellmann equation is analyzed for an introductory case. We then turn to an empirically justified model, and present introductory analysis. In both cases, {\\em pulsing} advertising strategies are recovered for resource allocation. Further numerical and functional analysis will appear shortly.
Active control of panel vibrations induced by boundary-layer flow
Chow, Pao-Liu
1991-01-01
Some problems in active control of panel vibration excited by a boundary layer flow over a flat plate are studied. In the first phase of the study, the optimal control problem of vibrating elastic panel induced by a fluid dynamical loading was studied. For a simply supported rectangular plate, the vibration control problem can be analyzed by a modal analysis. The control objective is to minimize the total cost functional, which is the sum of a vibrational energy and the control cost. By means of the modal expansion, the dynamical equation for the plate and the cost functional are reduced to a system of ordinary differential equations and the cost functions for the modes. For the linear elastic plate, the modes become uncoupled. The control of each modal amplitude reduces to the so-called linear regulator problem in control theory. Such problems can then be solved by the method of adjoint state. The optimality system of equations was solved numerically by a shooting method. The results are summarized.
Optimal control application to an Ebola model
Institute of Scientific and Technical Information of China (English)
Ebenezer Bonyah; Kingsley Badu; Samuel Kwesi Asiedu-Addo
2016-01-01
Ebola virus is a severe,frequently fatal illness,with a case fatality rate up to 90%.The outbreak of the disease has been acknowledged by World Health Organization as Public Health Emergency of International Concern.The threat of Ebola in West Africa is still a major setback to the socioeconomic development.Optimal control theory is applied to a system of ordinary differential equations which is modeling Ebola infection through three different routes including contact between humans and a dead body.In an attempt to reduce infection in susceptible population,a preventive control is put in the form of education and campaign and two treatment controls are applied to infected and late-stage infected(super) human population.The Pontryagins maximum principle is employed to characterize optimality control,which is then solved numerically.It is observed that time optimal control is existed in the model.The activation of each control showed a positive reduction of infection.The overall effect of activation of all the controls simultaneously reduced the effort required for the reduction of the infection quickly.The obtained results present a good framework for planning and designing cost-effective strategies for good interventions in dealing with Ebola disease.It is established that in order to reduce Ebola threat all the three controls must be taken into consideration concurrently.
OPTIMAL CONTROL ALGORITHMS FOR SECOND ORDER SYSTEMS
Directory of Open Access Journals (Sweden)
Danilo Pelusi
2013-01-01
Full Text Available Proportional Integral Derivative (PID controllers are widely used in industrial processes for their simplicity and robustness. The main application problems are the tuning of PID parameters to obtain good settling time, rise time and overshoot. The challenge is to improve the timing parameters to achieve optimal control performances. Remarkable findings are obtained through the use of Artificial Intelligence techniques as Fuzzy Logic, Genetic Algorithms and Neural Networks. The combination of these theories can give good results in terms of settling time, rise time and overshoot. In this study, suitable controllers able of improving timing performance of second order plants are proposed. The results show that the PID controller has good overshoot values and shows optimal robustness. The genetic-fuzzy controller gives a good value of settling time and a very good overshoot value. The neural-fuzzy controller gives the best timing parameters improving the control performances of the others two approaches. Further improvements are achieved designing a real-time optimization algorithm which works on a genetic-neuro-fuzzy controller.
MAXIMUM PRINCIPLE FOR THE OPTIMAL CONTROL OF AN ABLATION-TRANSPIRATION COOLING SYSTEM
Institute of Scientific and Technical Information of China (English)
SUN Bing; GUO Baozhu
2005-01-01
This paper is concerned with an optimal control problem of an ablationtranspiration cooling control system with Stefan-Signorini boundary condition. The existence of weak solution of the system is considered. The Dubovitskii and Milyutin approach is adopted in the investigation of the Pontryagin's maximum principle of the system. The optimality necessary condition is presented for the problem with fixed final horizon and phase constraints.
Optimal Control of Transient Flow in Natural Gas Networks
Zlotnik, Anatoly; Backhaus, Scott
2015-01-01
We outline a new control system model for the distributed dynamics of compressible gas flow through large-scale pipeline networks with time-varying injections, withdrawals, and control actions of compressors and regulators. The gas dynamics PDE equations over the pipelines, together with boundary conditions at junctions, are reduced using lumped elements to a sparse nonlinear ODE system expressed in vector-matrix form using graph theoretic notation. This system, which we call the reduced network flow (RNF) model, is a consistent discretization of the PDE equations for gas flow. The RNF forms the dynamic constraints for optimal control problems for pipeline systems with known time-varying withdrawals and injections and gas pressure limits throughout the network. The objectives include economic transient compression (ETC) and minimum load shedding (MLS), which involve minimizing compression costs or, if that is infeasible, minimizing the unfulfilled deliveries, respectively. These continuous functional optimiza...
Boundary Control of Linear Uncertain 1-D Parabolic PDE Using Approximate Dynamic Programming.
Talaei, Behzad; Jagannathan, Sarangapani; Singler, John
2017-03-02
This paper develops a near optimal boundary control method for distributed parameter systems governed by uncertain linear 1-D parabolic partial differential equations (PDE) by using approximate dynamic programming. A quadratic surface integral is proposed to express the optimal cost functional for the infinite-dimensional state space. Accordingly, the Hamilton-Jacobi-Bellman (HJB) equation is formulated in the infinite-dimensional domain without using any model reduction. Subsequently, a neural network identifier is developed to estimate the unknown spatially varying coefficient in PDE dynamics. Novel tuning law is proposed to guarantee the boundedness of identifier approximation error in the PDE domain. A radial basis network (RBN) is subsequently proposed to generate an approximate solution for the optimal surface kernel function online. The tuning law for near optimal RBN weights is created, such that the HJB equation error is minimized while the dynamics are identified and closed-loop system remains stable. Ultimate boundedness (UB) of the closed-loop system is verified by using the Lyapunov theory. The performance of the proposed controller is successfully confirmed by simulation on an unstable diffusion-reaction process.
Directory of Open Access Journals (Sweden)
Alireza Khosravi
2012-03-01
Full Text Available This paper deals with the design of optimal backstepping controller, by using the chaotic particle swarm optimization (CPSO algorithm to control of chaos in Lure like chaotic system. The backstepping method consists of parameters which could have positive values. The parameters are usually chosen optional by trial and error method. The controlled system provides different behaviors for different values of the parameters. It is necessary to select proper parameters to obtain a good response, because the improper selection of the parameters leads to inappropriate responses or even may lead to instability of the system. The proposed optimal backstepping controller without trial and error determines the parameters of backstepping controller automatically and intelligently by minimizing the Integral of Time multiplied Absolute Error (ITAE and squared controller output. Finally, the efficiency of the proposed optimal backstepping controller (OBSC is illustrated by implementing the method on the Lure like chaotic system.
Optimal Investment Control of Macroeconomic Systems
Institute of Scientific and Technical Information of China (English)
ZHAO Ke-jie; LIU Chuan-zhe
2006-01-01
Economic growth is always accompanied by economic fluctuation. The target of macroeconomic control is to keep a basic balance of economic growth, accelerate the optimization of economic structures and to lead a rapid, sustainable and healthy development of national economies, in order to propel society forward. In order to realize the above goal, investment control must be regarded as the most important policy for economic stability. Readjustment and control of investment includes not only control of aggregate investment, but also structural control which depends on economic-technology relationships between various industries of a national economy. On the basis of the theory of a generalized system, an optimal investment control model for government has been developed. In order to provide a scientific basis for government to formulate a macroeconomic control policy, the model investigates the balance of total supply and aggregate demand through an adjustment in investment decisions realizes a sustainable and stable growth of the national economy. The optimal investment decision function proposed by this study has a unique and specific expression, high regulating precision and computable characteristics.
Optimal control of anthracnose using mixed strategies.
Fotsa Mbogne, David Jaures; Thron, Christopher
2015-11-01
In this paper we propose and study a spatial diffusion model for the control of anthracnose disease in a bounded domain. The model is a generalization of the one previously developed in [15]. We use the model to simulate two different types of control strategies against anthracnose disease. Strategies that employ chemical fungicides are modeled using a continuous control function; while strategies that rely on cultivational practices (such as pruning and removal of mummified fruits) are modeled with a control function which is discrete in time (though not in space). For comparative purposes, we perform our analyses for a spatially-averaged model as well as the space-dependent diffusion model. Under weak smoothness conditions on parameters we demonstrate the well-posedness of both models by verifying existence and uniqueness of the solution for the growth inhibition rate for given initial conditions. We also show that the set [0, 1] is positively invariant. We first study control by impulsive strategies, then analyze the simultaneous use of mixed continuous and pulse strategies. In each case we specify a cost functional to be minimized, and we demonstrate the existence of optimal control strategies. In the case of pulse-only strategies, we provide explicit algorithms for finding the optimal control strategies for both the spatially-averaged model and the space-dependent model. We verify the algorithms for both models via simulation, and discuss properties of the optimal solutions. Copyright © 2015 Elsevier Inc. All rights reserved.
Optimal Control Design with Limited Model Information
Farokhi, F; Johansson, K H
2011-01-01
We introduce the family of limited model information control design methods, which construct controllers by accessing the plant's model in a constrained way, according to a given design graph. We investigate the achievable closed-loop performance of discrete-time linear time-invariant plants under a separable quadratic cost performance measure with structured static state-feedback controllers. We find the optimal control design strategy (in terms of the competitive ratio and domination metrics) when the control designer has access to the local model information and the global interconnection structure of the plant-to-be-controlled. At last, we study the trade-off between the amount of model information exploited by a control design method and the best closed-loop performance (in terms of the competitive ratio) of controllers it can produce.
Optimally Controlled Flexible Fuel Powertrain System
Energy Technology Data Exchange (ETDEWEB)
Hakan Yilmaz; Mark Christie; Anna Stefanopoulou
2010-12-31
The primary objective of this project was to develop a true Flex Fuel Vehicle capable of running on any blend of ethanol from 0 to 85% with reduced penalty in usable vehicle range. A research and development program, targeting 10% improvement in fuel economy using a direct injection (DI) turbocharged spark ignition engine was conducted. In this project a gasoline-optimized high-technology engine was considered and the hardware and configuration modifications were defined for the engine, fueling system, and air path. Combined with a novel engine control strategy, control software, and calibration this resulted in a highly efficient and clean FFV concept. It was also intended to develop robust detection schemes of the ethanol content in the fuel integrated with adaptive control algorithms for optimized turbocharged direct injection engine combustion. The approach relies heavily on software-based adaptation and optimization striving for minimal modifications to the gasoline-optimized engine hardware system. Our ultimate objective was to develop a compact control methodology that takes advantage of any ethanol-based fuel mixture and not compromise the engine performance under gasoline operation.
An asymptotically optimal nonparametric adaptive controller
Institute of Scientific and Technical Information of China (English)
郭雷; 谢亮亮
2000-01-01
For discrete-time nonlinear stochastic systems with unknown nonparametric structure, a kernel estimation-based nonparametric adaptive controller is constructed based on truncated certainty equivalence principle. Global stability and asymptotic optimality of the closed-loop systems are established without resorting to any external excitations.
On Optimal Control of a Brownian Motion.
1982-06-01
barriers. Puterman [9] uses diffusion processes to model production and inventory processes. In both cases they assume the existence of a stationary... Puterman , A diffusion model for a storage system, Logistic, M. Geisler ed., North-Holland 197S. [101 J. Rath, The optimal policy for a controlled
Optimizing discrete control systems with phase limitations
Energy Technology Data Exchange (ETDEWEB)
Shakhverdian, S.B.; Abramian, A.K.
1981-01-01
A new method is proposed for solving discrete problems of optimizing control systems with limitations on the phase coordinates. Results are given from experimental research which demonstrate the need to introduce tangential limitations independent of the method of accounting for the phase limitations.
Efficient evolutionary algorithms for optimal control
López Cruz, I.L.
2002-01-01
If optimal control problems are solved by means of gradient based local search methods, convergence to local solutions is likely. Recently, there has been an increasing interest in the use
Determination of optimal gains for constrained controllers
Energy Technology Data Exchange (ETDEWEB)
Kwan, C.M.; Mestha, L.K.
1993-08-01
In this report, we consider the determination of optimal gains, with respect to a certain performance index, for state feedback controllers where some elements in the gain matrix are constrained to be zero. Two iterative schemes for systematically finding the constrained gain matrix are presented. An example is included to demonstrate the procedures.
Optimization-based controller design for rotorcraft
Tsing, N.-K.; Fan, M. K. H.; Barlow, J.; Tits, A. L.; Tischler, M. B.
1993-01-01
An optimization-based methodology for linear control system design is outlined by considering the design of a controller for a UH-60 rotorcraft in hover. A wide range of design specifications is taken into account: internal stability, decoupling between longitudinal and lateral motions, handling qualities, and rejection of windgusts. These specifications are investigated while taking into account physical limitations in the swashplate displacements and rates of displacement. The methodology crucially relies on user-machine interaction for tradeoff exploration.
Asymptotic stability for a class of boundary control systems with non-linear damping
Zwart, Heiko J.; Ramirez, Hector; Le Gorrec, Yann
2016-01-01
The asymptotic stability of boundary controlled port-Hamiltonian systems defined on a 1D spatial domain interconnected to a class of non-linear boundary damping is addressed. It is shown that if the port-Hamiltonian system is approximately observable, then any boundary damping which behaves linear
Asymptotic stability for a class of boundary control systems with non-linear damping
Zwart, Heiko J.; Ramirez, Hector; Le Gorrec, Yann
2016-01-01
The asymptotic stability of boundary controlled port-Hamiltonian systems defined on a 1D spatial domain interconnected to a class of non-linear boundary damping is addressed. It is shown that if the port-Hamiltonian system is approximately observable, then any boundary damping which behaves linear for small velocities asymptotically stabilizes the system.
Helicopter trajectory planning using optimal control theory
Menon, P. K. A.; Cheng, V. H. L.; Kim, E.
1988-01-01
A methodology for optimal trajectory planning, useful in the nap-of-the-earth guidance of helicopters, is presented. This approach uses an adjoint-control transformation along with a one-dimensional search scheme for generating the optimal trajectories. In addition to being useful for helicopter nap-of-the-earth guidance, the trajectory planning solution is of interest in several other contexts, such as robotic vehicle guidance and terrain-following guidance for cruise missiles and aircraft. A distinguishing feature of the present research is that the terrain constraint and the threat envelopes are incorporated in the equations of motion. Second-order necessary conditions are examined.
Optimization for efficient structure-control systems
Oz, Hayrani; Khot, Narendra S.
1993-01-01
The efficiency of a structure-control system is a nondimensional parameter which indicates the fraction of the total control power expended usefully in controlling a finite-dimensional system. The balance of control power is wasted on the truncated dynamics serving no useful purpose towards the control objectives. Recently, it has been demonstrated that the concept of efficiency can be used to address a number of control issues encountered in the control of dynamic systems such as the spillover effects, selection of a good input configuration and obtaining reduced order control models. Reference (1) introduced the concept and presented analyses of several Linear Quadratic Regulator designs on the basis of their efficiencies. Encouraged by the results of Ref. (1), Ref. (2) introduces an efficiency modal analysis of a structure-control system which gives an internal characterization of the controller design and establishes the link between the control design and the initial disturbances to affect efficient structure-control system designs. The efficiency modal analysis leads to identification of principal controller directions (or controller modes) distinct from the structural natural modes. Thus ultimately, many issues of the structure-control system revolve around the idea of insuring compatibility of the structural modes and the controller modes with each other, the better the match the higher the efficiency. A key feature in controlling a reduced order model of a high dimensional (or infinity-dimensional distributed parameter system) structural dynamic system must be to achieve high efficiency of the control system while satisfying the control objectives and/or constraints. Formally, this can be achieved by designing the control system and structural parameters simultaneously within an optimization framework. The subject of this paper is to present such a design procedure.
Optimal control of vibrational transitions of HCl
Indian Academy of Sciences (India)
KRISHNA REDDY NANDIPATI; ARUN KUMAR KANAKATI
2016-10-01
Control of fundamental and overtone transitions of a vibration are studied for the diatomic molecule, HCl. Specifically, the results of the effect of variation of the penalty factor on the physical attributes of the system (i.e., probabilities) and pulse (i.e., amplitudes) considering three different pulse durations for each value of the penalty factor are shown and discussed. We have employed the optimal control theory to obtain infrared pulses for selective vibrational transitions. The optimization of initial guess field with Gaussian envelope, phrased as maximization of cost functional, is done using the conjugate gradient method. The interaction of the field with the molecule is treated within the semiclassical dipole approximation. The potential and the dipole moment functions used in the calculations of control dynamics are obtained from high level ab-initio calculations.
Recent developments in cooperative control and optimization
Murphey, Robert; Pardalos, Panos
2004-01-01
Over the past several years, cooperative control and optimization has un questionably been established as one of the most important areas of research in the military sciences. Even so, cooperative control and optimization tran scends the military in its scope -having become quite relevant to a broad class of systems with many exciting, commercial, applications. One reason for all the excitement is that research has been so incredibly diverse -spanning many scientific and engineering disciplines. This latest volume in the Cooperative Systems book series clearly illustrates this trend towards diversity and creative thought. And no wonder, cooperative systems are among the hardest systems control science has endeavored to study, hence creative approaches to model ing, analysis, and synthesis are a must! The definition of cooperation itself is a slippery issue. As you will see in this and previous volumes, cooperation has been cast into many different roles and therefore has assumed many diverse meanings. P...
Maximum process problems in optimal control theory
Directory of Open Access Journals (Sweden)
Goran Peskir
2005-01-01
Full Text Available Given a standard Brownian motion (Btt≥0 and the equation of motion dXt=vtdt+2dBt, we set St=max0≤s≤tXs and consider the optimal control problem supvE(Sτ−Cτ, where c>0 and the supremum is taken over all admissible controls v satisfying vt∈[μ0,μ1] for all t up to τ=inf{t>0|Xt∉(ℓ0,ℓ1} with μ0g∗(St, where s↦g∗(s is a switching curve that is determined explicitly (as the unique solution to a nonlinear differential equation. The solution found demonstrates that the problem formulations based on a maximum functional can be successfully included in optimal control theory (calculus of variations in addition to the classic problem formulations due to Lagrange, Mayer, and Bolza.
On the Optimal Controller for LTV Measurement Feedback Control Problem
Institute of Scientific and Technical Information of China (English)
Ting GONG; Yu Feng LU
2011-01-01
In this paper, we consider the measurement feedback control problem for discrete linear time-varying systems within the framework of nest algebra consisting of causal and bounded linear operators. Based on the inner-outer factorization of operators, we reduce the control problem to a distance from a certain operator to a special subspace of a nest algebra and show the existence of the optimal LTV controller in two different ways: one via the characteristic of the subspace in question directly, the other via the duality theory. The latter also gives a new formula for computing the optimal cost.
Optimization Algorithms for Nuclear Reactor Power Control
Energy Technology Data Exchange (ETDEWEB)
Kim, Yeong Min; Oh, Won Jong; Oh, Seung Jin; Chun, Won Gee; Lee, Yoon Joon [Jeju National University, Jeju (Korea, Republic of)
2010-10-15
One of the control techniques that could replace the present conventional PID controllers in nuclear plants is the linear quadratic regulator (LQR) method. The most attractive feature of the LQR method is that it can provide the systematic environments for the control design. However, the LQR approach heavily depends on the selection of cost function and the determination of the suitable weighting matrices of cost function is not an easy task, particularly when the system order is high. The purpose of this paper is to develop an efficient and reliable algorithm that could optimize the weighting matrices of the LQR system
Robust Structured Control Design via LMI Optimization
DEFF Research Database (Denmark)
Adegas, Fabiano Daher; Stoustrup, Jakob
2011-01-01
This paper presents a new procedure for discrete-time robust structured control design. Parameter-dependent nonconvex conditions for stabilizable and induced L2-norm performance controllers are solved by an iterative linear matrix inequalities (LMI) optimization. A wide class of controller...... structures including decentralized of any order, ﬁxed-order dynamic output feedback, static output feedback can be designed robust to polytopic uncertainties. Stability is proven by a parameter-dependent Lyapunov function. Numerical examples on robust stability margins shows that the proposed procedure can...
Optimal coordinated voltage control of power systems
Institute of Scientific and Technical Information of China (English)
LI Yan-jun; HILL David J.; WU Tie-jun
2006-01-01
An immune algorithm solution is proposed in this paper to deal with the problem of optimal coordination of local physically based controllers in order to preserve or retain mid and long term voltage stability. This problem is in fact a global coordination control problem which involves not only sequencing and timing different control devices but also tuning the parameters of controllers. A multi-stage coordinated control scheme is presented, aiming at retaining good voltage levels with minimal control efforts and costs after severe disturbances in power systems. A self-pattern-recognized vaccination procedure is developed to transfer effective heuristic information into the new generation of solution candidates to speed up the convergence of the search procedure to global optima. An example of four bus power system case study is investigated to show the effectiveness and efficiency of the proposed algorithm, compared with several existing approaches such as differential dynamic programming and tree-search.
Aerodynamic shape optimization using control theory
Reuther, James
1996-01-01
Aerodynamic shape design has long persisted as a difficult scientific challenge due its highly nonlinear flow physics and daunting geometric complexity. However, with the emergence of Computational Fluid Dynamics (CFD) it has become possible to make accurate predictions of flows which are not dominated by viscous effects. It is thus worthwhile to explore the extension of CFD methods for flow analysis to the treatment of aerodynamic shape design. Two new aerodynamic shape design methods are developed which combine existing CFD technology, optimal control theory, and numerical optimization techniques. Flow analysis methods for the potential flow equation and the Euler equations form the basis of the two respective design methods. In each case, optimal control theory is used to derive the adjoint differential equations, the solution of which provides the necessary gradient information to a numerical optimization method much more efficiently then by conventional finite differencing. Each technique uses a quasi-Newton numerical optimization algorithm to drive an aerodynamic objective function toward a minimum. An analytic grid perturbation method is developed to modify body fitted meshes to accommodate shape changes during the design process. Both Hicks-Henne perturbation functions and B-spline control points are explored as suitable design variables. The new methods prove to be computationally efficient and robust, and can be used for practical airfoil design including geometric and aerodynamic constraints. Objective functions are chosen to allow both inverse design to a target pressure distribution and wave drag minimization. Several design cases are presented for each method illustrating its practicality and efficiency. These include non-lifting and lifting airfoils operating at both subsonic and transonic conditions.
Optimal PID Controller Design Based on PSO-RBFNN for Wind Turbine Systems
Directory of Open Access Journals (Sweden)
Jau-Woei Perng
2014-01-01
Full Text Available A strategy was proposed to determine the optimal operating point for the proportional-integral-derivative (PID controller of a wind turbine, and identify the stability regions in the parameter space. The proposed approach combined particle swarm optimization (PSO and radial basis function neural network (RBFNN algorithms. These intelligent algorithms are artificial learning mechanisms that can determine the optimal operating points, and were used to generate the function representing the most favorable operating parameters from each parameter of for the stability region of the PID controller. A graphical method was used to determine the 2D or 3D vision boundaries of the PID-type controller space in closed-loop wind turbine systems. The proposed techniques were demonstrated using simulations of a drive train model without time delay and a pitch control model with time delay. Finally, the 3D stability boundaries were determined the proposed graphical approach with and without time delay systems.
Modeling and optimal vibration control of conical shell with piezoelectric actuators
Institute of Scientific and Technical Information of China (English)
Wang Weiyuan; Wei Yingjie; Wang Cong; Zou Zhenzhu
2008-01-01
In this paper numerical simulations of active vibration control for conical shell structure with distributed piezoelectric actuators is presented. The dynamic equations of conical shell structure are derived using the finite element model (FEM) based on Mindlin's plate theory. The results of modal calculations with FEM model are accurate enough for engineering applications in comparison with experiment results. The Electromechanical influence of distributed piezoelectric actuators is treated as a boundary condition for estimating the control force. The independent modal space control (IMSC) method is adopted and the optimal linear quadratic state feedback control is implemented so that the best control performance with the least control cost can be achieved. Optimal control effects are compared with controlled responses with other non-optimal control parameters. Numerical simulation results are given to demonstrate the effectiveness of the control scheme.
Linear systems optimal and robust control
Sinha, Alok
2007-01-01
Introduction Overview Contents of the Book State Space Description of a Linear System Transfer Function of a Single Input/Single Output (SISO) System State Space Realizations of a SISO System SISO Transfer Function from a State Space Realization Solution of State Space Equations Observability and Controllability of a SISO System Some Important Similarity Transformations Simultaneous Controllability and Observability Multiinput/Multioutput (MIMO) Systems State Space Realizations of a Transfer Function Matrix Controllability and Observability of a MIMO System Matrix-Fraction Description (MFD) MFD of a Transfer Function Matrix for the Minimal Order of a State Space Realization Controller Form Realization from a Right MFD Poles and Zeros of a MIMO Transfer Function Matrix Stability Analysis State Feedback Control and Optimization State Variable Feedback for a Single Input System Computation of State Feedback Gain Matrix for a Multiinput System State Feedback Gain Matrix for a Multi...
Iterative learning control an optimization paradigm
Owens, David H
2016-01-01
This book develops a coherent theoretical approach to algorithm design for iterative learning control based on the use of optimization concepts. Concentrating initially on linear, discrete-time systems, the author gives the reader access to theories based on either signal or parameter optimization. Although the two approaches are shown to be related in a formal mathematical sense, the text presents them separately because their relevant algorithm design issues are distinct and give rise to different performance capabilities. Together with algorithm design, the text demonstrates that there are new algorithms that are capable of incorporating input and output constraints, enable the algorithm to reconfigure systematically in order to meet the requirements of different reference signals and also to support new algorithms for local convergence of nonlinear iterative control. Simulation and application studies are used to illustrate algorithm properties and performance in systems like gantry robots and other elect...
Dynamics of Dengue epidemics using optimal control
Rodrigues, Helena Sofia; Torres, Delfim F M
2010-01-01
We present an application of optimal control theory to Dengue epidemics. This epidemiologic disease is an important theme in tropical countries due to the growing number of infected individuals. The dynamic model is described by a set of nonlinear ordinary differential equations, that depend on the dynamic of the Dengue mosquito, the number of infected individuals, and the people's motivation to combat the mosquito. The cost functional depends not only on the costs of medical treatment of the infected people but also on the costs related to educational and sanitary campaigns. Two approaches to solve the problem are considered: one using optimal control theory, another one by discretizing first the problem and then solving it with nonlinear programming. The results obtained with OC-ODE and IPOPT solvers are given and discussed. We observe that with current computational tools it is easy to obtain, in an efficient way, better solutions to Dengue problems, leading to a decrease of infected mosquitoes and individ...
Optimal control problem for a sixth-order Cahn-Hilliard equation with nonlinear diffusion
Directory of Open Access Journals (Sweden)
Changchun Liu
2012-08-01
Full Text Available In this article, we study the initial-boundary-value problem for a sixth-order Cahn-Hilliard type equation $$displaylines{ u_t=D^2mu, cr mu=gamma D^4u-a(uD^2u-frac{a'(u}2|D u|^2+f(u+ku_t, }$$ which describes the separation properties of oil-water mixtures, when a substance enforcing the mixing of the phases is added. The optimal control of the sixth order Cahn-Hilliard type equation under boundary condition is given and the existence of optimal solution to the sixth order Cahn-Hilliard type equation is proved.
Mesh refinement strategy for optimal control problems
Paiva, Luis Tiago; Fontes, Fernando,
2013-01-01
International audience; Direct methods are becoming the most used technique to solve nonlinear optimal control problems. Regular time meshes having equidistant spacing are frequently used. However, in some cases these meshes cannot cope accurately with nonlinear behavior. One way to improve the solution is to select a new mesh with a greater number of nodes. Another way, involves adaptive mesh refinement. In this case, the mesh nodes have non equidistant spacing which allow a non uniform node...
Optimal control of complex atomic quantum systems
van Frank, S.; Bonneau, M.; Schmiedmayer, J.; Hild, S.; Gross, C.; Cheneau, M.; Bloch, I.; Pichler, T.; Negretti, A.; Calarco, T.; Montangero, S.
2016-10-01
Quantum technologies will ultimately require manipulating many-body quantum systems with high precision. Cold atom experiments represent a stepping stone in that direction: a high degree of control has been achieved on systems of increasing complexity. However, this control is still sub-optimal. In many scenarios, achieving a fast transformation is crucial to fight against decoherence and imperfection effects. Optimal control theory is believed to be the ideal candidate to bridge the gap between early stage proof-of-principle demonstrations and experimental protocols suitable for practical applications. Indeed, it can engineer protocols at the quantum speed limit – the fastest achievable timescale of the transformation. Here, we demonstrate such potential by computing theoretically and verifying experimentally the optimal transformations in two very different interacting systems: the coherent manipulation of motional states of an atomic Bose-Einstein condensate and the crossing of a quantum phase transition in small systems of cold atoms in optical lattices. We also show that such processes are robust with respect to perturbations, including temperature and atom number fluctuations.
Active control of transient rotordynamic vibration by optimal control methods
Palazzolo, A. B.; Lin, R. R.; Alexander, R. M.; Kascak, A. F.
1988-01-01
Although considerable effort has been put into the study of steady state vibration control, there are few methods applicable to transient vibration control of rotorbearing systems. In this paper optimal control theory has been adopted to minimize rotor vibration due to sudden imbalance, e.g., blade loss. The system gain matrix is obtained by choosing the weighting matrices and solving the Riccati equation. Control forces are applied to the system via a feedback loop. A seven mass rotor system is simulated for illustration. A relationship between the number of sensors and the number of modes used in the optimal control model is investigated. Comparisons of responses are made for various configurations of modes, sensors, and actuators. Furthermore, spillover effect is examined by comparing results from collocated and noncollocated sensor configurations. Results show that shaft vibration is significantly attenuated in the closed loop system.
An optimal promotion cost control model for a markovian manpower ...
African Journals Online (AJOL)
An optimal promotion cost control model for a markovian manpower system. ... Log in or Register to get access to full text downloads. ... A theory concerning the existence of an optimal promotion control strategy for controlling a Markovian ...
Automatic Synthesis of Robust and Optimal Controllers
DEFF Research Database (Denmark)
Cassez, Franck; Jessen, Jan Jacob; Larsen, Kim Guldstrand;
2009-01-01
In this paper, we show how to apply recent tools for the automatic synthesis of robust and near-optimal controllers for a real industrial case study. We show how to use three different classes of models and their supporting existing tools, Uppaal-TiGA for synthesis, phaver for verification......, and Simulink for simulation, in a complementary way. We believe that this case study shows that our tools have reached a level of maturity that allows us to tackle interesting and relevant industrial control problems....
Tractable problems in optimal decentralized control
Rotkowitz, Michael Charles
2005-07-01
This thesis considers the problem of constructing optimal decentralized controllers. The problem is formulated as one of minimizing the closed-loop norm of a feedback system subject to constraints on the controller structure. The notion of quadratic invariance of a constraint set with respect to a system is defined. It is shown that quadratic invariance is necessary and sufficient for the constraint set to be preserved under feedback. It is further shown that if the constraint set has this property, this allows the constrained minimum-norm problem to be solved via convex programming. These results are developed in a very general framework, and are shown to hold for continuous-time systems, discrete-time systems, or operators on Banach spaces, for stable or unstable plants, and for the minimization of any norm. The utility of these results is then demonstrated on some specific constraint classes. An explicit test is derived for sparsity constraints on a controller to be quadratically invariant, and thus amenable to convex synthesis. Symmetric synthesis is also shown to be quadratically invariant. The problem of control over networks with delays is then addressed as another constraint class. Multiple subsystems are considered, each with its own controller, such that the dynamics of each subsystem may affect those of other subsystems with some propagation delays, and the controllers may communicate with each other with some transmission delays. It is shown that if the communication delays are less than the propagation delays, then the associated constraints are quadratically invariant, and thus optimal controllers can be synthesized. We further show that this result still holds in the presence of computational delays. This thesis unifies the few previous results on specific tractable decentralized control problems, identifies broad and useful classes of new solvable problems, and delineates the largest known class of convex problems in decentralized control.
On necessary optimality conditions in discrete control systems
Mardanov, M. J.; Melikov, T. K.; Mahmudov, N. I.
2015-10-01
The paper deals with a nonlinear discrete-time optimal control problem with a cost functional of terminal type. Using a new variation of the control and new properties of optimal controls, we prove the linearised optimality conditions extending such classical optimality conditions. Along with this, various optimality conditions of quasi-singular controls are obtained. Finally, the examples illustrating the rich content of the obtained results are illustrated.
Optimal feedback scheduling of model predictive controllers
Institute of Scientific and Technical Information of China (English)
Pingfang ZHOU; Jianying XIE; Xiaolong DENG
2006-01-01
Model predictive control (MPC) could not be reliably applied to real-time control systems because its computation time is not well defined. Implemented as anytime algorithm, MPC task allows computation time to be traded for control performance, thus obtaining the predictability in time. Optimal feedback scheduling (FS-CBS) of a set of MPC tasks is presented to maximize the global control performance subject to limited processor time. Each MPC task is assigned with a constant bandwidth server (CBS), whose reserved processor time is adjusted dynamically. The constraints in the FSCBS guarantee scheduler of the total task set and stability of each component. The FS-CBS is shown robust against the variation of execution time of MPC tasks at runtime. Simulation results illustrate its effectiveness.
Applied optimal control theory of distributed systems
Lurie, K A
1993-01-01
This book represents an extended and substantially revised version of my earlierbook, Optimal Control in Problems ofMathematical Physics,originally published in Russian in 1975. About 60% of the text has been completely revised and major additions have been included which have produced a practically new text. My aim was to modernize the presentation but also to preserve the original results, some of which are little known to a Western reader. The idea of composites, which is the core of the modern theory of optimization, was initiated in the early seventies. The reader will find here its implementation in the problem of optimal conductivity distribution in an MHD-generatorchannel flow.Sincethen it has emergedinto an extensive theory which is undergoing a continuous development. The book does not pretend to be a textbook, neither does it offer a systematic presentation of the theory. Rather, it reflects a concept which I consider as fundamental in the modern approach to optimization of dis tributed systems. ...
Liu, Zhao; Zheng, Chaorong; Wu, Yue
2017-09-01
Wind profilers have been widely adopted to observe the wind field information in the atmosphere for different purposes. But accuracy of its observation has limitations due to various noises or disturbances and hence need to be further improved. In this paper, the data measured under strong wind conditions, using a 1290-MHz boundary layer profiler (BLP), are quality controlled via a composite quality control (QC) procedure proposed by the authors. Then, through the comparison with the data measured by radiosonde flights (balloon observations), the critical thresholds in the composite QC procedure, including consensus average threshold T1 and vertical shear threshold T3, are systematically discussed. And the performance of the BLP operated under precipitation is also evaluated. It is found that to ensure the high accuracy and high data collectable rate, the optimal range of subsets is determined to be 4 m/s. Although the number of data rejected by the combined algorithm of vertical shear examination and small median test is quite limited, it is proved that the algorithm is quite useful to recognize the outlier with a large discrepancy. And the optimal wind shear threshold T3 can be recommended as 5 ms-1/100 m . During patchy precipitation, the quality of data measured by the four oblique beams (using the DBS measuring technique) can still be ensured. After the BLP data are quality controlled by the composite QC procedure, the output can show good agreement with the balloon observation.
Optimal control of circular cylinder wakes using long control horizons
Flinois, Thibault L B
2015-01-01
The classical problem of minimizing the drag of a circular cylinder by using body rotation is revisited in an adjoint-based optimal control framework. The cylinder's unsteady and fully unconstrained rotation rate is optimized at Reynolds numbers of 100 and 200 and over horizons that are longer than in previous studies, where they are typically of the order of a vortex shedding period or shorter. In the best configuration, the drag is reduced by $19\\%$, the vortex shedding is effectively suppressed, and this low drag state is maintained with minimal cylinder rotation after transients. Without closed-loop control, which maintains a specific phase relationship between the actuation and the shedding, the wake is not stabilized. A comparison is also given between the performance of optimizations for different horizon lengths and cost functions. It is shown that the long horizons used are necessary in order to stabilize the vortex shedding efficiently.
Directory of Open Access Journals (Sweden)
Christin Mellner
2015-01-01
Full Text Available Profound changes are taking place within working life, where established boundaries between work and personal life are challenged by increased global competition, ever-faster changing markets, and rapid development of boundary transcending information and communication technologies (ICT. The aim of this study was to investigate boundary management preferences in terms of keeping work and personal life domains separated or integrated, that is, segmenting or blending of domains, the perception of being in control of one´s preferred boundaries, and work-life balance among employees at a Swedish telecom company (N = 1,238, response rate 65%, men 73%, mean age 42 years. Psychosocial work factors, individual characteristics, sociodemographic factors, and work-life balance were investigated in relation to boundary management preferences and perceived boundary control. For high boundary control among segmenters, nearly all the studied psychosocial work factors were significant. Among integrators, this was the case only for clear expectations in work. For both groups, the individual capacity for self-regulation was associated with high boundary control. Regarding sociodemographic factors, cohabiting women with children who preferred segmentation had low boundary control. Finally, there was a main effect of boundary control on work-life balance. In particular, male segmenters perceiving high boundary control had better work-life balance than all others. Conclusions of the study are that segmenters need external boundaries in work for succesful boundary management. Moreover, self-regulation seems a crucial boundary competence in knowledge- intensive, flexible work. Results are of value for health promotion in modern work organizations in supporting employees achieving successful boundary control and subsequent work-life balance.
Exact Boundary Controllability for a Kind of Second-Order Quasilinear Hyperbolic Systems
Institute of Scientific and Technical Information of China (English)
Ke WANG
2011-01-01
Based on the theory of semi-global C1 solution and the local exact boundary controllability for first-order quasilinear hyperbolic systems,the local exact boundary controllability for a kind of second-order quasilinear hyperbolic systems is obtained by a constructive method.
Blasting neuroblastoma using optimal control of chemotherapy.
Collins, Craig; Fister, K Renee; Key, Bethany; Williams, Mary
2009-07-01
A mathematical model is used to investigate the effectiveness of the chemotherapy drug Topotecan against neuroblastoma. Optimal control theory is applied to minimize the tumor volume and the amount of drug utilized. The model incorporates a state constraint that requires the level of circulating neutrophils (white blood cells that form an integral part of the immune system) to remain above an acceptable value. The treatment schedule is designed to simultaneously satisfy this constraint and achieve the best results in fighting the tumor. Existence and uniqueness of the solution of the optimality system, which is the state system coupled with the adjoint system, is established. Numerical simulations are given to demonstrate the behavior of the tumor and the immune system components represented in the model.
Optimization-Based Approaches to Control of Probabilistic Boolean Networks
Directory of Open Access Journals (Sweden)
Koichi Kobayashi
2017-02-01
Full Text Available Control of gene regulatory networks is one of the fundamental topics in systems biology. In the last decade, control theory of Boolean networks (BNs, which is well known as a model of gene regulatory networks, has been widely studied. In this review paper, our previously proposed methods on optimal control of probabilistic Boolean networks (PBNs are introduced. First, the outline of PBNs is explained. Next, an optimal control method using polynomial optimization is explained. The finite-time optimal control problem is reduced to a polynomial optimization problem. Furthermore, another finite-time optimal control problem, which can be reduced to an integer programming problem, is also explained.
Optimal control of HIV/AIDS dynamic: Education and treatment
Sule, Amiru; Abdullah, Farah Aini
2014-07-01
A mathematical model which describes the transmission dynamics of HIV/AIDS is developed. The optimal control representing education and treatment for this model is explored. The existence of optimal Control is established analytically by the use of optimal control theory. Numerical simulations suggest that education and treatment for the infected has a positive impact on HIV/AIDS control.
Free boundary problems in controlled release pharmaceuticals: II. swelling-controlled release
Cohen, Donald S.; Erneux, Thomas
1988-01-01
A problem in controlled release pharmaceutical systems is formulated and studied. The device modeled is a polymer matrix containing an initially immobilized drug. The release of the drug is achieved by countercurrent diffusion through a penetrant solvent with the release rate being determined by the rate of diffusion of the solvent in the polymer. The mathematical theory yields a free boundary problem which is studied in various asymptotic regimes.
Controlling Electromagnetic Fields at Boundaries of Arbitrary Geometries
Teo, Jonathon Yi Han; Molardi, Carlo; Genevet, Patrice
2015-01-01
Rapid developments in the emerging field of stretchable and conformable photonics necessitate analytical expressions for boundary conditions at metasurfaces of arbitrary geometries. Here, we introduce the concept of conformal boundary optics: a design theory that determines the optical response for designer input and output fields at such interfaces. Given any object, we can realise coatings to achieve exotic effects like optical illusions and anomalous diffraction behaviour. This approach is relevant to a broad range of applications from conventional refractive optics to the design of the next-generation of wearable optical components. This concept can be generalized to other fields of research where designer interfaces with nontrivial geometries are encountered.
Controlling electromagnetic fields at boundaries of arbitrary geometries
Teo, Jonathon Yi Han; Wong, Liang Jie; Molardi, Carlo; Genevet, Patrice
2016-08-01
Rapid developments in the emerging field of stretchable and conformable photonics necessitate analytical expressions for boundary conditions at metasurfaces of arbitrary geometries. Here, we introduce the concept of conformal boundary optics: a design theory that determines the optical response for designer input and output fields at such interfaces. Given any object, we can realize coatings to achieve exotic effects like optical illusions and anomalous diffraction behavior. This approach is relevant to a broad range of applications from conventional refractive optics to the design of the next-generation of wearable optical components. This concept can be generalized to other fields of research where designer interfaces with nontrivial geometries are encountered.
Gradient zone boundary control in salt gradient solar ponds
Energy Technology Data Exchange (ETDEWEB)
Hull, John R. (Downers Grove, IL)
1984-01-01
A method and apparatus for suppressing zone boundary migration in a salt gradient solar pond includes extending perforated membranes across the pond at the boundaries, between the convective and non-convective zones, the perforations being small enough in size to prevent individual turbulence disturbances from penetrating the hole, but being large enough to allow easy molecular diffusion of salt thereby preventing the formation of convective zones in the gradient layer. The total area of the perforations is a sizable fraction of the membrane area to allow sufficient salt diffusion while preventing turbulent entrainment into the gradient zone.
On the signs of pulses in the problems of optimal control with fixed ends of the trajectories
Tokarev, VV
2001-01-01
For the problems of optimal control with fixed boundary values of the phase coordinates, a scheme for establishing the signs of pulses in the procedure of the Pontryagin maximum principle was proposed. It lies in passing from the original optimization problem to an equivalent problem where the bound
Fractional conservation laws in optimal control theory
Frederico, Gastao S F
2007-01-01
Using the recent formulation of Noether's theorem for the problems of the calculus of variations with fractional derivatives, the Lagrange multiplier technique, and the fractional Euler-Lagrange equations, we prove a Noether-like theorem to the more general context of the fractional optimal control. As a corollary, it follows that in the fractional case the autonomous Hamiltonian does not define anymore a conservation law. Instead, it is proved that the fractional conservation law adds to the Hamiltonian a new term which depends on the fractional-order of differentiation, the generalized momentum, and the fractional derivative of the state variable.
Optimal control of Rydberg lattice gases
Cui, Jian; van Bijnen, Rick; Pohl, Thomas; Montangero, Simone; Calarco, Tommaso
2017-09-01
We present optimal control protocols to prepare different many-body quantum states of Rydberg atoms in optical lattices. Specifically, we show how to prepare highly ordered many-body ground states, GHZ states as well as some superposition of symmetric excitation number Fock states, that inherit the translational symmetry from the Hamiltonian, within sufficiently short excitation times minimising detrimental decoherence effects. For the GHZ states, we propose a two-step detection protocol to experimentally verify the optimised preparation of the target state based only on standard measurement techniques. Realistic experimental constraints and imperfections are taken into account by our optimisation procedure making it applicable to ongoing experiments.
Optimal Coordinated Control of Power Extraction in LES of a Wind Farm with Entrance Effects
Directory of Open Access Journals (Sweden)
Jay P. Goit
2016-01-01
Full Text Available We investigate the use of optimal coordinated control techniques in large eddy simulations of wind farm boundary layer interaction with the aim of increasing the total energy extraction in wind farms. The individual wind turbines are considered as flow actuators, and their energy extraction is dynamically regulated in time, so as to optimally influence the flow field. We extend earlier work on wind farm optimal control in the fully-developed regime (Goit and Meyers 2015, J. Fluid Mech. 768, 5–50 to a ‘finite’ wind farm case, in which entrance effects play an important role. For the optimal control, a receding horizon framework is employed in which turbine thrust coefficients are optimized in time and per turbine. Optimization is performed with a conjugate gradient method, where gradients of the cost functional are obtained using adjoint large eddy simulations. Overall, the energy extraction is increased 7% by the optimal control. This increase in energy extraction is related to faster wake recovery throughout the farm. For the first row of turbines, the optimal control increases turbulence levels and Reynolds stresses in the wake, leading to better wake mixing and an inflow velocity for the second row that is significantly higher than in the uncontrolled case. For downstream rows, the optimal control mainly enhances the sideways mean transport of momentum. This is different from earlier observations by Goit and Meyers (2015 in the fully-developed regime, where mainly vertical transport was enhanced.
Exact Synchronization for a Coupled System of Wave Equations with Dirichlet Boundary Controls
Institute of Scientific and Technical Information of China (English)
Tatsien LI; Bopeng RAO
2013-01-01
In this paper,the exact synchronization for a coupled system of wave equations with Dirichlet boundary controls and some related concepts are introduced.By means of the exact null controllability of a reduced coupled system,under certain conditions of compatibility,the exact synchronization,the exact synchronization by groups,and the exact null controllability and synchronization by groups are all realized by suitable boundary controls.
Boundary Layer Simulation and Control in Wind Tunnels
1988-04-01
Vol. 1, No. 4, April 1963, pp. 931-933. AIAA 11. Maybe, Dennis G.: Some Remarks on Dynamic Aeroelastic Model Tests in Cryogenic Wind Tunnels...distribution). 42. Lindhout, J.P.F, Moek , C., Boer, E. de and Berg, B. van den: A Method for the Calculation of 3D Boundary Layers on Practical Wing
Boundary-field-driven control of discontinuous phase transitions on hyperbolic lattices
Lee, Yoju; Verstraete, Frank; Gendiar, Andrej
2016-08-01
The multistate Potts models on two-dimensional hyperbolic lattices are studied with respect to various boundary effects. The free energy is numerically calculated using the corner transfer matrix renormalization group method. We analyze phase transitions of the Potts models in the thermodynamic limit with respect to contracted boundary layers. A false phase transition is present even if a couple of the boundary layers are contracted. Its significance weakens, as the number of the contracted boundary layers increases, until the correct phase transition (deep inside the bulk) prevails over the false one. For this purpose, we derive a thermodynamic quantity, the so-called bulk excess free energy, which depends on the contracted boundary layers and memorizes additional boundary effects. In particular, the magnetic field is imposed on the outermost boundary layer. While the boundary magnetic field does not affect the second-order phase transition in the bulk if suppressing all the boundary effects on the hyperbolic lattices, the first-order (discontinuous) phase transition is significantly sensitive to the boundary magnetic field. Contrary to the phase transition on the Euclidean lattices, the discontinuous phase transition on the hyperbolic lattices can be continuously controlled (within a certain temperature coexistence region) by varying the boundary magnetic field.
Optimal Control of Non-well-posed Heat Equations
Institute of Scientific and Technical Information of China (English)
Geng Sheng WANG
2005-01-01
This work is concerned with Pontryagin's maximum principle of optimal control problems governed by some non-well-posed semilinear heat equations. A type of approach to the non-well-posed optimal control problem is given.
Optimal Control of Pseudoparabolic Variational Inequalities Involving State Constraint
Directory of Open Access Journals (Sweden)
Youjun Xu
2014-01-01
Full Text Available We establish the necessary condition of optimality for optimal control problem governed by some pseudoparabolic differential equations involving monotone graphs. Some approximating control process and examples are given.
Controlling automobile thermal comfort using optimized fuzzy controller
Energy Technology Data Exchange (ETDEWEB)
Farzaneh, Yadollah; Tootoonchi, Ali A. [Department of Mechanical Engineering, Ferdowsi University of Mashhad, Mashhad (Iran)
2008-10-15
Providing thermal comfort and saving energy are two main goals of heating, ventilation and air conditioning (HVAC) systems. A controller with temperature feedback cannot best achieve the thermal comfort. This is because thermal comfort is influenced by many variables such as, temperature, relative humidity, air velocity, environment radiation, activity level and cloths insulation. In this study Fanger's predicted mean value (PMV) index is used as controller feedback. It is simplified without introducing significant error. Thermal models of the cabin and HVAC system are developed. Evaporator cooling capacity is selected as a criterion for energy consumption. Two fuzzy controllers one with temperature as its feedback and the other PMV index as its feedback are designed. Results show that the PMV feedback controller better controls the thermal comfort and energy consumption than the system with temperature feedback. Next, the parameters of the fuzzy controller are optimized by genetic algorithm. Results indicate that thermal comfort level is further increased while energy consumption is decreased. Finally, robustness analysis is performed which shows the robustness of optimized controller to variables variations. (author)
Optimal Control of Finite Dimensional Quantum Systems
Mendonca, Paulo E M F
2009-01-01
This thesis addresses the problem of developing a quantum counter-part of the well established classical theory of control. We dwell on the fundamental fact that quantum states are generally not perfectly distinguishable, and quantum measurements typically introduce noise in the system being measured. Because of these, it is generally not clear whether the central concept of the classical control theory -- that of observing the system and then applying feedback -- is always useful in the quantum setting. We center our investigations around the problem of transforming the state of a quantum system into a given target state, when the system can be prepared in different ways, and the target state depends on the choice of preparation. We call this the "quantum tracking problem" and show how it can be formulated as an optimization problem that can be approached both numerically and analytically. This problem provides a simple route to the characterization of the quantum trade-off between information gain and distu...
Reproducibility, controllability, and optimization of LENR experiments
Energy Technology Data Exchange (ETDEWEB)
Nagel, David J. [The George Washington University, Washington DC 20052 (United States)
2006-07-01
Low-energy nuclear reaction (LENR) measurements are significantly, and increasingly reproducible. Practical control of the production of energy or materials by LENR has yet to be demonstrated. Minimization of costly inputs and maximization of desired outputs of LENR remain for future developments. The paper concludes by underlying that it is now clearly that demands for reproducible experiments in the early years of LENR experiments were premature. In fact, one can argue that irreproducibility should be expected for early experiments in a complex new field. As emphasized in the paper and as often happened in the history of science, experimental and theoretical progress can take even decades. It is likely to be many years before investments in LENR experiments will yield significant returns, even for successful research programs. However, it is clearly that a fundamental understanding of the anomalous effects observed in numerous experiments will significantly increase reproducibility, improve controllability, enable optimization of processes, and accelerate the economic viability of LENR.
On an Optimal -Control Problem in Coefficients for Linear Elliptic Variational Inequality
Directory of Open Access Journals (Sweden)
Olha P. Kupenko
2013-01-01
Full Text Available We consider optimal control problems for linear degenerate elliptic variational inequalities with homogeneous Dirichlet boundary conditions. We take the matrix-valued coefficients in the main part of the elliptic operator as controls in . Since the eigenvalues of such matrices may vanish and be unbounded in , it leads to the “noncoercivity trouble.” Using the concept of convergence in variable spaces and following the direct method in the calculus of variations, we establish the solvability of the optimal control problem in the class of the so-called -admissible solutions.
Optimal second order sliding mode control for nonlinear uncertain systems.
Das, Madhulika; Mahanta, Chitralekha
2014-07-01
In this paper, a chattering free optimal second order sliding mode control (OSOSMC) method is proposed to stabilize nonlinear systems affected by uncertainties. The nonlinear optimal control strategy is based on the control Lyapunov function (CLF). For ensuring robustness of the optimal controller in the presence of parametric uncertainty and external disturbances, a sliding mode control scheme is realized by combining an integral and a terminal sliding surface. The resulting second order sliding mode can effectively reduce chattering in the control input. Simulation results confirm the supremacy of the proposed optimal second order sliding mode control over some existing sliding mode controllers in controlling nonlinear systems affected by uncertainty.
Chernov, A. V.
2013-12-01
Approximating finite-dimensional mathematical programming problems are studied that arise from piecewise constant discretization of controls in the optimization of distributed systems of a fairly broad class. The smoothness of the approximating problems is established. Gradient formulas are derived that make use of the analytical solution of the original control system and its adjoint, thus providing an opportunity for algorithmic separation of numerical optimization and the task of solving a controlled initial-boundary value problem. The approximating problems are proved to converge to the original optimization problem with respect to the functional as the discretization is refined. The application of the approach to optimization problems is illustrated by solving the semilinear wave equation controlled by applying an integral criterion. The results of numerical experiments are analyzed.
Optimal control of quantum systems by chirped pulses
DEFF Research Database (Denmark)
Amstrup, Bjarne; Doll, J. D.; Sauerbrey, R. A.
1993-01-01
Research on optimal control of quantum systems has been severely restricted by the lack of experimentally feasible control pulses. Here, to overcome this obstacle, optimal control is considered with the help of chirped pulses. Simulated annealing is used as the optimizing procedure. The examples ...
Optimal Control Problems for Nonlinear Variational Evolution Inequalities
Directory of Open Access Journals (Sweden)
Eun-Young Ju
2013-01-01
Full Text Available We deal with optimal control problems governed by semilinear parabolic type equations and in particular described by variational inequalities. We will also characterize the optimal controls by giving necessary conditions for optimality by proving the Gâteaux differentiability of solution mapping on control variables.
Adjoint-based Optimal Flow Control for Compressible DNS
Otero, J Javier; Sandberg, Richard D
2016-01-01
A novel adjoint-based framework oriented to optimal flow control in compressible direct numerical simulations is presented. Also, a new formulation of the adjoint characteristic boundary conditions is introduced, which enhances the stability of the adjoint simulations. The flow configuration chosen as a case study consists of a two dimensional open cavity flow with aspect ratio $L/H=3$ and Reynolds number $Re=5000$. This flow configuration is of particular interest, as the turbulent and chaotic nature of separated flows pushes the adjoint approach to its limit. The target of the flow actuation, defined as cost, is the reduction of the pressure fluctuations at the sensor location. To exploit the advantages of the adjoint method, a large number of control parameters is used. The control consists of an actuating sub-domain where a two-dimensional body force is applied at every point within the sub-volume. This results in a total of $2.256 \\cdot 10^6$ control parameters. The final actuation achieved a successful ...
46 CFR 116.415 - Fire control boundaries.
2010-10-01
... Machinery spaces, voids, fuel and water tanks (12) C' 1 C' 1 Open decks (not safety areas) (13) C 1... decks (not safety areas) (13) A-0 A-0 A-0 C A-0 A-0 A-0 A-0 A-0 A-0 A-0 A-0 1 C 1 Boundaries of fuel..., superstructure, and deck houses of a vessel, except for a vehicle space on a vehicle ferry, must be subdivided by...
Optimal Sliding Mode Controllers for Attitude Stabilization of Flexible Spacecraft
Directory of Open Access Journals (Sweden)
Chutiphon Pukdeboon
2011-01-01
Full Text Available The robust optimal attitude control problem for a flexible spacecraft is considered. Two optimal sliding mode control laws that ensure the exponential convergence of the attitude control system are developed. Integral sliding mode control (ISMC is applied to combine the first-order sliding mode with optimal control and is used to control quaternion-based spacecraft attitude manoeuvres with external disturbances and an uncertainty inertia matrix. For the optimal control part the state-dependent Riccati equation (SDRE and optimal Lyapunov techniques are employed to solve the infinite-time nonlinear optimal control problem. The second method of Lyapunov is used to guarantee the stability of the attitude control system under the action of the proposed control laws. An example of multiaxial attitude manoeuvres is presented and simulation results are included to verify the usefulness of the developed controllers.
Control Optimization of Solar Thermally Driven Chillers
Directory of Open Access Journals (Sweden)
Antoine Dalibard
2016-10-01
Full Text Available Many installed solar thermally driven cooling systems suffer from high auxiliary electric energy consumption which makes them not more efficient than conventional compression cooling systems. A main reason for this is the use of non-efficient controls with constant set points that do not allow a chiller power modulation at partial-load and therefore lead to unnecessary high power consumption of the parasitics. The aims of this paper are to present a method to control efficiently solar thermally driven chillers, to demonstrate experimentally its applicability and to quantify the benefits. It has been shown that the cooling capacity of a diffusion absorption chiller can be modulated very effectively by adjusting both the temperature and the flow rate of the cooling water. With the developed approach and the use of optimization algorithms, both the temperature and the flow rate can be controlled simultaneously in a way that the cooling load is matched and the electricity consumption is minimized. Depending on the weather and operating conditions, electricity savings between 20% and 60% can be achieved compared to other tested control approaches. The highest savings are obtained when the chiller is operated at partial load. The presented method is not restricted to solar cooling systems and can also be applied to other conventional heating ventilation and air conditioning (HVAC systems.
Continuous Control Artificial Potential Function Methods and Optimal Control
2014-03-27
Method, namely r̈VDSVAPF = −K̇SKR∇φ−KSK̇R∇φ−KSKRH(φ)ṙ −KD (KSKR∇φ+ ṙ) . The above dynamics are very nonlinear due to the trigonometric functions (inside...constraints (on KS and θ) and the deletion of trigonometric functions . The suspected reasons for the larger computa- tional expense are twofold. First, this...Continuous Control Artificial Potential Function Methods and Optimal Control THESIS R. Andrew Fields, Civ, USAF AFIT-ENY-14-M-20 DEPARTMENT OF THE
Energy Technology Data Exchange (ETDEWEB)
Matsuuchi, K.; Yamamura, N. [University of Tsukuba, Tsukuba (Japan); Eguchi, Y. [Honda Motor Co. Ltd., Tokyo (Japan); Adachi, T. [Osaka Sangyo Univ., Osaka (Japan); Onda, M. [Mechanical Engineering Lab., Tokyo (Japan)
1997-03-25
Our aim is to optimize the aerodynamic shape of airships, which cruise at high Reynolds number. A cryogenic wind tunnel is used to achieve the desired flow. In the present paper we discuss the drag coefficient for airship models incorporating suction slots, for the purpose of boundary layer control. The pressure distributions on the models are measured over a wide range of Reynolds number for various suction discharges. By integrating the pressure distributions, it was found that the profile drag could be reduced using boundary layer control as low as the theoretical limit. Furthermore, the flow patterns around the models can be classified into four categories. The relationship between suction and surface velocity was also examined, which is critical in understanding drag reduction. 7 refs., 12 figs., 2 tabs.
The reconstruction of sound speed in the Marmousi model by the boundary control method
Ivanov, I B; Semenov, V S
2016-01-01
We present the results on numerical testing of the Boundary Control Method in the sound speed determination for the acoustic equation on semiplane. This method for solving multidimensional inverse problems requires no a priory information about the parameters under reconstruction. The application to the realistic Marmousi model demonstrates that the boundary control method is workable in the case of complicated and irregular field of acoustic rays. By the use of the chosen boundary controls, an `averaged' profile of the sound speed is recovered (the relative error is about $10-15\\%$). Such a profile can be further utilized as a starting approximation for high resolution iterative reconstruction methods.
Multiresolution strategies for the numerical solution of optimal control problems
Jain, Sachin
There exist many numerical techniques for solving optimal control problems but less work has been done in the field of making these algorithms run faster and more robustly. The main motivation of this work is to solve optimal control problems accurately in a fast and efficient way. Optimal control problems are often characterized by discontinuities or switchings in the control variables. One way of accurately capturing the irregularities in the solution is to use a high resolution (dense) uniform grid. This requires a large amount of computational resources both in terms of CPU time and memory. Hence, in order to accurately capture any irregularities in the solution using a few computational resources, one can refine the mesh locally in the region close to an irregularity instead of refining the mesh uniformly over the whole domain. Therefore, a novel multiresolution scheme for data compression has been designed which is shown to outperform similar data compression schemes. Specifically, we have shown that the proposed approach results in fewer grid points in the grid compared to a common multiresolution data compression scheme. The validity of the proposed mesh refinement algorithm has been verified by solving several challenging initial-boundary value problems for evolution equations in 1D. The examples have demonstrated the stability and robustness of the proposed algorithm. The algorithm adapted dynamically to any existing or emerging irregularities in the solution by automatically allocating more grid points to the region where the solution exhibited sharp features and fewer points to the region where the solution was smooth. Thereby, the computational time and memory usage has been reduced significantly, while maintaining an accuracy equivalent to the one obtained using a fine uniform mesh. Next, a direct multiresolution-based approach for solving trajectory optimization problems is developed. The original optimal control problem is transcribed into a
Optimal control theory for sustainable environmental management.
Shastri, Yogendra; Diwekar, Urmila; Cabezas, Heriberto
2008-07-15
Sustainable ecosystem management aims to promote the structure and operation of the human components of the system while simultaneously ensuring the persistence of the structures and operation of the natural component. Given the complexity of this task owing to the diverse temporal and spatial scales and multidisciplinary interactions, a systems theory approach based on sound mathematical techniques is essential. Two important aspects of this approach are formulation of sustainability-based objectives and development of the management strategies. Fisher information can be used as the basis of a sustainability hypothesis to formulate relevant mathematical objectives for disparate systems, and optimal control theory provides the means to derive time-dependent management strategies. Partial correlation coefficient analysis is an efficient technique to identify the appropriate control variables for policy development. This paper represents a proof of concept for this approach using a model system that includes an ecosystem, humans, a very rudimentary industrial process, and a very simple agricultural system. Formulation and solution of the control problems help in identifying the effective management options which offer guidelines for policies in real systems. The results also emphasize that management using multiple parameters of different nature can be distinctly effective.
Numerical methods for control optimization in linear systems
Tyatyushkin, A. I.
2015-05-01
Numerical methods are considered for solving optimal control problems in linear systems, namely, terminal control problems with control and phase constraints and time-optimal control problems. Several algorithms with various computer storage requirements are proposed for solving these problems. The algorithms are intended for finding an optimal control in linear systems having certain features, for example, when the reachable set of a system has flat faces.
Active Control of Airfoil Boundary Layer Separation and Wake using Ns-DBD Plasma Actuators
Durasiewicz, Claudia; Castro Maldonado, Jorge; Little, Jesse
2016-11-01
Nanosecond pulse driven dielectric barrier discharge (ns-DBD) plasma actuators are employed to control boundary layer separation and the wake of a NACA 0012 airfoil having aspect ratio of three. Ns-DBD plasma actuators are known to operate via a thermal mechanism in contrast to ac-DBDs which are momentum-based devices. Nominally 2D forcing is applied to the airfoil leading edge with pulse energy of 0.35 mJ/cm. Experiments are conducted at a Reynolds number of 0 . 74 ×106 primarily at 18° incidence which is well within the stalled regime. Baseline and controlled flow fields are studied using surface pressure measurements, constant temperature anemometry (CTA) and PIV. Forcing at a dimensionless frequency of F+ = fc /U∞ = 1 . 14 results in reattachment of nominally separated flow to the airfoil surface. Lower frequency forcing is less optimal for separation control, but produces strong fluctuations in the wake which are intended for use in the study of vortex body interaction in the future. Actuation below F+ = 0 . 23 shows behavior consistent with an impulse-like response while forcing in the range 0 . 23
A Galerkin-Parameterization Method for the Optimal Control of Smart Microbeams
Directory of Open Access Journals (Sweden)
Marwan Abukhaled
2009-01-01
Full Text Available A proposed computational method is applied to damp out the excess vibrations in smart microbeams, where the control action is implemented using piezoceramic actuators. From a mathematical point of view, we wish to determine the optimal boundary actuators that minimize a given energy-based performance measure. The minimization of the performance measure over the actuators is subjected to the full motion of the structural vibrations of the micro-beams. A direct state-control parametrization approach is proposed where the shifted Legendre polynomials are employed to solve the optimization problem. Legendre operational matrix and the properties of Kronecker product are utilized to find the approximated optimal trajectory and optimal control law of the lumped parameter systems with respect to the quadratic cost function by solving linear algebraic equations. Numerical examples are provided to demonstrate the applicability and efficiency of the proposed approach.
Stability Boundaries for Offshore Wind Park Distributed Voltage Control
DEFF Research Database (Denmark)
Gryning, Mikkel P.S.; Wu, Qiuwei; Kocewiak, Lukasz
2017-01-01
pilot control. Using data from the actual wind power plant, all stabilizing subsystem voltage proportional-integral controller parameters are first characterized based on their Hurwitz signature. Inner loop current control is then designed using Internal Mode Control principles, and guidelines for feed...
Directory of Open Access Journals (Sweden)
Ada Cheng
2006-01-01
Full Text Available Boundary control systems arises naturally in many applications. Any modelling of real systems involve uncertainty. Sufficient conditions for well-posededness for additive or multiplicative uncertainty are presented through the use of matrix theory.
On a Highly Nonlinear Self-Obstacle Optimal Control Problem
Energy Technology Data Exchange (ETDEWEB)
Di Donato, Daniela, E-mail: daniela.didonato@unitn.it [University of Trento, Department of Mathematics (Italy); Mugnai, Dimitri, E-mail: dimitri.mugnai@unipg.it [Università di Perugia, Dipartimento di Matematica e Informatica (Italy)
2015-10-15
We consider a non-quadratic optimal control problem associated to a nonlinear elliptic variational inequality, where the obstacle is the control itself. We show that, fixed a desired profile, there exists an optimal solution which is not far from it. Detailed characterizations of the optimal solution are given, also in terms of approximating problems.
Skinner Rusk unified formalism for optimal control systems and applications
Barbero-Liñán, María; Echeverría-Enríquez, Arturo; Martín de Diego, David; Muñoz-Lecanda, Miguel C.; Román-Roy, Narciso
2007-10-01
A geometric approach to time-dependent optimal control problems is proposed. This formulation is based on the Skinner and Rusk formalism for Lagrangian and Hamiltonian systems. The corresponding unified formalism developed for optimal control systems allows us to formulate geometrically the necessary conditions given by a weak form of Pontryagin's maximum principle, provided that the differentiability with respect to controls is assumed and the space of controls is open. Furthermore, our method is also valid for implicit optimal control systems and, in particular, for the so-called descriptor systems (optimal control problems including both differential and algebraic equations).
Boundary Control of Linear Evolution PDEs - Continuous and Discrete
DEFF Research Database (Denmark)
Rasmussen, Jan Marthedal
2004-01-01
of literature exists in the area of theoretical results concerning control of partial differential equations. The results have included existence and uniqueness of controls, minimum time requirements, regularity of domains, and many others. Another huge research field is that of control theory for ordinary di......- and exact controllability. We will consider discrete systems with a viewpoint similar to that used for the continuous systems. Most importantly, we study what is required of a discretization scheme in order for computed control functions to converge to the true, continuous, control function. Examples exist...
Institute of Scientific and Technical Information of China (English)
Wei Gong; Ningning Yan
2009-01-01
In this paper.we discuss the a posteriori error estimate of the finite element approximation for the boundary control problems governed by the parabolic partial differential equations.Three different a posteriori error estimators are provided for the parabolic boundary control problems with the observations of the distributed state.the boundary state and the final state.It is proven that these estimators are reliable bounds of the finite element approximation errors,which can be used as the indicators of the mesh refinement in adaptive finite element methods.
Feed Forward Neural Network and Optimal Control Problem with Control and State Constraints
Kmet', Tibor; Kmet'ová, Mária
2009-09-01
A feed forward neural network based optimal control synthesis is presented for solving optimal control problems with control and state constraints. The paper extends adaptive critic neural network architecture proposed by [5] to the optimal control problems with control and state constraints. The optimal control problem is transcribed into a nonlinear programming problem which is implemented with adaptive critic neural network. The proposed simulation method is illustrated by the optimal control problem of nitrogen transformation cycle model. Results show that adaptive critic based systematic approach holds promise for obtaining the optimal control with control and state constraints.
Neural Network for Optimization of Existing Control Systems
DEFF Research Database (Denmark)
Madsen, Per Printz
1995-01-01
The purpose of this paper is to develop methods to use Neural Network based Controllers (NNC) as an optimization tool for existing control systems.......The purpose of this paper is to develop methods to use Neural Network based Controllers (NNC) as an optimization tool for existing control systems....
Control Methods Utilizing Energy Optimizing Schemes in Refrigeration Systems
DEFF Research Database (Denmark)
Larsen, L.S; Thybo, C.; Stoustrup, Jakob
2003-01-01
The potential energy savings in refrigeration systems using energy optimal control has been proved to be substantial. This however requires an intelligent control that drives the refrigeration systems towards the energy optimal state. This paper proposes an approach for a control, which drives th...... the condenser pressure towards an optimal state. The objective of this is to present a feasible method that can be used for energy optimizing control. A simulation model of a simple refrigeration system will be used as basis for testing the control method.......The potential energy savings in refrigeration systems using energy optimal control has been proved to be substantial. This however requires an intelligent control that drives the refrigeration systems towards the energy optimal state. This paper proposes an approach for a control, which drives...
Optimal Power Flow Control by Rotary Power Flow Controller
Directory of Open Access Journals (Sweden)
KAZEMI, A.
2011-05-01
Full Text Available This paper presents a new power flow model for rotary power flow controller (RPFC. RPFC injects a series voltage into the transmission line and provides series compensation and phase shifting simultaneously. Therefore, it is able to control the transmission line impedance and the active power flow through it. An RPFC is composed mainly of two rotary phase shifting transformers (RPST and two conventional (series and shunt transformers. Structurally, an RPST consists of two windings (stator and rotor windings. The rotor windings of the two RPSTs are connected in parallel and their stator windings are in series. The injected voltage is proportional to the vector sum of the stator voltages and so its amplitude and angle are affected by the rotor position of the two RPSTs. This paper, describes the steady state operation and single-phase equivalent circuit of the RPFC. Also in this paper, a new power flow model, based on power injection model of flexible ac transmission system (FACTS controllers, suitable for the power flow analysis is introduced. Proposed model is used to solve optimal power flow (OPF problem in IEEE standard test systems incorporating RPFC and the optimal settings and location of the RPFC is determined.
Goodrich, John W.
2017-01-01
This paper presents results from numerical experiments for controlling the error caused by a damping layer boundary treatment when simulating the propagation of an acoustic signal from a continuous pressure source. The computations are with the 2D Linearized Euler Equations (LEE) for both a uniform mean flow and a steady parallel jet. The numerical experiments are with algorithms that are third, fifth, seventh and ninth order accurate in space and time. The numerical domain is enclosed in a damping layer boundary treatment. The damping is implemented in a time accurate manner, with simple polynomial damping profiles of second, fourth, sixth and eighth power. At the outer boundaries of the damping layer the propagating solution is uniformly set to zero. The complete boundary treatment is remarkably simple and intrinsically independant from the dimension of the spatial domain. The reported results show the relative effect on the error from the boundary treatment by varying the damping layer width, damping profile power, damping amplitude, propagtion time, grid resolution and algorithm order. The issue that is being addressed is not the accuracy of the numerical solution when compared to a mathematical solution, but the effect of the complete boundary treatment on the numerical solution, and to what degree the error in the numerical solution from the complete boundary treatment can be controlled. We report maximum relative absolute errors from just the boundary treatment that range from O[10-2] to O[10-7].
Dynamic optimization the calculus of variations and optimal control in economics and management
Kamien, Morton I
2012-01-01
Since its initial publication, this text has defined courses in dynamic optimization taught to economics and management science students. The two-part treatment covers the calculus of variations and optimal control. 1998 edition.
Optimality of feedback control strategies for qubit purification
Wiseman, Howard M.; Bouten, Luc
2007-01-01
Recently two papers [K. Jacobs, Phys. Rev. A {\\bf 67}, 030301(R) (2003); H. M. Wiseman and J. F. Ralph, New J. Physics {\\bf 8}, 90 (2006)] have derived control strategies for rapid purification of qubits, optimized with respect to various goals. In the former paper the proof of optimality was not mathematically rigorous, while the latter gave only heuristic arguments for optimality. In this paper we provide rigorous proofs of optimality in all cases, by applying simple concepts from optimal c...
Stability Boundaries for Offshore Wind Park Distributed Voltage Control
DEFF Research Database (Denmark)
Gryning, Mikkel P.S.; Wu, Qiuwei; Kocewiak, Lukasz;
2016-01-01
In order to identify mechanisms causing slow reactive power oscillations observed in an existing offshore wind power plant, and be able to avoid similar events in the future, voltage control is studied in this paper for a plant with a static synchronous compensator, type-4 wind turbines and a park...... pilot control. Using data from the actual wind power plant, all stabilizing subsystem voltage proportional-integral controller parameters are first characterized based on their Hurwitz signature. Inner loop current control is then designed using Internal Mode Control principles, and guidelines for feed...... forward filter design are given to obtain required disturbance rejection properties. The paper contributes by providing analytical relations between power plant control, droop, sampling time, electrical parameters and voltage control characteristics, and by assessing frequencies and damping of reactive...
Robust and optimal attitude control of spacecraft with disturbances
Park, Yonmook
2015-05-01
In this paper, a robust and optimal attitude control design that uses the Euler angles and angular velocities feedback is presented for regulation of spacecraft with disturbances. In the control design, it is assumed that the disturbance signal has the information of the system state. In addition, it is assumed that the disturbance signal tries to maximise the same performance index that the control input tries to minimise. After proposing a robust attitude control law that can stabilise the complete attitude motion of spacecraft with disturbances, the optimal attitude control problem of spacecraft is formulated as the optimal game-theoretic problem. Then it is shown that the proposed robust attitude control law is the optimal solution of the optimal game-theoretic problem. The stability of the closed-loop system for the proposed robust and optimal control law is proven by the LaSalle invariance principle. The theoretical results presented in this paper are illustrated by a numerical example.
Directory of Open Access Journals (Sweden)
B. Kafash
2014-04-01
Full Text Available In this paper, we present a computational method for solving optimal control problems and the controlled Duffing oscillator. This method is based on state parametrization. In fact, the state variable is approximated by Boubaker polynomials with unknown coefficients. The equation of motion, performance index and boundary conditions are converted into some algebraic equations. Thus, an optimal control problem converts to a optimization problem, which can then be solved easily. By this method, the numerical value of the performance index is obtained. Also, the control and state variables can be approximated as functions of time. Convergence of the algorithms is proved. Numerical results are given for several test examples to demonstrate the applicability and efficiency of the method.
Su, Hao; Tang, Gong-You
2016-09-01
This paper proposes a successive approximation design approach of observer-based optimal tracking controllers for time-delay systems with external disturbances. To solve a two-point boundary value problem with time-delay and time-advance terms and obtain the optimal tracking control law, two sequences of vector differential equations are constructed first. Second, the convergence of the sequences of the vector differential equations is proved to guarantee the existence and uniqueness of the control law. Third, a design algorithm of the optimal tracking control law is presented and the physically realisable problem is addressed by designing a disturbance state observer and a reference input state observer. An example of an industrial electric heater is given to demonstrate the efficiency of the proposed approach.
Kumar, Ajeet
2009-01-01
We introduce a new and efficient numerical method for multicriterion optimal control and single criterion optimal control under integral constraints. The approach is based on extending the state space to include information on a "budget" remaining to satisfy each constraint; the augmented Hamilton-Jacobi-Bellman PDE is then solved numerically. The efficiency of our approach hinges on the causality in that PDE, i.e., the monotonicity of characteristic curves in one of the newly added dimensions. A semi-Lagrangian "marching" method is used to approximate the discontinuous viscosity solution efficiently. We compare this to a recently introduced "weighted sum" based algorithm for the same problem. We illustrate our method using examples from flight path planning and robotic navigation in the presence of friendly and adversarial observers.
Optimal control problems with switching points. Ph.D. Thesis, 1990 Final Report
Seywald, Hans
1991-01-01
An overview is presented of the problems and difficulties that arise in solving optimal control problems with switching points. A brief discussion of existing optimality conditions is given and a numerical approach for solving the multipoint boundary value problems associated with the first-order necessary conditions of optimal control is presented. Two real-life aerospace optimization problems are treated explicitly. These are altitude maximization for a sounding rocket (Goddard Problem) in the presence of a dynamic pressure limit, and range maximization for a supersonic aircraft flying in the vertical, also in the presence of a dynamic pressure limit. In the second problem singular control appears along arcs with active dynamic pressure limit, which in the context of optimal control, represents a first-order state inequality constraint. An extension of the Generalized Legendre-Clebsch Condition to the case of singular control along state/control constrained arcs is presented and is applied to the aircraft range maximization problem stated above. A contribution to the field of Jacobi Necessary Conditions is made by giving a new proof for the non-optimality of conjugate paths in the Accessory Minimum Problem. Because of its simple and explicit character, the new proof may provide the basis for an extension of Jacobi's Necessary Condition to the case of the trajectories with interior point constraints. Finally, the result that touch points cannot occur for first-order state inequality constraints is extended to the case of vector valued control functions.
Optimal Control of Airfoil Flow Separation using Fluidic Excitation
Shahrabi, Arireza F.
This thesis deals with the control of flow separation around a symmetric airfoils with the aid of multiple synthetic jet actuators (SJAs). CFD simulation methods have been implemented to uncover the flow separation regimes and associated properties such as frequencies and momentum ratio. In the first part of the study, the SJA was studied thoroughly. Large Eddy Simulations (LES) were performed for one individual cavity; the time history of SJA of the outlet velocity profile and the net momentum imparted to the flow were analyzed. The studied SJA is asymmetrical and operates with the aid of a piezoelectric (PZT) ceramic circular plate actuator. A three-dimensional mesh for the computational domain of the SJA and the surrounding volume was developed and was used to evaluate the details of the airflow conditions inside the SJA as well as at the outlet. The vibration of the PZT ceramic actuator was used as a boundary condition in the computational model to drive the SJA. Particular attention was given to developing a predictive model of the SJA outlet velocity. Results showed that the SJA velocity output is correlated to the PZT ceramic plate vibration, especially for the first frequency mode. SJAs are a particular class of zero net mass flux (ZNMF) fluidic devices with net imparted momentum to the flow. The net momentum imparted to the flow in the separated region is such that positive enhancement during AFC operations is achieved. Flows around the NACA 0015 airfoil were simulated for a range of operating conditions. Attention was given to the active open and closed loop control solutions for an airfoil with SJA at different angles of attack and flap angles. A large number of simulations using RANS & LES models were performed to study the effects of the momentum ratio (Cμ) in the range of 0 to 11% and of the non-dimensional frequency, F+, in the range of 0 to 2 for the control of flow separation at a practical angle of attack and flap angle. The optimum value of C
A Multiobjective Optimization Framework for Stochastic Control of Complex Systems
Energy Technology Data Exchange (ETDEWEB)
Malikopoulos, Andreas [ORNL; Maroulas, Vasileios [ORNL; Xiong, Professor Jie [The University of Tennessee
2015-01-01
This paper addresses the problem of minimizing the long-run expected average cost of a complex system consisting of subsystems that interact with each other and the environment. We treat the stochastic control problem as a multiobjective optimization problem of the one-stage expected costs of the subsystems, and we show that the control policy yielding the Pareto optimal solution is an optimal control policy that minimizes the average cost criterion for the entire system. For practical situations with constraints consistent to those we study here, our results imply that the Pareto control policy may be of value in deriving online an optimal control policy in complex systems.
Institute of Scientific and Technical Information of China (English)
Bing SUN; Baozhu GUO
2005-01-01
This paper is concerned with an optimal control problem of an ablation-transpiration cooling control system with Stefan-Signorini boundary condition.As the continuation of the authors'previous paper,the Dubovits Rii-Milyutin functional approach is again adopted in investigation of the Pontryagin's maximun principle of the system.The necessary optimality condition is presented for the problem with free final horizon and phase constraints.
Directory of Open Access Journals (Sweden)
Javed Ali
2012-01-01
Full Text Available We solve some higher-order boundary value problems by the optimal homotopy asymptotic method (OHAM. The proposed method is capable to handle a wide variety of linear and nonlinear problems effectively. The numerical results given by OHAM are compared with the exact solutions and the solutions obtained by Adomian decomposition (ADM, variational iteration (VIM, homotopy perturbation (HPM, and variational iteration decomposition method (VIDM. The results show that the proposed method is more effective and reliable.
Mesh refinement strategy for optimal control problems
Paiva, L. T.; Fontes, F. A. C. C.
2013-10-01
Direct methods are becoming the most used technique to solve nonlinear optimal control problems. Regular time meshes having equidistant spacing are frequently used. However, in some cases these meshes cannot cope accurately with nonlinear behavior. One way to improve the solution is to select a new mesh with a greater number of nodes. Another way, involves adaptive mesh refinement. In this case, the mesh nodes have non equidistant spacing which allow a non uniform nodes collocation. In the method presented in this paper, a time mesh refinement strategy based on the local error is developed. After computing a solution in a coarse mesh, the local error is evaluated, which gives information about the subintervals of time domain where refinement is needed. This procedure is repeated until the local error reaches a user-specified threshold. The technique is applied to solve the car-like vehicle problem aiming minimum consumption. The approach developed in this paper leads to results with greater accuracy and yet with lower overall computational time as compared to using a time meshes having equidistant spacing.
Optimal control theory for unitary transformations
Palao, J P; Palao, Jose P.
2003-01-01
The dynamics of a quantum system driven by an external field is well described by a unitary transformation generated by a time dependent Hamiltonian. The inverse problem of finding the field that generates a specific unitary transformation is the subject of study. The unitary transformation which can represent an algorithm in a quantum computation is imposed on a subset of quantum states embedded in a larger Hilbert space. Optimal control theory (OCT) is used to solve the inversion problem irrespective of the initial input state. A unified formalism, based on the Krotov method is developed leading to a new scheme. The schemes are compared for the inversion of a two-qubit Fourier transform using as registers the vibrational levels of the $X^1\\Sigma^+_g$ electronic state of Na$_2$. Raman-like transitions through the $A^1\\Sigma^+_u$ electronic state induce the transitions. Light fields are found that are able to implement the Fourier transform within a picosecond time scale. Such fields can be obtained by pulse-...
Optimal decentralized feedback control for a truss structure
Cagle, A.; Ozguner, U.
1989-01-01
One approach to the decentralized control of large flexible space structures involves the design of controllers for the substructures of large systems and their subsequent application to the entire coupled system. This approach is presently developed for the case of active vibration damping on an experimental large struss structure. The isolated boundary loading method is used to define component models by FEM; component controllers are designed using an interlocking control concept which minimizes the motion of the boundary nodes, thereby reducing the exchange of mechanical disturbances among components.
Optimal Control Of Nonlinear Wave Energy Point Converters
DEFF Research Database (Denmark)
Nielsen, Søren R.K.; Zhou, Qiang; Kramer, Morten
2013-01-01
In this paper the optimal control law for a single nonlinear point absorber in irregular sea-states is derived, and proven to be a closed-loop controller with feedback from measured displacement, velocity and acceleration of the floater. However, a non-causal integral control component dependent...... idea behind the control strategy is to enforce the stationary velocity response of the absorber into phase with the wave excitation force at any time. The controller is optimal under monochromatic wave excitation. It is demonstrated that the devised causal controller, in plane irregular sea states......, absorbs almost the same power as the optimal controller....
Optimal Control for a Parallel Hybrid Hydraulic Excavator Using Particle Swarm Optimization
Directory of Open Access Journals (Sweden)
Dong-yun Wang
2013-01-01
Full Text Available Optimal control using particle swarm optimization (PSO is put forward in a parallel hybrid hydraulic excavator (PHHE. A power-train mathematical model of PHHE is illustrated along with the analysis of components’ parameters. Then, the optimal control problem is addressed, and PSO algorithm is introduced to deal with this nonlinear optimal problem which contains lots of inequality/equality constraints. Then, the comparisons between the optimal control and rule-based one are made, and the results show that hybrids with the optimal control would increase fuel economy. Although PSO algorithm is off-line optimization, still it would bring performance benchmark for PHHE and also help have a deep insight into hybrid excavators.
Aircraft nonlinear optimal control using fuzzy gain scheduling
Nusyirwan, I. F.; Kung, Z. Y.
2016-10-01
Fuzzy gain scheduling is a common solution for nonlinear flight control. The highly nonlinear region of flight dynamics is determined throughout the examination of eigenvalues and the irregular pattern of root locus plots that show the nonlinear characteristic. By using the optimal control for command tracking, the pitch rate stability augmented system is constructed and the longitudinal flight control system is established. The outputs of optimal control for 21 linear systems are fed into the fuzzy gain scheduler. This research explores the capability in using both optimal control and fuzzy gain scheduling to improve the efficiency in finding the optimal control gains and to achieve Level 1 flying qualities. The numerical simulation work is carried out to determine the effectiveness and performance of the entire flight control system. The simulation results show that the fuzzy gain scheduling technique is able to perform in real time to find near optimal control law in various flying conditions.
Presentation of Malaria Epidemics Using Multiple Optimal Controls
Directory of Open Access Journals (Sweden)
Abid Ali Lashari
2012-01-01
Full Text Available An existing model is extended to assess the impact of some antimalaria control measures, by re-formulating the model as an optimal control problem. This paper investigates the fundamental role of three type of controls, personal protection, treatment, and mosquito reduction strategies in controlling the malaria. We work in the nonlinear optimal control framework. The existence and the uniqueness results of the solution are discussed. A characterization of the optimal control via adjoint variables is established. The optimality system is solved numerically by a competitive Gauss-Seidel-like implicit difference method. Finally, numerical simulations of the optimal control problem, using a set of reasonable parameter values, are carried out to investigate the effectiveness of the proposed control measures.
Control Methods Utilizing Energy Optimizing Schemes in Refrigeration Systems
DEFF Research Database (Denmark)
Larsen, L.S; Thybo, C.; Stoustrup, Jakob;
2003-01-01
The potential energy savings in refrigeration systems using energy optimal control has been proved to be substantial. This however requires an intelligent control that drives the refrigeration systems towards the energy optimal state. This paper proposes an approach for a control, which drives...
Combined Optimal Sizing and Control for a Hybrid Tracked Vehicle
Directory of Open Access Journals (Sweden)
Huei Peng
2012-11-01
Full Text Available The optimal sizing and control of a hybrid tracked vehicle is presented and solved in this paper. A driving schedule obtained from field tests is used to represent typical tracked vehicle operations. Dynamics of the diesel engine-permanent magnetic AC synchronous generator set, the lithium-ion battery pack, and the power split between them are modeled and validated through experiments. Two coupled optimizations, one for the plant parameters, forming the outer optimization loop and one for the control strategy, forming the inner optimization loop, are used to achieve minimum fuel consumption under the selected driving schedule. The dynamic programming technique is applied to find the optimal controller in the inner loop while the component parameters are optimized iteratively in the outer loop. The results are analyzed, and the relationship between the key parameters is observed to keep the optimal sizing and control simultaneously.
Optimization and control methods in industrial engineering and construction
Wang, Xiangyu
2014-01-01
This book presents recent advances in optimization and control methods with applications to industrial engineering and construction management. It consists of 15 chapters authored by recognized experts in a variety of fields including control and operation research, industrial engineering, and project management. Topics include numerical methods in unconstrained optimization, robust optimal control problems, set splitting problems, optimum confidence interval analysis, a monitoring networks optimization survey, distributed fault detection, nonferrous industrial optimization approaches, neural networks in traffic flows, economic scheduling of CCHP systems, a project scheduling optimization survey, lean and agile construction project management, practical construction projects in Hong Kong, dynamic project management, production control in PC4P, and target contracts optimization. The book offers a valuable reference work for scientists, engineers, researchers and practitioners in industrial engineering and c...
Optimal control of a fed-batch fermentation
Energy Technology Data Exchange (ETDEWEB)
Dekkers, R.M.
1984-01-01
The common cultivation of bakers' yeast is an aerobic fed-batch fermentation under sugar-limited growth. The ultimate objective of on-line computer control is to optimize the process through maximizing the productivity of biomass formation while minimizing the consumption of raw materials for the product. Results obtained on the optimal control of a fed-batch fermentation are given. The aspects to be considered are instrumentation, state estimation, optimization and process control.
Dynamic consistency for Stochastic Optimal Control problems
Carpentier, Pierre; Cohen, Guy; De Lara, Michel; Girardeau, Pierre
2010-01-01
For a sequence of dynamic optimization problems, we aim at discussing a notion of consistency over time. This notion can be informally introduced as follows. At the very first time step $t_0$, the decision maker formulates an optimization problem that yields optimal decision rules for all the forthcoming time step $t_0, t_1, ..., T$; at the next time step $t_1$, he is able to formulate a new optimization problem starting at time $t_1$ that yields a new sequence of optimal decision rules. This process can be continued until final time $T$ is reached. A family of optimization problems formulated in this way is said to be time consistent if the optimal strategies obtained when solving the original problem remain optimal for all subsequent problems. The notion of time consistency, well-known in the field of Economics, has been recently introduced in the context of risk measures, notably by Artzner et al. (2007) and studied in the Stochastic Programming framework by Shapiro (2009) and for Markov Decision Processes...
A non-standard optimal control problem arising in an economics application
Directory of Open Access Journals (Sweden)
Alan Zinober
2013-04-01
Full Text Available A recent optimal control problem in the area of economics has mathematical properties that do not fall into the standard optimal control problem formulation. In our problem the state value at the final time the state, y(T = z, is free and unknown, and additionally the Lagrangian integrand in the functional is a piecewise constant function of the unknown value y(T. This is not a standard optimal control problem and cannot be solved using Pontryagin's Minimum Principle with the standard boundary conditions at the final time. In the standard problem a free final state y(T yields a necessary boundary condition p(T = 0, where p(t is the costate. Because the integrand is a function of y(T, the new necessary condition is that y(T should be equal to a certain integral that is a continuous function of y(T. We introduce a continuous approximation of the piecewise constant integrand function by using a hyperbolic tangent approach and solve an example using a C++ shooting algorithm with Newton iteration for solving the Two Point Boundary Value Problem (TPBVP. The minimising free value y(T is calculated in an outer loop iteration using the Golden Section or Brent algorithm. Comparative nonlinear programming (NP discrete-time results are also presented.
Contact position controlling for two-dimensional motion bodies by the boundary element method
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
An algorithm is presented for controlling two-dimensional motion contact bodies with conforming discretization. Since a kind of special boundary element is utilized in the algorithm, the displacement compatibility and traction equilibrium conditions at nodes can be satisfied simultaneously in arbitrary locations of the contact interface. In addition, a method is also proposed in which the contact boundary location can be moved flexibly on the possible contact boundary. This method is effective to deal with moving and rolling contact problems on a possible larger moving or rolling contact region. Numerical examples show effectiveness of the presented scheme.
Lyapunov-based boundary feedback control in multi-reach canals
Institute of Scientific and Technical Information of China (English)
CEN LiHui; XI YuGeng
2009-01-01
This paper presents a Lyapunov-based approach to design the boundary feedback control for an open-channel network composed of a cascade of multi-reach canals, each described by a pair of Saint-Venant equations. The weighted sum of entropies of the multi-reaches is adopted to construct the Lyapunov function. The time derivative of the Lyapunov function is expressed by the water depth variations at the gate boundaries, based on which a class of boundary feedback controllers is presented to guarantee the local asymptotic closed-loop stability. The advantage of this approach is that only the water level depths at the gate boundaries are measured as the feedback.
Control Parameters for Boundary-Layer Instabilities in Unsteady Shock Interactions
Directory of Open Access Journals (Sweden)
LaVar King Isaacson
2012-01-01
Full Text Available This article presents the computation of a set of control parameters for the deterministic prediction of laminar boundary-layer instabilities induced by an imposed unsteady shock interaction. The objective of the study is exploratory in nature by computing a supersonic flight environment for flow over a blunt body and the deterministic prediction of the spectral entropy rates for the boundary layer subjected to an unsteady pressure disturbance. The deterministic values for the spectral entropy rate within the instabilities are determined for each control parameter. Computational results imply that the instabilities are of a span-wise vortex form, that the maximum vertical velocity wave vector components are produced in the region nearest the wall and that extended transient coherent structures are produced in the boundary layer at a vertical location slightly below the mid-point of the boundary layer.
Calculus of variations and optimal control theory a concise introduction
Liberzon, Daniel
2011-01-01
This textbook offers a concise yet rigorous introduction to calculus of variations and optimal control theory, and is a self-contained resource for graduate students in engineering, applied mathematics, and related subjects. Designed specifically for a one-semester course, the book begins with calculus of variations, preparing the ground for optimal control. It then gives a complete proof of the maximum principle and covers key topics such as the Hamilton-Jacobi-Bellman theory of dynamic programming and linear-quadratic optimal control. Calculus of Variations and Optimal Control Theory
Boundary-induced nucleation control: a theoretical perspective
Buller, Oleg; Wang, Wenchong; Chi, Lifeng; Heuer, Andreas
2015-01-01
The prepatterning of a substrate with gold allows one to generate a variety of structures in vapor deposition experiments of organic semiconducting molecules. A particular interesting structure is generated if the gold is forming a rectangular grid. For specific combinations of the molecule flux, the substrate temperature and the lattice size it is possible to generate exactly one cluster per cell, denoted nucleation control. Here we show that the experimental observations of nucleation control can be very well understood from a theoretical perspective. For this purpose we perform, on the one hand, kinetic Monte Carlo simulations and, on the other hand, use scaling arguments to rationalize the observed behavior. For several observables, characterizing nucleation control, we find a very good agreement between experiment and theory.
A mathematical formulation for optimal control of air pollution
Institute of Scientific and Technical Information of China (English)
朱江; 曾庆存
2003-01-01
The problem of optimal control of air pollution using weather forecastresults and numerical air pollution models is discussed. A mathematical formulation of the problem is presented. The control is an act on pollution sources with feasible constraints. Based on forecasted weather conditions, the objective ofthe optimal control is to minimize total cost caused by control under the constraint that the pollution concentrations over a certain period and a certain spatial domain are less than some specified values. Using the adjoint method, an effective algorithm is given. Since the optimal solutions are based on weather forecasts, the errors in weather forecasts will cause uncertainties in the optimal solutions. Estimation of impacts of weather forecast errors on the optimal solutions is discussed using the adjoint sensitivity analysis technique that is an approximated, however very effective method. The adjoint sensitivity analysis technique can be used to calculate the impacts of errors in wind, temperature and initial pollutant concentration fields on performances of the optimal control.
Optimal parametric sensitivity control for a fed-batch reactor
Stigter, J.D.; Keesman, K.J.
2001-01-01
The paper presents a method to derive an optimal parametric sensitivity controller for optimal estimation of a set of parameters in an experiment. The method is demonstrated for a fed batch bio-reactor case study for optimal estimation of the saturation constant Ks and, albeit intuitively, the param
Minimum energy control and optimal-satisfactory control of Boolean control network
Energy Technology Data Exchange (ETDEWEB)
Li, Fangfei, E-mail: li_fangfei@163.com; Lu, Xiwen
2013-12-09
In the literatures, to transfer the Boolean control network from the initial state to the desired state, the expenditure of energy has been rarely considered. Motivated by this, this Letter investigates the minimum energy control and optimal-satisfactory control of Boolean control network. Based on the semi-tensor product of matrices and Floyd's algorithm, minimum energy, constrained minimum energy and optimal-satisfactory control design for Boolean control network are given respectively. A numerical example is presented to illustrate the efficiency of the obtained results.
Using Lyapunov function to design optimal controller for AQM routers
Institute of Scientific and Technical Information of China (English)
ZHANG Peng; YE Cheng-qing; MA Xue-ying; CHEN Yan-hua; LI Xin
2007-01-01
It was shown that active queue management schemes implemented in the routers of communication networks supporting transmission control protocol (TCP) flows can be modelled as a feedback control system. In this paper based on Lyapunov function we developed an optimal controller to improve active queue management (AQM) router's stability and response time,which are often in conflict with each other in system performance. Ns-2 simulations showed that optimal controller outperforms PI controller significantly.
Directory of Open Access Journals (Sweden)
Yangwei Liu
2014-11-01
Full Text Available Control of corner separation has attracted much interest due to its improvement of performance and energy utilization in turbomachinery. Numerical studies have been performed under both design and off-design flow conditions to investigate the effects of boundary layer suction (BLS on corner separation in a highly loaded compressor cascade. Two new BLS slot configurations are proposed and a total of five suction slot configurations were studied and compared. Averaged static pressure rise, exit loss coefficient, passage blockage and flow turning angle have been given and compared systematically over a range of operation incidence angles. Distributions of significant loss removal, blade loading, exit deviation and total pressure loss at 3 degree and 7 degree incidence have also been studied. Under the same suction mass flows of 0.7% of the inlet mass flows, the pitchwise suction slot on the endwall shows a better optimal performance over the whole operation incidence among single suction slots. By using of the new proposed compound slot configuration with one spanwise slot on the blade suction side and one pitchwise slot on the endwall, the maximum reduction of total pressure loss at 7 degree incidence can be 39.4%.
Hierarchical control based on Hopfield network for nonseparable optimization problems
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
The nonseparable optimization control problem is considered, where the overall objective function is not of an additive form with respect to subsystems. Since there exists the problem that computation is very slow when using iterative algorithms in multiobjective optimization, Hopfield optimization hierarchical network based on IPM is presented to overcome such slow computation difficulty. Asymptotic stability of this Hopfield network is proved and its equilibrium point is the optimal point of the original problem. The simulation shows that the net is effective to deal with the optimization control problem for large-scale nonseparable steady state systems.
H2-optimal control with generalized state-space models for use in control-structure optimization
Wette, Matt
1991-01-01
Several advances are provided solving combined control-structure optimization problems. The author has extended solutions from H2 optimal control theory to the use of generalized state space models. The generalized state space models preserve the sparsity inherent in finite element models and hence provide some promise for handling very large problems. Also, expressions for the gradient of the optimal control cost are derived which use the generalized state space models.
Study on optimization control method based on artificial neural network
Institute of Scientific and Technical Information of China (English)
FU Hua; SUN Shao-guang; XU Zhen-Iiang
2005-01-01
In the goal optimization and control optimization process the problems with common artificial neural network algorithm are unsure convergence, insufficient post-training network precision, and slow training speed, in which partial minimum value question tends to occur. This paper conducted an in-depth study on the causes of the limitations of the algorithm, presented a rapid artificial neural network algorithm, which is characterized by integrating multiple algorithms and by using their complementary advantages. The salient feature of the method is self-organization, which can effectively prevent the optimized results from tending to be partial minimum values. Overall optimization can be achieved with this method, goal function can be searched for in overall scope. With optimization control of coal mine ventilator as a practical application, the paper proves that by integrating multiple artificial neural network algorithms, best control optimization and goal optimized can be achieved.
OPTIMAL CONTROL OF CNC CUTTING PROCESS
Institute of Scientific and Technical Information of China (English)
无
1999-01-01
The intelligent optimizing method of cutting parameters and the cutting stable districts searching method are set up. The cutting parameters of each cutting pass could be optimized automatically, the cutting chatter is predicted through setting up the dynamic cutting force AR(2) model on-line, the spindle rotation speed is adjusted according to the predicting results so as to ensure the cutting system work in stable district.
The Merlin Control Language for strategic optimization
Papageorgiou, D. G.; Demetropoulos, I. N.; Lagaris, I. E.
1998-04-01
MCL is the programming language of the MERLIN optimization environment. It can be used for the implementation of efficient optimization strategies, abolishing to a great extend the need for user intervention. The language is simple to learn and its structure is similar to Fortran. We report on successful applications where MCL played an instrumental role, as for example in molecular physics problems and in the training of neural networks.
Effect of boundary on controlled memristor-based oscillator
Fouda, Mohamed E.
2012-10-01
Recently, the applications of memristors have spread into many fields and especially in the circuit theory. Many models have been proposed for the HP-memristor based on the window functions. In this paper, we introduce a complete mathematical analysis of the controlled reactance-less oscillator for two different window functions of Joglekar\\'s model (linear and nonlinear dopant drift) to discuss the effect of changing the window function on the oscillator\\'s behavior. The generalized necessary and sufficient conditions based on the circuit elements and control voltages for both the linear and nonlinear models are introduced. Moreover, closed form expressions for the oscillation frequency and duty cycle are derived for these models and verified using PSPICE simulations showing an excellent matching. Finally a comparison between the linear and nonlinear models which shows their effect on the oscillation frequency and conditions of oscillation is introduced. © 2012 IEEE.
Nonlinear model predictive control based on collective neurodynamic optimization.
Yan, Zheng; Wang, Jun
2015-04-01
In general, nonlinear model predictive control (NMPC) entails solving a sequential global optimization problem with a nonconvex cost function or constraints. This paper presents a novel collective neurodynamic optimization approach to NMPC without linearization. Utilizing a group of recurrent neural networks (RNNs), the proposed collective neurodynamic optimization approach searches for optimal solutions to global optimization problems by emulating brainstorming. Each RNN is guaranteed to converge to a candidate solution by performing constrained local search. By exchanging information and iteratively improving the starting and restarting points of each RNN using the information of local and global best known solutions in a framework of particle swarm optimization, the group of RNNs is able to reach global optimal solutions to global optimization problems. The essence of the proposed collective neurodynamic optimization approach lies in the integration of capabilities of global search and precise local search. The simulation results of many cases are discussed to substantiate the effectiveness and the characteristics of the proposed approach.
Empirical Reduced-Order Modeling for Boundary Feedback Flow Control
Directory of Open Access Journals (Sweden)
Seddik M. Djouadi
2008-01-01
Full Text Available This paper deals with the practical and theoretical implications of model reduction for aerodynamic flow-based control problems. Various aspects of model reduction are discussed that apply to partial differential equation- (PDE- based models in general. Specifically, the proper orthogonal decomposition (POD of a high dimension system as well as frequency domain identification methods are discussed for initial model construction. Projections on the POD basis give a nonlinear Galerkin model. Then, a model reduction method based on empirical balanced truncation is developed and applied to the Galerkin model. The rationale for doing so is that linear subspace approximations to exact submanifolds associated with nonlinear controllability and observability require only standard matrix manipulations utilizing simulation/experimental data. The proposed method uses a chirp signal as input to produce the output in the eigensystem realization algorithm (ERA. This method estimates the system's Markov parameters that accurately reproduce the output. Balanced truncation is used to show that model reduction is still effective on ERA produced approximated systems. The method is applied to a prototype convective flow on obstacle geometry. An H∞ feedback flow controller is designed based on the reduced model to achieve tracking and then applied to the full-order model with excellent performance.
Ruiz-Cruz, Riemann; Sanchez, Edgar N; Ornelas-Tellez, Fernando; Loukianov, Alexander G; Harley, Ronald G
2013-12-01
In this paper, the authors propose a particle swarm optimization (PSO) for a discrete-time inverse optimal control scheme of a doubly fed induction generator (DFIG). For the inverse optimal scheme, a control Lyapunov function (CLF) is proposed to obtain an inverse optimal control law in order to achieve trajectory tracking. A posteriori, it is established that this control law minimizes a meaningful cost function. The CLFs depend on matrix selection in order to achieve the control objectives; this matrix is determined by two mechanisms: initially, fixed parameters are proposed for this matrix by a trial-and-error method and then by using the PSO algorithm. The inverse optimal control scheme is illustrated via simulations for the DFIG, including the comparison between both mechanisms.
SUPERCONVERGENCE AND A POSTERIORI ERROR ESTIMATES FOR BOUNDARY CONTROL GOVERNED BY STOKES EQUATIONS
Institute of Scientific and Technical Information of China (English)
Hui-po Liu; Ning-ning Yan
2006-01-01
In this paper, the superconvergence results are derived for a class of boundary control problems governed by Stokes equations. We derive superconvergence results for both the control and the state approximation. Base on superconvergence results, we obtain asymptotically exact a posteriori error estimates.
Directory of Open Access Journals (Sweden)
Fengyan Yang
2016-09-01
Full Text Available This article studies the exact controllability of an Euler-Bernoulli plate equation with variable coefficients, subject to the simply supported boundary condition. By the Riemannian geometry approach, the duality method, the multiplier technique, and the compactness-uniqueness argument, we establish the corresponding observability inequality and obtain the exact controllability results.
Directory of Open Access Journals (Sweden)
Ioan Bejenaru
2001-07-01
Full Text Available In this paper we prove an approximate controllability result for an abstract semilinear evolution equation in a Hilbert space and we obtain as consequences the approximate controllability for some classes of elliptic and parabolic problems subjected to nonlinear, possible non monotone, dynamic boundary conditions.
Ramirez, Hector; Le Gorrec, Yann; Zwart, Hans
2013-01-01
This paper deals with the control of a class of simplified models for flexible micro-grippers for DNA manipulation. The overall system is first modeled as a boundary controlled port-Hamiltonian system made up as the interconnection of an infinite-dimensional systems (modeled as an undamped Timoshenk
Robust output LQ optimal control via integral sliding modes
Fridman, Leonid; Bejarano, Francisco Javier
2014-01-01
Featuring original research from well-known experts in the field of sliding mode control, this monograph presents new design schemes for implementing LQ control solutions in situations where the output system is the only information provided about the state of the plant. This new design works under the restrictions of matched disturbances without losing its desirable features. On the cutting-edge of optimal control research, Robust Output LQ Optimal Control via Integral Sliding Modes is an excellent resource for both graduate students and professionals involved in linear systems, optimal control, observation of systems with unknown inputs, and automatization. In the theory of optimal control, the linear quadratic (LQ) optimal problem plays an important role due to its physical meaning, and its solution is easily given by an algebraic Riccati equation. This solution turns out to be restrictive, however, because of two assumptions: the system must be free from disturbances and the entire state vector must be kn...
Optimization and Convergence of Observation Channels in Stochastic Control
Yüksel, Serdar
2010-01-01
This paper studies the optimization of observation channels (stochastic kernels) in partially observed stochastic control problems. In particular, existence, continuity, and convexity properties are investigated. Continuity properties of the optimal cost in channels are explored under total variation, setwise convergence and weak convergence. Sufficient conditions for sequential compactness under total variation and setwise convergence are presented. It is shown that the optimization is concave in observation channels. This implies that the optimization problem is non-convex in quantization/coding policies for a class of networked control problems. Applications in optimal quantizer/coder design and robust control are presented, where new results on the existence of optimal quantizers are obtained. Furthermore, the paper explains why a class of decentralized control problems, under the non-classical information structure, is non-convex when {\\em signaling} is present. Finally, empirical con sistency of a class...
Optimal control of stochastic difference Volterra equations an introduction
Shaikhet, Leonid
2015-01-01
This book showcases a subclass of hereditary systems, that is, systems with behaviour depending not only on their current state but also on their past history; it is an introduction to the mathematical theory of optimal control for stochastic difference Volterra equations of neutral type. As such, it will be of much interest to researchers interested in modelling processes in physics, mechanics, automatic regulation, economics and finance, biology, sociology and medicine for all of which such equations are very popular tools. The text deals with problems of optimal control such as meeting given performance criteria, and stabilization, extending them to neutral stochastic difference Volterra equations. In particular, it contrasts the difference analogues of solutions to optimal control and optimal estimation problems for stochastic integral Volterra equations with optimal solutions for corresponding problems in stochastic difference Volterra equations. Optimal Control of Stochastic Difference Volterra Equation...
Optimal control of photoelectron emission by realistic waveforms
Solanpää, Janne; Räsänen, Esa
2016-01-01
Recent experimental techniques in multicolor waveform synthesis allow the temporal shaping of strong femtosecond laser pulses with applications in the control of quantum mechanical processes in atoms, molecules, and nanostructures. Prediction of the shapes of the optimal waveforms can be done computationally using quantum optimal control theory (QOCT). In this work we bring QOCT to experimental feasibility by providing an optimal control scheme with realistic pulse representation. We apply the technique to optimal control of above-threshold photoelectron emission from a one-dimensional hydrogen atom. By mixing different spectral channels and thus lowering the intensity requirements for individual channels, the resulting optimal pulses can extend the cutoff energies by at least up to 50% and bring up the electron yield by several orders of magnitude. Insights into the electron dynamics for optimized photoelectron emission are obtained with a semiclassical two-step model.
Optimal Control of Vehicular Formations with Nearest Neighbor Interactions
Lin, Fu; Jovanović, Mihailo R
2011-01-01
We consider the design of optimal localized feedback gains for one-dimensional formations in which vehicles only use information from their immediate neighbors. The control objective is to enhance coherence of the formation by making it behave like a rigid lattice. For the single-integrator model with symmetric gains, we establish convexity, implying that the globally optimal controller can be computed efficiently. We also identify a class of convex problems for double-integrators by restricting the controller to symmetric position and uniform diagonal velocity gains. To obtain the optimal non-symmetric gains for both the single- and the double-integrator models, we solve a parameterized family of optimal control problems ranging from an easily solvable problem to the problem of interest as the underlying parameter increases. When this parameter is kept small, we employ perturbation analysis to decouple the matrix equations that result from the optimality conditions, thereby rendering the unique optimal feedb...
A time-delay equation: well-posedness to optimal control
Directory of Open Access Journals (Sweden)
Yildirim Kenan
2016-01-01
Full Text Available In this paper, well-posedness, controllability and optimal control for a time-delay beam equation are studied. The equation of motion is modeled as a time-delayed distributed parameter system(DPS and includes Heaviside functions and their spatial derivatives due to the finite size of piezoelectric patch actuators used to suppress the excessive vibrations based on displacement and moment conditions. The optimal control problem is defined with the performance index including a weighted quadratic functional of the displacement and velocity which is to be minimized at a given terminal time and a penalty term defined as the control voltage used in the control duration. Optimal control law is obtained by using Maximum principle and hence, the optimal control problem is transformed the into a boundary-, initial and terminal value problem.The explicit solution of the control problem is obtained by eigenfunction expansions of the state and adjoint variables. Numerical results are presented to show the effectiveness and applicability of the piezoelectric control.
Directory of Open Access Journals (Sweden)
Anzhou Cao
2013-01-01
Full Text Available Based on the theory of inverse problem, the optimization of open boundary conditions (OBCs in a 3D internal tidal model is investigated with the adjoint method. Fourier coefficients of M2 internal tide on four open boundaries, which are regarded as OBCs, are inverted simultaneously. During the optimization, the steepest descent method is used to minimize cost function. The reasonability and feasibility of the model are tested by twin experiments (TEs. In TE1, OBCs on four open boundaries are successfully inverted by using independent point (IP strategy, suggesting that IP strategy is useful in parameter estimation. Results of TE2 indicate that the model is effective even by assimilating inaccurate “observations.” Based on conclusions of TEs, the M2 internal tide around Hawaii is simulated by assimilating T/P data in practical experiment. The simulated cochart shows good agreement with that obtained from the Oregon State University tidal model and T/P observations. Careful inspection shows that the major difference between simulated results and OSU model results is short-scale fluctuations superposed on coamplitude lines, which can be treated as the surface manifestation modulated by the internal tide. The computed surface manifestation along T/P tracks is comparable to the estimation in previous work.
Optimal Control for a Class of Chaotic Systems
Directory of Open Access Journals (Sweden)
Jianxiong Zhang
2012-01-01
Full Text Available This paper proposes the optimal control methods for a class of chaotic systems via state feedback. By converting the chaotic systems to the form of uncertain piecewise linear systems, we can obtain the optimal controller minimizing the upper bound on cost function by virtue of the robust optimal control method of piecewise linear systems, which is cast as an optimization problem under constraints of bilinear matrix inequalities (BMIs. In addition, the lower bound on cost function can be achieved by solving a semidefinite programming (SDP. Finally, numerical examples are given to illustrate the results.
PID control for chaotic synchronization using particle swarm optimization
Energy Technology Data Exchange (ETDEWEB)
Chang, W.-D. [Department of Computer and Communication, Shu-Te University, Kaohsiung 824, Taiwan (China)], E-mail: wdchang@mail.stu.edu.tw
2009-01-30
In this paper, we attempt to use the proportional-integral-derivative (PID) controller to achieve the chaos synchronization for delayed discrete chaotic systems. Three PID control gains can be optimally determined by means of using a novel optimization algorithm, called the particle swarm optimization (PSO). The algorithm is motivated from the organism behavior of fish schooling and bird flocking, and involves the social psychology principles in socio-cognition human agents and evolutionary computations. It has a good numerical convergence for solving optimization problem. To show the validity of the PSO-based PID control for chaos synchronization, several cases with different initial populations are considered and some simulation results are shown.
Stochastic Optimal Control for Series Hybrid Electric Vehicles
Energy Technology Data Exchange (ETDEWEB)
Malikopoulos, Andreas [ORNL
2013-01-01
Increasing demand for improving fuel economy and reducing emissions has stimulated significant research and investment in hybrid propulsion systems. In this paper, we address the problem of optimizing online the supervisory control in a series hybrid configuration by modeling its operation as a controlled Markov chain using the average cost criterion. We treat the stochastic optimal control problem as a dual constrained optimization problem. We show that the control policy that yields higher probability distribution to the states with low cost and lower probability distribution to the states with high cost is an optimal control policy, defined as an equilibrium control policy. We demonstrate the effectiveness of the efficiency of the proposed controller in a series hybrid configuration and compare it with a thermostat-type controller.
Optimal Vibration Control for Tracked Vehicle Suspension Systems
Directory of Open Access Journals (Sweden)
Yan-Jun Liang
2013-01-01
Full Text Available Technique of optimal vibration control with exponential decay rate and simulation for vehicle active suspension systems is developed. Mechanical model and dynamic system for a class of tracked vehicle suspension vibration control is established and the corresponding system of state space form is described. In order to prolong the working life of suspension system and improve ride comfort, based on the active suspension vibration control devices and using optimal control approach, an optimal vibration controller with exponential decay rate is designed. Numerical simulations are carried out, and the control effects of the ordinary optimal controller and the proposed controller are compared. Numerical simulation results illustrate the effectiveness of the proposed technique.
Fuzzy controller based on chaos optimal design and its application
Institute of Scientific and Technical Information of China (English)
邹恩; 李祥飞; 张泰山
2004-01-01
In order to overcome difficulty of tuning parameters of fuzzy controller, a chaos optimal design method based on annealing strategy is proposed. First, apply the chaotic variables to search for parameters of fuzzy controller, and transform the optimal variables into chaotic variables by carrier-wave method. Making use of the intrinsic stochastic property and ergodicity of chaos movement to escape from the local minimum and direct optimization searching within global range, an approximate global optimal solution is obtained. Then, the chaos local searching and optimization based on annealing strategy are cited, the parameters are optimized again within the limits of the approximate global optimal solution, the optimization is realized by means of combination of global and partial chaos searching, which can converge quickly to global optimal value. Finally, the third order system and discrete nonlinear system are simulated and compared with traditional method of fuzzy control. The results show that the new chaos optimal design method is superior to fuzzy control method, and that the control results are of high precision, with no overshoot and fast response.
Robustified time-optimal control of uncertain structural dynamic systems
Liu, Qiang; Wie, Bong
1991-01-01
A new approach for computing open-loop time-optimal control inputs for uncertain linear dynamical systems is developed. In particular, the single-axis, rest-to-rest maneuvering problem of flexible spacecraft in the presence of uncertainty in model parameters is considered. Robustified time-optimal control inputs are obtained by solving a parameter optimization problem subject to robustness constraints. A simple dynamical system with a rigid-body mode and one flexible mode is used to illustrate the concept.
ON THE OPTIMAL CONTROL COMPUTATION OF LINEAR SYSTEMS
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H. Tjahjana
2012-05-01
Full Text Available In this paper, we consider a numerical method for designing optimal controlon Linear Quadratic Regulator (LQR problem. In the optimal control design process through Pontryagin Maximum Principle (PMP, we obtain a system of diferential equations in state and costate variables. This system lacks of initial condition on the adjoint variables, and this situation creates classic dificulty for solving optimal control problems.This paper proposes a constructive method to approximate the initial condition of the adjoint system.
Optimal Control with Time Delays via the Penalty Method
Directory of Open Access Journals (Sweden)
Mohammed Benharrat
2014-01-01
Full Text Available We prove necessary optimality conditions of Euler-Lagrange type for a problem of the calculus of variations with time delays, where the delay in the unknown function is different from the delay in its derivative. Then, a more general optimal control problem with time delays is considered. Main result gives a convergence theorem, allowing us to obtain a solution to the delayed optimal control problem by considering a sequence of delayed problems of the calculus of variations.
Hocker, David Lance
The control of quantum systems occurs across a broad range of length and energy scales in modern science, and efforts have demonstrated that locating suitable controls to perform a range of objectives has been widely successful. The justification for this success arises from a favorable topology of a quantum control landscape, defined as a mapping of the controls to a cost function measuring the success of the operation. This is summarized in the landscape principle that no suboptimal extrema exist on the landscape for well-suited control problems, explaining a trend of successful optimizations in both theory and experiment. This dissertation explores what additional lessons may be gleaned from the quantum control landscape through numerical and theoretical studies. The first topic examines the experimentally relevant problem of assessing and reducing disturbances due to noise. The local curvature of the landscape is found to play an important role on noise effects in the control of targeted quantum unitary operations, and provides a conceptual framework for assessing robustness to noise. Software for assessing noise effects in quantum computing architectures was also developed and applied to survey the performance of current quantum control techniques for quantum computing. A lack of competition between robustness and perfect unitary control operation was discovered to fundamentally limit noise effects, and highlights a renewed focus upon system engineering for reducing noise. This convergent behavior generally arises for any secondary objective in the situation of high primary objective fidelity. The other dissertation topic examines the utility of quantum control for a class of nonlinear Hamiltonians not previously considered under the landscape principle. Nonlinear Schrodinger equations are commonly used to model the dynamics of Bose-Einstein condensates (BECs), one of the largest known quantum objects. Optimizations of BEC dynamics were performed in which the
Mikic, Gregor Veble; Stoll, Alex; Bevirt, JoeBen; Grah, Rok; Moore, Mark D.
2016-01-01
Theoretical and numerical aspects of aerodynamic efficiency of propulsion systems are studied. Focus is on types of propulsion that closely couples to the aerodynamics of the complete vehicle. We discuss the effects of local flow fields, which are affected both by conservative flow acceleration as well as total pressure losses, on the efficiency of boundary layer immersed propulsion devices. We introduce the concept of a boundary layer retardation turbine that helps reduce skin friction over the fuselage. We numerically investigate efficiency gains offered by boundary layer and wake interacting devices. We discuss the results in terms of a total energy consumption framework and show that efficiency gains offered depend on all the elements of the propulsion system.
Pseudospectral Optimal Control: Hidden Properties and Flight Results
2011-11-30
on solving optimal control problems , we focus on developing PS methods over arbitrary grids for Problem B. Such research can provides a unified...more efficient algorithms for solving optimal control problems , for example, multiscale PS methods for dynamical systems with different timescales
Educational Tool for Optimal Controller Tuning Using Evolutionary Strategies
Carmona Morales, D.; Jimenez-Hornero, J. E.; Vazquez, F.; Morilla, F.
2012-01-01
In this paper, an optimal tuning tool is presented for control structures based on multivariable proportional-integral-derivative (PID) control, using genetic algorithms as an alternative to traditional optimization algorithms. From an educational point of view, this tool provides students with the necessary means to consolidate their knowledge on…
On-line optimal control of greenhouse crop cultivation.
Straten, van G.
1996-01-01
Thus far, optimal control has primarily been investigated for seasonal crop growth optimization. On-line aspects have received much less attention. The decomposition between long term strategies and on-line control, however, is not trivial. Appreciable losses occur when set-points generated by seaso
On-line optimal control of greenhouse crop cultivation.
Straten, van G.
1996-01-01
Thus far, optimal control has primarily been investigated for seasonal crop growth optimization. On-line aspects have received much less attention. The decomposition between long term strategies and on-line control, however, is not trivial. Appreciable losses occur when set-points generated by seaso
Boundary control of a Timoshenko beam system with input dead-zone
He, Wei; Meng, Tingting; Liu, Jin-Kun; Qin, Hui
2015-06-01
In this paper, boundary control is designed for a Timoshenko beam system with the input dead-zone. By the Hamilton's principle, the dynamics of the Timoshenko beam system is represented by a distributed parameter model with two partial differential equations and four ordinary differential equations. The bounded part is separated from the input dead-zone and then forms the disturbance-like term together with the boundary disturbance, which finally acts on the Timoshenko beam system. Boundary control, based on the Lyapunov's direct method, is proposed to ensure the Timoshenko beam converge into a small neighbourhood of zero, where stability of the system is also analysed. Besides, the existence and uniqueness of the solution of the Timoshenko beam system are proved. Simulations are provided to reveal the applicability and effectiveness of the proposed control scheme.
Flow Modification over Rotor Blade with Suction Boundary Layer Control Technique
Directory of Open Access Journals (Sweden)
Navneet Kumar
2016-06-01
Full Text Available The efficiency of transonic aircraft engines depend upon the performance of compressor rotor. To increase compressor rotors performance flow separation around rotor blades must be delayed and controlled. The aim was to control the flow separation of blades using suction boundary layer control method. Rotor blade has been modelled in designing software CATIA and then a suction surface has been created on blade and then import these geometries to ANSYS-CFX 14.5 for computational analysis of flow around blades. Suction slot has been applied at the trailing edge of suction surface and Shear stress transport model has been used for computational analysis. Two different suction mass flow rates 1 kg/s and 1.5 kg/s have been used here and boundary layer separation effects have been changed and this could be readily seen that the velocity vectors have reattached, preventing the boundary layer separation at the suction surface of the blade.
Exploiting Higher-order Derivatives in Computational Optimal Control
Ross, I. Michael; Rea, Jeremy; Fahroo, Fariba
2002-01-01
Proceedings of the 10th Mediterranean Conference on Control and Automation -- MED 2002 , Lisbon, Portugal, July7 9-12, 2002 To facilitate generation of real-time solutions to nonlinear optimal control problems, we present a new way of approximating higher-order derivatives that arise in control systems. A Legendre pseudospectral method is presented to efficiently and accurately discretize optimal control problems governed by higher-order dynamical constraints. For mechanical systems, a re...
Turbulent boundary-layer control with spanwise travelling waves
Energy Technology Data Exchange (ETDEWEB)
Whalley, Richard D; Choi, Kwing-So, E-mail: Richard.Whalley@nottingham.ac.uk, E-mail: Kwing-So.Choi@nottingham.ac.uk [Faculty of Engineering, University of Nottingham, Nottingham, NG7 2RD (United Kingdom)
2011-12-22
It has been demonstrated through numerical simulations using Lorentz forcing that spanwise travelling waves on turbulent wall flows can lead to a skin-friction drag reduction on the order of 30%. As an aeronautical application of this innovative flow control technique, we have investigated into the use of Dielectric-Barrier-Discharge (DBD) plasma actuators to generate spanwise travelling waves in air. The near-wall structures modified by the spanwise travelling waves were studied using the PIV technique in a wind tunnel, while the associated turbulence statistics were carefully documented using hot-wire anemometry. We observed the spreading of low-speed fluid by the spanwise travelling streamwise vortices, which seems to have greatly attenuated the turbulence production process. This is very much in line with the finding of DNS studies, where wide low-speed ribbons replaced the low-speed streaks.
Optimization and Control of Electric Power Systems
Energy Technology Data Exchange (ETDEWEB)
Lesieutre, Bernard C. [Univ. of Wisconsin, Madison, WI (United States); Molzahn, Daniel K. [Univ. of Wisconsin, Madison, WI (United States)
2014-10-17
The analysis and optimization needs for planning and operation of the electric power system are challenging due to the scale and the form of model representations. The connected network spans the continent and the mathematical models are inherently nonlinear. Traditionally, computational limits have necessitated the use of very simplified models for grid analysis, and this has resulted in either less secure operation, or less efficient operation, or both. The research conducted in this project advances techniques for power system optimization problems that will enhance reliable and efficient operation. The results of this work appear in numerous publications and address different application problems include optimal power flow (OPF), unit commitment, demand response, reliability margins, planning, transmission expansion, as well as general tools and algorithms.
Directory of Open Access Journals (Sweden)
Ali Saghafinia
2013-12-01
Full Text Available Physical sensors have a key role in implementation of real-time vector control for an induction motor (IM drive. This paper presents a novel boundary layer fuzzy controller (NBLFC based on the boundary layer approach for speed control of an indirect field-oriented control (IFOC of an induction motor (IM drive using physical sensors. The boundary layer approach leads to a trade-off between control performances and chattering elimination. For the NBLFC, a fuzzy system is used to adjust the boundary layer thickness to improve the tracking performance and eliminate the chattering problem under small uncertainties. Also, to eliminate the chattering under the possibility of large uncertainties, the integral filter is proposed inside the variable boundary layer. In addition, the stability of the system is analyzed through the Lyapunov stability theorem. The proposed NBLFC based IM drive is implemented in real-time using digital signal processor (DSP board TI TMS320F28335. The experimental and simulation results show the effectiveness of the proposed NBLFC based IM drive at different operating conditions.
OPTIMAL THICKNESS OF A CYLINDRICAL SHELL - AN OPTIMAL CONTROL PROBLEM IN LINEAR ELASTICITY THEORY
Directory of Open Access Journals (Sweden)
Peter Nestler
2013-01-01
Full Text Available In this paper we discuss optimization problems for cylindrical tubeswhich are loaded by an applied force. This is a problem of optimal control in linear elasticity theory (shape optimization. We are looking for an optimal thickness minimizing the deflection (deformation of the tube under the influence of an external force. From basic equations of mechanics, we derive the equation of deformation. We apply the displacement approach from shell theory and make use of the hypotheses of Mindlin and Reissner. A corresponding optimal control problem is formulated and first order necessary conditions for the optimal solution (optimal thickness are derived. We present numerical examples which were solved by the finite element method.
Discrete-time optimal control and games on large intervals
Zaslavski, Alexander J
2017-01-01
Devoted to the structure of approximate solutions of discrete-time optimal control problems and approximate solutions of dynamic discrete-time two-player zero-sum games, this book presents results on properties of approximate solutions in an interval that is independent lengthwise, for all sufficiently large intervals. Results concerning the so-called turnpike property of optimal control problems and zero-sum games in the regions close to the endpoints of the time intervals are the main focus of this book. The description of the structure of approximate solutions on sufficiently large intervals and its stability will interest graduate students and mathematicians in optimal control and game theory, engineering, and economics. This book begins with a brief overview and moves on to analyze the structure of approximate solutions of autonomous nonconcave discrete-time optimal control Lagrange problems.Next the structures of approximate solutions of autonomous discrete-time optimal control problems that are discret...
Intrinsic Optimal Control for Mechanical Systems on Lie Group
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Chao Liu
2017-01-01
Full Text Available The intrinsic infinite horizon optimal control problem of mechanical systems on Lie group is investigated. The geometric optimal control problem is built on the intrinsic coordinate-free model, which is provided with Levi-Civita connection. In order to obtain an analytical solution of the optimal problem in the geometric viewpoint, a simplified nominal system on Lie group with an extra feedback loop is presented. With geodesic distance and Riemann metric on Lie group integrated into the cost function, a dynamic programming approach is employed and an analytical solution of the optimal problem on Lie group is obtained via the Hamilton-Jacobi-Bellman equation. For a special case on SO(3, the intrinsic optimal control method is used for a quadrotor rotation control problem and simulation results are provided to show the control performance.
Constrained optimal steady-state control for isolated traffic intersections
Institute of Scientific and Technical Information of China (English)
Jack HADDAD; David MAHALEL; Ilya IOSLOVICH; Per-Olof GUTMAN
2014-01-01
The steady-state or cyclic control problem for a simplified isolated traffic intersection is considered. The optimization problem for the green-red switching sequence is formulated with the help of a discrete-event max-plus model. Two steady-state control problems are formulated: optimal steady-state with green duration constraints, and optimal steady-state control with lost time. In the case when the criterion is a strictly increasing, linear function of the queue lengths, the steady-state control problems can be solved analytically. The structure of constrained optimal steady-state traffic control is revealed, and the effect of the lost time on the optimal solution is illustrated.
Optimal control of ratchets without spatial asymmetry
Energy Technology Data Exchange (ETDEWEB)
Chacon, Ricardo [Departamento de Fisica Aplicada, Escuela de IngenierIas Industriales, Universidad de Extremadura, Apartado Postal 382, E-06071 Badajoz (Spain)
2007-06-01
This work presents the following conjecture: to optimally enhance directed transport by symmetry breaking of temporal forces there exists a particular force waveform which allows us to deduce simple scaling laws from a quantitative interpretation of Curie's principle. These scaling laws explain in a general setting previous results for a great diversity of systems subjected to a standard biharmonic force and provide a quantitative criterion to optimize the application of the ratchet effect induced by symmetry breaking of temporal forces. Mathematical arguments justifying this conjecture are discussed. (fast track communication)
New Applications of Variational Analysis to Optimization and Control
Mordukhovich, Boris S.
We discuss new applications of advanced tools of variational analysis and generalized differentiation to a number of important problems in optimization theory, equilibria, optimal control, and feedback control design. The presented results are largely based on the recent work by the author and his collaborators. Among the main topics considered and briefly surveyed in this paper are new calculus rules for generalized differentiation of nonsmooth and set-valued mappings; necessary and sufficient conditions for new notions of linear subextremality and suboptimality in constrained problems; optimality conditions for mathematical problems with equilibrium constraints; necessary optimality conditions for optimistic bilevel programming with smooth and nonsmooth data; existence theorems and optimality conditions for various notions of Pareto-type optimality in problems of multiobjective optimization with vector-valued and set-valued cost mappings; Lipschitzian stability and metric regularity aspects for constrained and variational systems.
Active Optimal Control of the KdV Equation Using the Variational Iteration Method
Directory of Open Access Journals (Sweden)
Ismail Kucuk
2010-01-01
Full Text Available The optimal pointwise control of the KdV equation is investigated with an objective of minimizing a given performance measure. The performance measure is specified as a quadratic functional of the final state and velocity functions along with the energy due to open- and closed-loop controls. The minimization of the performance measure over the controls is subjected to the KdV equation with periodic boundary conditions and appropriate initial condition. In contrast to standard optimal control or variational methods, a direct control parameterization is used in this study which presents a distinct approach toward the solution of optimal control problems. The method is based on finite terms of Fourier series approximation of each time control variable with unknown Fourier coefficients and frequencies. He's variational iteration method for the nonlinear partial differential equations is applied to the problem and thus converting the optimal control of lumped parameter systems into a mathematical programming. A numerical simulation is provided to exemplify the proposed method.
Zhang, Huaguang; Feng, Tao; Yang, Guang-Hong; Liang, Hongjing
2015-07-01
In this paper, the inverse optimal approach is employed to design distributed consensus protocols that guarantee consensus and global optimality with respect to some quadratic performance indexes for identical linear systems on a directed graph. The inverse optimal theory is developed by introducing the notion of partial stability. As a result, the necessary and sufficient conditions for inverse optimality are proposed. By means of the developed inverse optimal theory, the necessary and sufficient conditions are established for globally optimal cooperative control problems on directed graphs. Basic optimal cooperative design procedures are given based on asymptotic properties of the resulting optimal distributed consensus protocols, and the multiagent systems can reach desired consensus performance (convergence rate and damping rate) asymptotically. Finally, two examples are given to illustrate the effectiveness of the proposed methods.
Stable MIMO Constrained Predictive Control with Steady state Objective Optimization
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
A two-stage multi-objective optimization model-predictive control algorithms(MPC) strategy is pre sented. A domain MPC controller with input constraints is used to increase freedom for steady-state objective and enhance stabilization of the controller. A steady-state objective optimization algorithm oriented to transient process is adopted to realize optimization of objectives else than dynamic control. It is proved that .the stabilization for both dynamic control and steady-state objective optimization can be guaranteed. The theoretical results are demonstrated and discussed using a distillation tower as the model. Theoretical analysis and simulation results show that this control strategy is efficient and provides a good strategic solution to practical process control.
Investigation of optimal control system for arc spraying
Institute of Scientific and Technical Information of China (English)
Li Heqi; Li Chunxu
2005-01-01
Arc-voltage feedback PID ( Proportional plus Integral plus Differential) controller and arc-current feedback PID controller are designed with an algorithm of discrete PID. In order to realize parameters optimization and adaptation of the arc-spraying process and to reduce blindness in selecting process parameters, a serial communication interface between PC and MCU (Micro Control Unit) is designed so that on-line modification of the PID control parameters is implemented. A genetic algorithm is adopted to optimize PID control parameters. Meanwhile, the error between the actual value and the setting value of spraying current is selected as the judgment criterion to determine the adaptability for the algorithm. The best optimal population of PID control parameters can be obtained, so that the optimal controlling in arc-spraying process is realized and an excellent coating of arc-spraying is obtained.
Effect of wind turbine response time on optimal dynamic induction control of wind farms
Munters, Wim; Meyers, Johan
2016-09-01
In this work, we extend recent research efforts on induction-based optimal control in large-eddy simulations of wind farms in the turbulent atmospheric boundary layer. More precisely, we investigate the effect of wind turbine response time to requested power setpoints on achievable power gains. We do this by including a time-filtering of the thrust coefficient setpoints in the optimal control framework. We consider simulation cases restricted to underinduction compared to the Betz limit, as well as cases that also allow overinduction. Optimization results show that, except for the most restrictive underinductive slow-response case, all cases still yield increases in energy extraction in the order of 10% and more.
Directory of Open Access Journals (Sweden)
Bankov Dimitrov Nikolay
2012-01-01
Full Text Available This work examines a series resonant DC/DC optimal trajectory controlled converter during operation above resonant frequency, taking into account the influence of the snubbers and matching transformer. We obtain expressions for the load characteristics, boundary curves between possible modes and limits of the soft commutation area. Computer simulation and experimental observation confirm the theoretical results.
Bankov Dimitrov Nikolay; Vuchev Stoyanov Aleksandar
2012-01-01
This work examines a series resonant DC/DC optimal trajectory controlled converter during operation above resonant frequency, taking into account the influence of the snubbers and matching transformer. We obtain expressions for the load characteristics, boundary curves between possible modes and limits of the soft commutation area. Computer simulation and experimental observation confirm the theoretical results.
Edge orientation for optimizing controllability of complex networks.
Xiao, Yan-Dong; Lao, Song-Yang; Hou, Lv-Lin; Bai, Liang
2014-10-01
Recently, as the controllability of complex networks attracts much attention, how to design and optimize the controllability of networks has become a common and urgent problem in the field of controlling complex networks. Previous work focused on the structural perturbation and neglected the role of edge direction to optimize the network controllability. In a recent work [Phys. Rev. Lett. 103, 228702 (2009)], the authors proposed a simple method to enhance the synchronizability of networks by assignment of link direction while keeping network topology unchanged. However, the controllability is fundamentally different from synchronization. In this work, we systematically propose the definition of assigning direction to optimize controllability, which is called the edge orientation for optimal controllability problem (EOOC). To solve the EOOC problem, we construct a switching network and transfer the EOOC problem to find the maximum independent set of the switching network. We prove that the principle of our optimization method meets the sense of unambiguity and optimum simultaneously. Furthermore, the relationship between the degree-degree correlations and EOOC are investigated by experiments. The results show that the disassortativity pattern could weaken the orientation for optimal controllability, while the assortativity pattern has no correlation with EOOC. All the experimental results of this work verify that the network structure determines the network controllability and the optimization effects.
Dynamics systems vs. optimal control--a unifying view.
Schaal, Stefan; Mohajerian, Peyman; Ijspeert, Auke
2007-01-01
In the past, computational motor control has been approached from at least two major frameworks: the dynamic systems approach and the viewpoint of optimal control. The dynamic system approach emphasizes motor control as a process of self-organization between an animal and its environment. Nonlinear differential equations that can model entrainment and synchronization behavior are among the most favorable tools of dynamic systems modelers. In contrast, optimal control approaches view motor control as the evolutionary or development result of a nervous system that tries to optimize rather general organizational principles, e.g., energy consumption or accurate task achievement. Optimal control theory is usually employed to develop appropriate theories. Interestingly, there is rather little interaction between dynamic systems and optimal control modelers as the two approaches follow rather different philosophies and are often viewed as diametrically opposing. In this paper, we develop a computational approach to motor control that offers a unifying modeling framework for both dynamic systems and optimal control approaches. In discussions of several behavioral experiments and some theoretical and robotics studies, we demonstrate how our computational ideas allow both the representation of self-organizing processes and the optimization of movement based on reward criteria. Our modeling framework is rather simple and general, and opens opportunities to revisit many previous modeling results from this novel unifying view.
SQUEEZE-E: The optimal solution for molecular simulations with periodic boundary conditions
Wassenaar, T.A.; de Vries, S.J.; Bonvin, A.M.J.J.; Bekker, H.
2012-01-01
In molecular simulations of macromolecules, it is desirable to limit the amount of solvent in the system to avoid spending computational resources on uninteresting solvent−solvent interactions. As a consequence, periodic boundary conditions are commonly used, with a simulation box chosen as small as
SQUEEZE-E : The Optimal Solution for Molecular Simulations with Periodic Boundary Conditions
Wassenaar, Tsjerk A.; de Vries, Sjoerd; Bonvin, Alexandre M. J. J.; Bekker, Henk
2012-01-01
In molecular simulations of macromolecules, it is desirable to limit the amount of solvent in the system to avoid spending computational resources on uninteresting solvent−solvent interactions. As a consequence, periodic boundary conditions are commonly used, with a simulation box chosen as small as
Eleiwi, Fadi
2015-07-01
This paper presents a nonlinear Lyapunov-based boundary control for the temperature difference of a membrane distillation boundary layers. The heat transfer mechanisms inside the process are modeled with a 2D advection-diffusion equation. The model is semi-descretized in space, and a nonlinear state-space representation is provided. The control is designed to force the temperature difference along the membrane sides to track a desired reference asymptotically, and hence a desired flux would be generated. Certain constraints are put on the control law inputs to be within an economic range of energy supplies. The effect of the controller gain is discussed. Simulations with real process parameters for the model, and the controller are provided. © 2015 American Automatic Control Council.
Analysis of Controlled Trajectory Optimization for Canard Trajectory Correction Fuze
Institute of Scientific and Technical Information of China (English)
郭泽荣; 李世义; 申强
2004-01-01
The optimization method of the canard trajectory correction fuze's controlled trajectory phase is researched by using the aerodynamics of aerocraft and the optimal control theory, the trajectory parameters of the controlled trajectory phase based on the least energy cost are determined. On the basis of determining the control starting point and the target point, the optimal trajectory and the variation rule of the normal overload with the least energy cost are provided, when there is no time restriction in the simulation process. The results provide a theoretical basis for the structure design of the canard mechanism.
Optimal control structure of combustion in coke oven battery
Directory of Open Access Journals (Sweden)
Karol Kostúr
2006-10-01
Full Text Available Big energetic aggregates require a complicated control system, which provide an effective running or production. Among these aggregates belongs the coke – oven battery. This article contains a proposal of the two – level control system. The basic control is realized by a direct digital control. The advanced control continuously optimalizes regulator parameters of the basic control. The present control system has been verified in real conditions of a coking plant.
Van Dijk, N.P.
2012-01-01
This thesis aims at understanding and improving topology optimization techniques focusing on density-based level-set methods and geometrical nonlinearities. Central in this work are the numerical modeling of the mechanical response of a design and the consistency of the optimization process itself.
Approximate optimal tracking control for near-surface AUVs with wave disturbances
Yang, Qing; Su, Hao; Tang, Gongyou
2016-10-01
This paper considers the optimal trajectory tracking control problem for near-surface autonomous underwater vehicles (AUVs) in the presence of wave disturbances. An approximate optimal tracking control (AOTC) approach is proposed. Firstly, a six-degrees-of-freedom (six-DOF) AUV model with its body-fixed coordinate system is decoupled and simplified and then a nonlinear control model of AUVs in the vertical plane is given. Also, an exosystem model of wave disturbances is constructed based on Hirom approximation formula. Secondly, the time-parameterized desired trajectory which is tracked by the AUV's system is represented by the exosystem. Then, the coupled two-point boundary value (TPBV) problem of optimal tracking control for AUVs is derived from the theory of quadratic optimal control. By using a recently developed successive approximation approach to construct sequences, the coupled TPBV problem is transformed into a problem of solving two decoupled linear differential sequences of state vectors and adjoint vectors. By iteratively solving the two equation sequences, the AOTC law is obtained, which consists of a nonlinear optimal feedback item, an expected output tracking item, a feedforward disturbances rejection item, and a nonlinear compensatory term. Furthermore, a wave disturbances observer model is designed in order to solve the physically realizable problem. Simulation is carried out by using the Remote Environmental Unit (REMUS) AUV model to demonstrate the effectiveness of the proposed algorithm.
Institute of Scientific and Technical Information of China (English)
TANG Hua-ping; PENG Ya-qing
2005-01-01
A kind of active vibration control method was presented through optimal design of driving load of multi-body system with quick startup and brake. Dynamical equation of multi-body system with quick startup and brake was built, and mathematical model of representing vibration control was also set up according to the moving process from startup to brake. Then optimization vibration control model of system driving load was founded by applying theory of optimization control, which takes rigid body moving variable of braking moment as the known condition, and vibration control equation of multi-body system with quick startup and brake was converted into boundary value problem of differential equation. The transient control algorithm of vibration was put forward, which is the analysis basis for the further research. Theoretical analysis and calculation of numerical examples show that the optimal design method for the multi-body system driving load can decrease the vibration of system with duplication.
Optimal Control and Forecasting of Complex Dynamical Systems
Grigorenko, Ilya
2006-01-01
This important book reviews applications of optimization and optimal control theory to modern problems in physics, nano-science and finance. The theory presented here can be efficiently applied to various problems, such as the determination of the optimal shape of a laser pulse to induce certain excitations in quantum systems, the optimal design of nanostructured materials and devices, or the control of chaotic systems and minimization of the forecast error for a given forecasting model (for example, artificial neural networks). Starting from a brief review of the history of variational calcul
Optimization of nonlinear controller with an enhanced biogeography approach
Directory of Open Access Journals (Sweden)
Mohammed Salem
2014-07-01
Full Text Available This paper is dedicated to the optimization of nonlinear controllers basing of an enhanced Biogeography Based Optimization (BBO approach. Indeed, The BBO is combined to a predator and prey model where several predators are used with introduction of a modified migration operator to increase the diversification along the optimization process so as to avoid local optima and reach the optimal solution quickly. The proposed approach is used in tuning the gains of PID controller for nonlinear systems. Simulations are carried out over a Mass spring damper and an inverted pendulum and has given remarkable results when compared to genetic algorithm and BBO.
A New Optimal Control System Design for Chemical Processes
Institute of Scientific and Technical Information of China (English)
丛二丁; 胡明慧; 涂善东; 邵惠鹤
2013-01-01
Based on frequency response and convex optimization, a novel optimal control system was developed for chemical processes. The feedforward control is designed to improve the tracking performance of closed loop chemical systems. The parametric model is not required because the system directly utilizes the frequency response of the loop transfer function, which can be measured accurately. In particular, the extremal values of magnitude and phase can be solved according to constrained quadratic programming optimizer and convex optimization. Simula-tion examples show the effectiveness of the method. The design method is simple and easily adopted in chemical industry.
Investigation of Optimal Control System for Arc Spraying
Institute of Scientific and Technical Information of China (English)
LIHe-qi; LIChun-xu; CHENKe-xuan; LUGuang
2004-01-01
An arc voltage feedback PID controller and arc current feedback PID controller are designed with a controlal gorithm of discrete PID separately to realize optimal control in computer controlling arc-spraying system. In order to realize optimization and adaptation of the arc-spraying process parameters as well as to reduce blindness in selecting process parameters, a serial communication interface between a PC for spraying data acquisition and a MCU of the control system is designed so that on-line modification of the PID control parameters is implemented. At the same time, a genetic algorithm is adopted to optimize the control parameters of PID controller, where the difference between the actually sampled value and the setting value of spraying current is made as the judgment criterion to determine the adaptability. The given range of control parameters varies from 0 to 15 and is to be encoded by a coding of four-bit binary string. The optimal population of control parameters of the PID controller can be obtained through reproduction, crossing and mutation, so that the optimal controlling in arc-spraying process is realized and an excellent coating of arc spraying is obtained.
Investigation of Optimal Control System for Arc Spraying
Institute of Scientific and Technical Information of China (English)
LI He-qi; LI Chun-xu; CHEN Ke-xuan; LU Guang
2004-01-01
An arc voltage feedback PID controller and arc current feedback PID controller are designed with a control algorithm of discrete PID separately to realize optimal control in computer controlling arc-spraying system. In order to realize optimization and adaptation of the arc-spraying process parameters as well as to reduce blindness in selecting process parameters, a serial communication interface between a PC for spraying data acquisition and a MCU of the control system is designed so that on-line modification of the PID control parameters is implemented. At the same time, a genetic algorithm is adopted to optimize the control parameters of PID controller, where the difference between the actually sampled value and the setting value of spraying current is made as the judgment criterion to determine the adaptability. The given range of control parameters varies from 0 to 15 and is to be encoded by a coding of four-bit binary string. The optimal population of control parameters of the PID controller can be obtained through reproduction, crossing and mutation,so that the optimal controlling in arc-spraying process is realized and an excellent coating of arc spraying is obtained.
5th International Conference on Optimization and Control with Applications
Teo, Kok; Zhang, Yi
2014-01-01
This book presents advances in state-of-the-art solution methods and their applications to real life practical problems in optimization, control and operations research. Contributions from world-class experts in the field are collated here in two parts, dealing first with optimization and control theory and then with techniques and applications. Topics covered in the first part include control theory on infinite dimensional Banach spaces, history-dependent inclusion and linear programming complexity theory. Chapters also explore the use of approximations of Hamilton-Jacobi-Bellman inequality for solving periodic optimization problems and look at multi-objective semi-infinite optimization problems, and production planning problems. In the second part, the authors address techniques and applications of optimization and control in a variety of disciplines, such as chaos synchronization, facial expression recognition and dynamic input-output economic models. Other applications considered here include image retr...
Optimal control of switched systems arising in fermentation processes
Liu, Chongyang
2014-01-01
The book presents, in a systematic manner, the optimal controls under different mathematical models in fermentation processes. Variant mathematical models – i.e., those for multistage systems; switched autonomous systems; time-dependent and state-dependent switched systems; multistage time-delay systems and switched time-delay systems – for fed-batch fermentation processes are proposed and the theories and algorithms of their optimal control problems are studied and discussed. By putting forward novel methods and innovative tools, the book provides a state-of-the-art and comprehensive systematic treatment of optimal control problems arising in fermentation processes. It not only develops nonlinear dynamical system, optimal control theory and optimization algorithms, but can also help to increase productivity and provide valuable reference material on commercial fermentation processes.
A weak Hamiltonian finite element method for optimal control problems
Hodges, Dewey H.; Bless, Robert R.
1990-01-01
A temporal finite element method based on a mixed form of the Hamiltonian weak principle is developed for dynamics and optimal control problems. The mixed form of Hamilton's weak principle contains both displacements and momenta as primary variables that are expanded in terms of nodal values and simple polynomial shape functions. Unlike other forms of Hamilton's principle, however, time derivatives of the momenta and displacements do not appear therein; instead, only the virtual momenta and virtual displacements are differentiated with respect to time. Based on the duality that is observed to exist between the mixed form of Hamilton's weak principle and variational principles governing classical optimal control problems, a temporal finite element formulation of the latter can be developed in a rather straightforward manner. Several well-known problems in dynamics and optimal control are illustrated. The example dynamics problem involves a time-marching problem. As optimal control examples, elementary trajectory optimization problems are treated.
Weak Hamiltonian finite element method for optimal control problems
Hodges, Dewey H.; Bless, Robert R.
1991-01-01
A temporal finite element method based on a mixed form of the Hamiltonian weak principle is developed for dynamics and optimal control problems. The mixed form of Hamilton's weak principle contains both displacements and momenta as primary variables that are expanded in terms of nodal values and simple polynomial shape functions. Unlike other forms of Hamilton's principle, however, time derivatives of the momenta and displacements do not appear therein; instead, only the virtual momenta and virtual displacements are differentiated with respect to time. Based on the duality that is observed to exist between the mixed form of Hamilton's weak principle and variational principles governing classical optimal control problems, a temporal finite element formulation of the latter can be developed in a rather straightforward manner. Several well-known problems in dynamics and optimal control are illustrated. The example dynamics problem involves a time-marching problem. As optimal control examples, elementary trajectory optimization problems are treated.
Optimization of Feedback Control of Flow over a Circular Cylinder
Son, Donggun; Kim, Euiyoung; Choi, Haecheon
2012-11-01
We perform a feedback gain optimization of the proportional-integral-differential (PID) control for flow over a circular cylinder at Re = 60 and 100. We measure the transverse velocity at a centerline location in the wake as a sensing variable and provide blowing and suction at the upper and lower slots on the cylinder surface as an actuation. The cost function to minimize is defined as the mean square of the sensing variable, and the PID control gains are optimized by iterative feedback tuning method which is a typical model free gain optimization method. In this method, the control gains are iteratively updated by the gradient of cost function until the control system satisfies a certain stopping criteria. The PID control with optimal control gains successfully reduces the velocity fluctuations at the sensing location and attenuates (or annihilates) vortex shedding in the wake, resulting in the reduction in the mean drag and lift fluctuations. Supported by the NRF Program (2011-0028032).
Optimal Control of Thermo--Fluid Phenomena in Variable Domains
Volkov, Oleg; Protas, Bartosz
2008-11-01
This presentation concerns our continued research on adjoint--based optimization of viscous incompressible flows (the Navier--Stokes problem) coupled with heat conduction involving change of phase (the Stefan problem), and occurring in domains with variable boundaries. This problem is motivated by optimization of advanced welding techniques used in automotive manufacturing, where the goal is to determine an optimal heat input, so as to obtain a desired shape of the weld pool surface upon solidification. We argue that computation of sensitivities (gradients) in such free--boundary problems requires the use of the shape--differential calculus as a key ingredient. We also show that, with such tools available, the computational solution of the direct and inverse (optimization) problems can in fact be achieved in a similar manner and in a comparable computational time. Our presentation will address certain mathematical and computational aspects of the method. As an illustration we will consider the two--phase Stefan problem with contact point singularities where our approach allows us to obtain a thermodynamically consistent solution.
Control of Pollutants in the Trans-Boundary Area of Taihu Basin, Yangtze Delta
Directory of Open Access Journals (Sweden)
Xiao Wang
2016-12-01
Full Text Available This work focuses on pollution control in the trans-boundary area of Taihu Basin. Considering the unique characteristics of the river network in the study area, a new methodology of pollution control is proposed aiming at improving the water quality in the trans-boundary area and reducing conflicts between up and downstream regions. Based on monitoring data and statistical analysis, important trans-boundary cross sections identified by the regional government were selected as important areas for consideration in developing management objectives; using a 1-D mathematicmodel and an effective weight evaluation model, the trans-boundary effective control scope (TECS of the study area was identified as the scope for pollutant control; the acceptable pollution load was then estimated using an established model targeting bi-directional flow. The results suggest that the water environmental capacity for chemical oxygen demand (COD, in order to guarantee reaching the target water quality standard in the TECS, is 160,806 t/year, and amounts to 16,098 t/year, 3493 t/year, and 39,768 t/year for ammonia nitrogen, total nitrogen, and total phosphorus, respectively. Our study method and results have been incorporated into the local government management project, and have been proven to be useful in designing a pollution control strategy and management policy.
Asymptotically optimal feedback control for a system of linear oscillators
Ovseevich, Alexander; Fedorov, Aleksey
2013-12-01
We consider problem of damping of an arbitrary number of linear oscillators under common bounded control. We are looking for a feedback control steering the system to the equilibrium. The obtained control is asymptotically optimal: the ratio of motion time to zero with this control to the minimum one is close to 1, if the initial energy of the system is large.
Gollub, Caroline; Kowalewski, Markus; de Vivie-Riedle, Regina
2008-08-15
We present a modified optimal control scheme based on the Krotov method, which allows for strict limitations on the spectrum of the optimized laser fields. A frequency constraint is introduced and derived mathematically correct, without losing monotonic convergence of the algorithm. The method guarantees a close link to learning loop control experiments and is demonstrated for the challenging control of nonresonant Raman transitions, which are used to implement a set of global quantum gates for molecular vibrational qubits.
J. Lang; J.G. Verwer (Jan)
2013-01-01
htmlabstractThis paper addresses consistency and stability of W-methods up to order three for nonlinear ODE-constrained control problems with possible restrictions on the control. The analysis is based on the transformed adjoint system and the control uniqueness property. These methods can also be
Optimal resonant control of flexible structures
DEFF Research Database (Denmark)
Krenk, Steen; Høgsberg, Jan Becker
2009-01-01
When introducing a resonant controller for a particular vibration mode in a structure this mode splits into two. A design principle is developed for resonant control based oil equal damping of these two modes. First the design principle is developed for control of a system with a single degree of...
Trajectory Control and Optimization for Responsive Spacecraft
2012-03-22
functions. The scalar function φ defines the cost associated with the terminal conditions, and is referred to as the Mayer cost. The scalar function L...defines the cost associated with the values of x and u throughout the trajectory, and is referred to as the Lagrange cost. When J contains both a Mayer ...optimal space trajectories and is a fundamental reference in a vast majority of the literature on this subject. [22] Building on Lawden’s work, Jean
Aeroelastic passive control optimization of supersonic composite wing with external stores
Sulaeman, E.; Abdullah, N. A.; Kashif, S. M.
2017-03-01
This paper provides a study on passive aeroelastic control optimization, by means of aeroelastic tailoring, of a composite supersonic wing equipped with external stores. The objective of the optimization is to minimize wing weight by considering the aeroelastic flutter and divergence instability speeds as constraints at several flight altitudes. The optimization variables are the composite ply angle and skin thickness of the wing box, wing rib and its control surfaces. The aeroelastic instability speed is set as constraint such that it should be higher than the flutter speed of a metallic base line model of supersonic wing having previously published. A finite element analysis is applied to determine the stiffness and mass matric of the wing and its multi stores. The boundary element method in the form of doublet lattice method is used to model the unsteady aerodynamic load. The results indicate that, for the present wing configuration, the high modulus Graphite/Epoxy composite provides a desired higher flutter speed and lower wing weight compare to that of Kevlar/Epoxy composite as well as the base line metallic wing materials. The aeroelastic boundary thus can be enlarged to higher speed zone and in the same time reduce the structural weight which is important for a further optimization process.
A Riccati approach for constrained linear quadratic optimal control
Sideris, Athanasios; Rodriguez, Luis A.
2011-02-01
An active-set method is proposed for solving linear quadratic optimal control problems subject to general linear inequality path constraints including mixed state-control and state-only constraints. A Riccati-based approach is developed for efficiently solving the equality constrained optimal control subproblems generated during the procedure. The solution of each subproblem requires computations that scale linearly with the horizon length. The algorithm is illustrated with numerical examples.
Adaptive Mixed Finite Element Methods for Parabolic Optimal Control Problems
Zuliang Lu
2011-01-01
We will investigate the adaptive mixed finite element methods for parabolic optimal control problems. The state and the costate are approximated by the lowest-order Raviart-Thomas mixed finite element spaces, and the control is approximated by piecewise constant elements. We derive a posteriori error estimates of the mixed finite element solutions for optimal control problems. Such a posteriori error estimates can be used to construct more efficient and reliable adaptive mixed finite element ...
Design Gradient Descent Optimal Sliding Mode Control of Continuum Robots
Farzin Piltan; Shahnaz Tayebi Haghighi
2012-01-01
In this research, a new approach for gradient descent optimal sliding mode controller for continuum robots is proposed. Based on the new dynamic models developed, a novel technique for nonlinear control of continuum manipulators to be employed in various situations has also been proposed and developed. A section of a continuum arm is modeled using lumped model elements (masses, springs and dampers) and control by nonlinear methodology (sliding mode method) and optimization the sliding surface...
On an optimal control design for Roessler system
Energy Technology Data Exchange (ETDEWEB)
Rafikov, Marat [Universidade Regional do Noroeste do Estado do Rio Grande do Sul, 98700-000 Ijui, RS (Brazil)]. E-mail: rafikov@admijui.unijui.tche.br; Balthazar, Jose Manoel [Universidade Estadual Paulista, C.P. 178, 13500-230 Rio Claro, SP (Brazil)
2004-12-06
In this Letter, an optimal control strategy that directs the chaotic motion of the Roessler system to any desired fixed point is proposed. The chaos control problem is then formulated as being an infinite horizon optimal control nonlinear problem that was reduced to a solution of the associated Hamilton-Jacobi-Bellman equation. We obtained its solution among the correspondent Lyapunov functions of the considered dynamical system.
Development of plasma streamwise vortex generators for increased boundary layer control authority
Bowles, Patrick; Schatzman, David; Corke, Thomas; Thomas, Flint
2009-11-01
This experimental study focuses on active boundary layer flow control utilizing streamwise vorticity produced by a single dielectric barrier discharge plasma actuator. A novel plasma streamwise vortex generator (PSVG) layout is presented that mimics the passive flow control characteristics of the trapezoidal vane vortex generator. The PSVG consists of a common insulated electrode and multiple, exposed streamwise oriented electrodes used to produce counter-rotating vortical structures. Smoke and oil surface visualization of boundary layer flow over a flat plate compare the characteristics of passive control techniques and different PSVG designs. Passive and active control over a generic wall-mounted hump model, Rec = 288,000-575,000, are compared through static wall pressure measurements along the model's centerline. Different geometric effects of the PSVG electrode configuration were investigated. PSVG's with triangular exposed electrodes outperformed ordinary PSVG's under certain circumstances. The electrode arrangement produced flow control mechanisms and effectiveness similar to the passive trapezoidal vane vortex generators.
Optimal control design that accounts for model mismatch errors
Energy Technology Data Exchange (ETDEWEB)
Kim, T.J. [Sandia National Labs., Albuquerque, NM (United States); Hull, D.G. [Texas Univ., Austin, TX (United States). Dept. of Aerospace Engineering and Engineering Mechanics
1995-02-01
A new technique is presented in this paper that reduces the complexity of state differential equations while accounting for modeling assumptions. The mismatch controls are defined as the differences between the model equations and the true state equations. The performance index of the optimal control problem is formulated with a set of tuning parameters that are user-selected to tune the control solution in order to achieve the best results. Computer simulations demonstrate that the tuned control law outperforms the untuned controller and produces results that are comparable to a numerically-determined, piecewise-linear optimal controller.
Neighboring extremal optimal control design including model mismatch errors
Energy Technology Data Exchange (ETDEWEB)
Kim, T.J. [Sandia National Labs., Albuquerque, NM (United States); Hull, D.G. [Texas Univ., Austin, TX (United States). Dept. of Aerospace Engineering and Engineering Mechanics
1994-11-01
The mismatch control technique that is used to simplify model equations of motion in order to determine analytic optimal control laws is extended using neighboring extremal theory. The first variation optimal control equations are linearized about the extremal path to account for perturbations in the initial state and the final constraint manifold. A numerical example demonstrates that the tuning procedure inherent in the mismatch control method increases the performance of the controls to the level of a numerically-determined piecewise-linear controller.
Discrete-time inverse optimal control for nonlinear systems
Sanchez, Edgar N
2013-01-01
Discrete-Time Inverse Optimal Control for Nonlinear Systems proposes a novel inverse optimal control scheme for stabilization and trajectory tracking of discrete-time nonlinear systems. This avoids the need to solve the associated Hamilton-Jacobi-Bellman equation and minimizes a cost functional, resulting in a more efficient controller. Design More Efficient Controllers for Stabilization and Trajectory Tracking of Discrete-Time Nonlinear Systems The book presents two approaches for controller synthesis: the first based on passivity theory and the second on a control Lyapunov function (CLF). Th
Scalable algorithms for optimal control of stochastic PDEs
Ghattas, Omar
2016-01-07
We present methods for the optimal control of systems governed by partial differential equations with infinite-dimensional uncertain parameters. We consider an objective function that involves the mean and variance of the control objective, leading to a risk-averse optimal control formulation. To make the optimal control problem computationally tractable, we employ a local quadratic approximation of the objective with respect to the uncertain parameter. This enables computation of the mean and variance of the control objective analytically. The resulting risk-averse optimization problem is formulated as a PDE-constrained optimization problem with constraints given by the forward and adjoint PDEs for the first and second-order derivatives of the quantity of interest with respect to the uncertain parameter, and with an objective that involves the trace of a covariance-preconditioned Hessian (of the objective with respect to the uncertain parameters) operator. A randomized trace estimator is used to make tractable the trace computation. Adjoint-based techniques are used to derive an expression for the infinite-dimensional gradient of the risk-averse objective function via the Lagrangian, leading to a quasi-Newton method for solution of the optimal control problem. A specific problem of optimal control of a linear elliptic PDE that describes flow of a fluid in a porous medium with uncertain permeability field is considered. We present numerical results to study the consequences of the local quadratic approximation and the efficiency of the method.
Balkunde, Rachappa; Kitagawa, Munenori; Xu, Xianfeng Morgan; Wang, Jing; Jackson, David
2017-05-01
The shoot stem cell niche, contained within the shoot apical meristem (SAM) is maintained in Arabidopsis by the homeodomain protein SHOOT MERISTEMLESS (STM). STM is a mobile protein that traffics cell-to-cell, presumably through plasmodesmata. In maize, the STM homolog KNOTTED1 shows clear differences between mRNA and protein localization domains in the SAM. However, the STM mRNA and protein localization domains are not obviously different in Arabidopsis, and the functional relevance of STM mobility is unknown. Using a non-mobile version of STM (2xNLS-YFP-STM), we show that STM mobility is required to suppress axillary meristem formation during embryogenesis, to maintain meristem size, and to precisely specify organ boundaries throughout development. STM and organ boundary genes CUP SHAPED COTYLEDON1 (CUC1), CUC2 and CUC3 regulate each other during embryogenesis to establish the embryonic SAM and to specify cotyledon boundaries, and STM controls CUC expression post-embryonically at organ boundary domains. We show that organ boundary specification by correct spatial expression of CUC genes requires STM mobility in the meristem. Our data suggest that STM mobility is critical for its normal function in shoot stem cell control. © 2017 The Authors The Plant Journal © 2017 John Wiley & Sons Ltd.
Optimal Force Control of Vibro-Impact Systems for Autonomous Drilling Applications
Aldrich, Jack B.; Okon, Avi B.
2012-01-01
The need to maintain optimal energy efficiency is critical during the drilling operations performed on future and current planetary rover missions (see figure). Specifically, this innovation seeks to solve the following problem. Given a spring-loaded percussive drill driven by a voice-coil motor, one needs to determine the optimal input voltage waveform (periodic function) and the optimal hammering period that minimizes the dissipated energy, while ensuring that the hammer-to-rock impacts are made with sufficient (user-defined) impact velocity (or impact energy). To solve this problem, it was first observed that when voice-coil-actuated percussive drills are driven at high power, it is of paramount importance to ensure that the electrical current of the device remains in phase with the velocity of the hammer. Otherwise, negative work is performed and the drill experiences a loss of performance (i.e., reduced impact energy) and an increase in Joule heating (i.e., reduction in energy efficiency). This observation has motivated many drilling products to incorporate the standard bang-bang control approach for driving their percussive drills. However, the bang-bang control approach is significantly less efficient than the optimal energy-efficient control approach solved herein. To obtain this solution, the standard tools of classical optimal control theory were applied. It is worth noting that these tools inherently require the solution of a two-point boundary value problem (TPBVP), i.e., a system of differential equations where half the equations have unknown boundary conditions. Typically, the TPBVP is impossible to solve analytically for high-dimensional dynamic systems. However, for the case of the spring-loaded vibro-impactor, this approach yields the exact optimal control solution as the sum of four analytic functions whose coefficients are determined using a simple, easy-to-implement algorithm. Once the optimal control waveform is determined, it can be used
Structured controllers for uncertain systems a stochastic optimization approach
Toscano, Rosario
2013-01-01
Structured Controllers for Uncertain Systems focuses on the development of easy-to-use design strategies for robust low-order or fixed-structure controllers (particularly the industrially ubiquitous PID controller). These strategies are based on a recently-developed stochastic optimization method termed the "Heuristic Kalman Algorithm" (HKA) the use of which results in a simplified methodology that enables the solution of the structured control problem without a profusion of user-defined parameters. An overview of the main stochastic methods employable in the context of continuous non-convex optimization problems is also provided and various optimization criteria for the design of a structured controller are considered; H∞, H2, and mixed H2/H∞ each merits a chapter to itself. Time-domain-performance specifications can be easily incorporated in the design. Advances in Industrial Control aims to report and encourage the transfer of technology in control engineering. The rapid development of control technolo...
Optimal Multilevel Control for Large Scale Interconnected Systems
Directory of Open Access Journals (Sweden)
Ahmed M. A. Alomar,
2014-04-01
Full Text Available A mathematical model of the finishing mill as an example of a large scale interconnected dynamical system is represented. First the system response due to disturbance only is presented. Then,the control technique applied to the finishing hot rolling steel mill is the optimal multilevel control using state feedback. An optimal controller is developed based on the integrated system model, but due to the complexity of the controllers and tremendous computational efforts involved, a multilevel technique is used in designing and implementing the controllers .The basis of the multilevel technique is described and a computational algorithm is discussed for the control of the finishing mill system . To reduce the mass storage , memory requirements and the computational time of the processor, a sub-optimal multilevel technique is applied to design the controllers of the finishing mill . Comparison between these controllers and conclusion is presented.
Coupled Low-thrust Trajectory and System Optimization via Multi-Objective Hybrid Optimal Control
Vavrina, Matthew A.; Englander, Jacob Aldo; Ghosh, Alexander R.
2015-01-01
The optimization of low-thrust trajectories is tightly coupled with the spacecraft hardware. Trading trajectory characteristics with system parameters ton identify viable solutions and determine mission sensitivities across discrete hardware configurations is labor intensive. Local independent optimization runs can sample the design space, but a global exploration that resolves the relationships between the system variables across multiple objectives enables a full mapping of the optimal solution space. A multi-objective, hybrid optimal control algorithm is formulated using a multi-objective genetic algorithm as an outer loop systems optimizer around a global trajectory optimizer. The coupled problem is solved simultaneously to generate Pareto-optimal solutions in a single execution. The automated approach is demonstrated on two boulder return missions.
Optimization of the Forcing Term for the Solution of Two-Point Boundary Value Problems
Directory of Open Access Journals (Sweden)
Gianni Arioli
2013-01-01
by standard methods of constrained optimization, for example, with Lagrange multipliers. We provide an application of this algorithm to the planar restricted three body problem in order to study the planning of low-thrust transfer orbits.
Changing the boundaries of the firm - Adopting and designing efficient management control structures
Vosselman, E.G.J.; van der Meer-Kooistra, J.
2006-01-01
Purpose - To develop a model in which alternative patterns of management control are confronted with situational and institutional features in the context of transactional relationships. The model could be of use to managers in making rational decisions regarding the boundaries of the organization.
46 CFR 116.433 - Windows and air ports in fire control boundaries.
2010-10-01
...) Windows or air ports must be of tempered or laminated glass of at least 6.5 millimeters (0.25 inches) in... independent of the glass, are fitted in the passageway. (c) Windows or air ports in A-Class bulkheads must be... material must be installed to hold glass in place in windows or air ports in a fire control boundary...
Port Hamiltonian Formulation of Infinite Dimensional Systems II. Boundary Control by Interconnection
Macchelli, Alessandro; Schaft, Arjan J. van der; Melchiorri, Claudio
2004-01-01
In this paper, some new results concerning the boundary control of distributed parameter systems in port Hamiltonian form are presented. The classical finite dimensional port Hamiltonian formulation of a dynamical system has been generalized to the distributed parameter and multi-variable case by ex
Port Hamiltonian formulation of infinite dimensional systems II. Boundary control by interconnection
Macchelli, Alessandro; Schaft, van der Arjan J.; Melchiorri, Claudio
2004-01-01
In this paper, some new results concerning the boundary control of distributed parameter systems in port Hamiltonian form are presented. The classical finite dimensional port Hamiltonian formulation of a dynamical system has been generalized to the distributed parameter and multivariable case by ext
Null exact controllability of the parabolic equations with equivalued surface boundary condition
Directory of Open Access Journals (Sweden)
2006-01-01
Full Text Available This paper is devoted to showing the null exact controllability for a class of parabolic equations with equivalued surface boundary condition. Our method is based on the duality argument and global Carleman-type estimate for a parabolic operator.
Time-optimal control of the magnetically levitated photolithography platen
Energy Technology Data Exchange (ETDEWEB)
Redmond, J.; Tucker, S.
1995-01-01
This report summarizes two approaches to time-optimal control of a nonlinear magnetically levitated platen. The system of interest is a candidate technology for next-generation photolithography machines used in the manufacture of integrated circuits. The dynamics and the variable peak control force of the electro-magnetic actuators preclude the direct application of classical time-optimal control methodologies for determining optimal rest-to-rest maneuver strategies. Therefore, this study explores alternate approaches using a previously developed computer simulation. In the first approach, conservative estimates of the available control forces are used to generate suboptimal switching curves. In the second approach, exact solutions are determined iteratively and used as a training set for an artificial neural network. The trained network provides optimal actuator switching times that incorporate the full nonlinearities of the magnetic levitation actuators. Sample problems illustrate the effectiveness of these techniques as compared to traditional proportional-derivative control.
Flocking in Distributed Control and Optimization
2015-06-01
IEEE Transactions on Automatic Control . In this paper, In this paper we develop a mathematical model for analyzing the benefits...Z. Lin “Noise Reduction by Swarming in Social Foraging” under review at IEEE Transactions on Automatic Control . 10. P. Shi and A. Garcia “Flocking...P. Shi, A. Garcia and Z. Lin ``Noise Reduction by Swarming in Social Foraging" under review at IEEE Transactions on Automatic Control . 10. P.
Optimization-Based Robust Nonlinear Control
2006-08-01
IEEE Transactions on Automatic Control , vol. 51, no. 4, pp. 661...systems with two time scales", A.R. Teel, L. Moreau and D. Nesic, IEEE Transactions on Automatic Control , vol. 48, no. 9, pp. 1526-1544, September 2003...Turner, L. Zaccarian, IEEE Transactions on Automatic Control , vol. 48, no. 9, pp. 1509- 1525, September 2003. 5. "Nonlinear Scheduled anti-windup
A Computationally Efficient Aggregation Optimization Strategy of Model Predictive Control
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
Model Predictive Control (MPC) is a popular technique and has been successfully used in various industrial applications. However, the big drawback of MPC involved in the formidable on-line computational effort limits its applicability to relatively slow and/or small processes with a moderate number of inputs. This paper develops an aggregation optimization strategy for MPC that can improve the computational efficiency of MPC. For the regulation problem, an input decaying aggregation optimization algorithm is presented by aggregating all the original optimized variables on control horizon with the decaying sequence in respect of the current control action.
Engineering applications of discrete-time optimal control
DEFF Research Database (Denmark)
Vidal, Rene Victor Valqui; Ravn, Hans V.
1990-01-01
of some well-known and new results in discrete time optimal control methods applicable to practical problem solving within engineering. Emphasis is placed on dynamic programming, the classical maximum principle and generalized versions of the maximum principle for optimal control of discrete time systems......Many problems of design and operation of engineering systems can be formulated as optimal control problems where time has been discretisized. This is also true even if 'time' is not involved in the formulation of the problem, but rather another one-dimensional parameter. This paper gives a review...
Engineering applications of discrete-time optimal control
DEFF Research Database (Denmark)
Vidal, Rene Victor Valqui; Ravn, Hans V.
1990-01-01
Many problems of design and operation of engineering systems can be formulated as optimal control problems where time has been discretisized. This is also true even if 'time' is not involved in the formulation of the problem, but rather another one-dimensional parameter. This paper gives a review...... of some well-known and new results in discrete time optimal control methods applicable to practical problem solving within engineering. Emphasis is placed on dynamic programming, the classical maximum principle and generalized versions of the maximum principle for optimal control of discrete time systems...
Time dependent optimal switching controls in online selling models
Energy Technology Data Exchange (ETDEWEB)
Bradonjic, Milan [Los Alamos National Laboratory; Cohen, Albert [MICHIGAN STATE UNIV
2010-01-01
We present a method to incorporate dishonesty in online selling via a stochastic optimal control problem. In our framework, the seller wishes to maximize her average wealth level W at a fixed time T of her choosing. The corresponding Hamilton-Jacobi-Bellmann (HJB) equation is analyzed for a basic case. For more general models, the admissible control set is restricted to a jump process that switches between extreme values. We propose a new approach, where the optimal control problem is reduced to a multivariable optimization problem.
IMPORTANCE OF KINETIC MEASURES IN TRAJECTORY PREDICTION WITH OPTIMAL CONTROL
Directory of Open Access Journals (Sweden)
Ömer GÜNDOĞDU
2001-02-01
Full Text Available A two-dimensional sagittally symmetric human-body model was established to simulate an optimal trajectory for manual material handling tasks. Nonlinear control techniques and genetic algorithms were utilized in the optimizations to explore optimal lifting patterns. The simulation results were then compared with the experimental data. Since the kinetic measures such as joint reactions and moments are vital parameters in injury determination, the importance of comparing kinetic measures rather than kinematical ones was emphasized.
Optimal control of electrostatic self-assembly of binary monolayers
Shestopalov, N. V.; Henkelman, G.; Powell, C. T.; Rodin, G. J.
2009-05-01
A simple macroscopic model is used to determine an optimal annealing schedule for self-assembly of binary monolayers of spherical particles. The model assumes that a single rate-controlling mechanism is responsible for the formation of spatially ordered structures and that its rate follows an Arrhenius form. The optimal schedule is derived in an analytical form using classical optimization methods. Molecular dynamics simulations of the self-assembly demonstrate that the proposed schedule outperforms other schedules commonly used for simulated annealing.
Joint optimization traffic signal control for an urban arterial road
Institute of Scientific and Technical Information of China (English)
LI Yin-fei; CHEN Shu-ping
2009-01-01
This paper considers the optimal traffic signal setting for an urban arterial road. By introducing the concepts of synchronization rate and non-synchronization degree, a mathematical model is constructed and an optimization problem is posed. Then, a new iterative algorithm is developed to solve this optimal traffic control signal setting problem. Convergence properties for this iterative algorithm are established. Finally, a numerical example is solved to illustrate the effectiveness of the method.
Near time optimal control with perturbation estimation for flexible spacecraft slewing maneuvers
Institute of Scientific and Technical Information of China (English)
Cen Xiaofeng; Wang Qingchao; Ma Xingrui
2005-01-01
A feedforward approach for generating near time optimal controller for flexible spacecraft rest-to-rest maneuvers is presented with the objective insensitivity to modeling errors, parameter uncertainty and minimizing the residual energy of the flexible modes. The perturbation estimation of flexible appendages to the rigid-hub is accomplished simply via compare the output of real plant with the reference model, and the approach is based on combine this estimation with the bang-bang control for the rigid-hub modes through analysis the basic constraint and the additional constraint, i.e. zero coupling torque and zero coupling torque derivative for general two orders system and three orders system with considerate attitude acceleration mode near time optimal controls. These time optimal controls with control constraints and state constraints leads to forming a boundary- value problem, and resolved the problem using an iterative numerical algorithm.The near time optimal control with perturbation estimation shows a good robust to parameter uncertainty and can suppress the vibration and minimizing the residual energy. The capability of this approach is demonstrated through a numerical example in detail.
Optimization of PID Controllers Using Ant Colony and Genetic Algorithms
Ünal, Muhammet; Topuz, Vedat; Erdal, Hasan
2013-01-01
Artificial neural networks, genetic algorithms and the ant colony optimization algorithm have become a highly effective tool for solving hard optimization problems. As their popularity has increased, applications of these algorithms have grown in more than equal measure. While many of the books available on these subjects only provide a cursory discussion of theory, the present book gives special emphasis to the theoretical background that is behind these algorithms and their applications. Moreover, this book introduces a novel real time control algorithm, that uses genetic algorithm and ant colony optimization algorithms for optimizing PID controller parameters. In general, the present book represents a solid survey on artificial neural networks, genetic algorithms and the ant colony optimization algorithm and introduces novel practical elements related to the application of these methods to process system control.
Optimal Selective Harmonic Control for Power Harmonics Mitigation
DEFF Research Database (Denmark)
Zhou, Keliang; Yang, Yongheng; Blaabjerg, Frede
2015-01-01
the cost, the complexity and the performance: high accuracy, fast transient response, easy-implementation, cost-effective, and also easy-to-design. The analysis and synthesis of the optimal SHC system are addressed. The proposed SHC offers power convert-ers a tailor-made optimal control solution......This paper proposes an Internal Model Principle (IMP) based optimal Selective Harmonic Controller (SHC) for power converters to mitigate power harmonics. According to the harmonics distribution caused by power converters, a universal recursive SHC module is developed to deal with a featured group...... of power harmonics. The proposed optimal SHC is of hybrid structure: all recursive SHC modules with weighted gains are connected in parallel. It bridges the real “nk+-m order RC” and the complex “parallel structure RC”. Compared to other IMP based control solutions, it offers an optimal trade-off among...
Soft Computing Applications in Optimization, Control, and Recognition
Castillo, Oscar
2013-01-01
Soft computing includes several intelligent computing paradigms, like fuzzy logic, neural networks, and bio-inspired optimization algorithms. This book describes the application of soft computing techniques to intelligent control, pattern recognition, and optimization problems. The book is organized in four main parts. The first part deals with nature-inspired optimization methods and their applications. Papers included in this part propose new models for achieving intelligent optimization in different application areas. The second part discusses hybrid intelligent systems for achieving control. Papers included in this part make use of nature-inspired techniques, like evolutionary algorithms, fuzzy logic and neural networks, for the optimal design of intelligent controllers for different kind of applications. Papers in the third part focus on intelligent techniques for pattern recognition and propose new methods to solve complex pattern recognition problems. The fourth part discusses new theoretical concepts ...
Approximate design of optimal tracking controller for time-delay systems
Institute of Scientific and Technical Information of China (English)
TANG Gongyou; LI Chao; ZHAO Yandong
2006-01-01
Successive approximate design of the optimal tracking controller for linear systems with time-delay is developed. By applying the successive approximation theory of differential equations, the two-point boundary value (TPBV) problem with both time-delay and time-advance terms derived from the original optimal tracking control (OTC) problem is transformed into a sequence of linear TPBV problems without delay and advance terms. The solution sequence of the linear TPBV problems uniformly converges to the solution of the original OTC problem. The obtained OTC law consists of analytic state feedback terms and a compensation term which is the limit of the adjoint vector sequence. The compensation term can be obtained from an iteration formula of adjoint vectors. By using a finite term of the adjoint vector sequence, a suboptimal tracking control law is revealed. Numerical examples show the effectiveness of the algorithm.
Design Gradient Descent Optimal Sliding Mode Control of Continuum Robots
Directory of Open Access Journals (Sweden)
Farzin Piltan
2012-08-01
Full Text Available In this research, a new approach for gradient descent optimal sliding mode controller for continuum robots is proposed. Based on the new dynamic models developed, a novel technique for nonlinear control of continuum manipulators to be employed in various situations has also been proposed and developed. A section of a continuum arm is modeled using lumped model elements (masses, springs and dampers and control by nonlinear methodology (sliding mode method and optimization the sliding surface slope by gradient descent method. It is shown that this type of control methodology, although used to a certain model, can be used to conveniently control the dynamics of the arm with suitable tradeoff in accuracy of modeling. This relatively controller is more plausible to implement in an actual real-time when compared to other techniques of nonlinear controller methodology of continuum arms. Principles of sliding mode methodology is based on derive the sliding surface slope and nonlinear dynamic model and applied in the system. Based on the gradient descent optimization method, the sliding surface slope and gain updating factor has been developed in certain and partly uncertain continuum robots. This methodology is represented in certain and uncertain area whose only optimization for certain area and test this optimization for uncertainty. The new techniques proposed and methodologies adopted in this paper supported by MATLAB/SIMULINK results represent a significant contribution to the field of design an optimized nonlinear sliding mode controller for continuum robots.
Directory of Open Access Journals (Sweden)
Jing Lei
2013-01-01
Full Text Available The paper considers the problem of variable structure control for nonlinear systems with uncertainty and time delays under persistent disturbance by using the optimal sliding mode surface approach. Through functional transformation, the original time-delay system is transformed into a delay-free one. The approximating sequence method is applied to solve the nonlinear optimal sliding mode surface problem which is reduced to a linear two-point boundary value problem of approximating sequences. The optimal sliding mode surface is obtained from the convergent solutions by solving a Riccati equation, a Sylvester equation, and the state and adjoint vector differential equations of approximating sequences. Then, the variable structure disturbance rejection control is presented by adopting an exponential trending law, where the state and control memory terms are designed to compensate the state and control delays, a feedforward control term is designed to reject the disturbance, and an adjoint compensator is designed to compensate the effects generated by the nonlinearity and the uncertainty. Furthermore, an observer is constructed to make the feedforward term physically realizable, and thus the dynamical observer-based dynamical variable structure disturbance rejection control law is produced. Finally, simulations are demonstrated to verify the effectiveness of the presented controller and the simplicity of the proposed approach.
On optimal temperature control in hothouses
Astashova, I. V.; Filinovskiy, A. V.; Lashin, D. A.
2017-07-01
We study the problem of control over the temperature conditions in industrial hothouses. We consider a model based on the one-dimensional heat equation on a bounded interval with quadratic cost functional, examine the existence and uniqueness of a control function from a prescribed set, and study the structure of the set of accessible temperature functions.
Optimal actuator location of minimum norm controls for heat equation with general controlled domain
Guo, Bao-Zhu; Xu, Yashan; Yang, Dong-Hui
2016-09-01
In this paper, we study optimal actuator location of the minimum norm controls for a multi-dimensional heat equation with control defined in the space L2 (Ω × (0 , T)). The actuator domain is time-varying in the sense that it is only required to have a prescribed Lebesgue measure for any moment. We select an optimal actuator location so that the optimal control takes its minimal norm over all possible actuator domains. We build a framework of finding the Nash equilibrium so that we can develop a sufficient and necessary condition to characterize the optimal relaxed solutions for both actuator location and corresponding optimal control of the open-loop system. The existence and uniqueness of the optimal classical solutions are therefore concluded. As a result, we synthesize both optimal actuator location and corresponding optimal control into a time-varying feedbacks.
Control and Optimization Methods for Electric Smart Grids
Ilić, Marija
2012-01-01
Control and Optimization Methods for Electric Smart Grids brings together leading experts in power, control and communication systems,and consolidates some of the most promising recent research in smart grid modeling,control and optimization in hopes of laying the foundation for future advances in this critical field of study. The contents comprise eighteen essays addressing wide varieties of control-theoretic problems for tomorrow’s power grid. Topics covered include: Control architectures for power system networks with large-scale penetration of renewable energy and plug-in vehicles Optimal demand response New modeling methods for electricity markets Control strategies for data centers Cyber-security Wide-area monitoring and control using synchronized phasor measurements. The authors present theoretical results supported by illustrative examples and practical case studies, making the material comprehensible to a wide audience. The results reflect the exponential transformation that today’s grid is going...
An Optimal Controller Architecture for Poset-Causal Systems
Shah, Parikshit
2011-01-01
We propose a novel and natural architecture for decentralized control that is applicable whenever the underlying system has the structure of a partially ordered set (poset). This controller architecture is based on the concept of Moebius inversion for posets, and enjoys simple and appealing separation properties, since the closed-loop dynamics can be analyzed in terms of decoupled subsystems. The controller structure provides rich and interesting connections between concepts from order theory such as Moebius inversion and control-theoretic concepts such as state prediction, correction, and separability. In addition, using our earlier results on H_2-optimal decentralized control for arbitrary posets, we prove that the H_2-optimal controller in fact possesses the proposed structure, thereby establishing the optimality of the new controller architecture.
Modelling and optimization of computer network traffic controllers
Directory of Open Access Journals (Sweden)
N. U. Ahmed
2005-01-01
operation of the controller and evaluate the benefits of using a genetic algorithm approach to speed up the optimization process. Our results show that the use of the genetic algorithm proves particularly useful in reducing the computation time required to optimize the operation of a system consisting of multiple token-bucket-regulated sources.
Evolutionary Computing for Intelligent Power System Optimization and Control
DEFF Research Database (Denmark)
This new book focuses on how evolutionary computing techniques benefit engineering research and development tasks by converting practical problems of growing complexities into simple formulations, thus largely reducing development efforts. This book begins with an overview of the optimization the...... theory and modern evolutionary computing techniques, and goes on to cover specific applications of evolutionary computing to power system optimization and control problems....
Optimal parametric sensitivity control of a fed-batch reactor
Stigter, J.D.; Keesman, K.J.
2004-01-01
The paper presents an optimal parametric sensitivity controller for estimation of a set of parameters in an experiment. The method is demonstrated for a fed-batch bioreactor case study for optimal estimation of the half-saturation constant KS and the parameter combination µmaxX/Y in which µmax is th
Optimal Control Strategies in Delayed Sharing Information Structures
Nayyar, Ashutosh; Teneketzis, Demosthenis
2010-01-01
The $n$-step delayed sharing information structure is investigated. This information structure comprises of $K$ controllers that share their information with a delay of $n$ time steps. This information structure is a link between the classical information structure, where information is shared perfectly between the controllers, and a non-classical information structure, where there is no "lateral" sharing of information among the controllers. Structural results for optimal control strategies for systems with such information structures are presented. A sequential methodology for finding the optimal strategies is also derived. The solution approach provides an insight for identifying structural results and sequential decomposition for general decentralized stochastic control problems.
Boundary control design for extensible marine risers in three dimensional space
Do, K. D.
2017-02-01
A design of boundary controllers is proposed for (practical) exponential stabilization of extensible marine risers in three-dimensional (3D) space under sea loads. The design removes flaws in existing works. Two Lyapunov-type theorems are developed for study of existence and uniqueness, and stability of nonlinear evolution systems in Hilbert space. These theorems have their potential use in control design and stability analysis for flexible systems including marine risers.
Effects of boundary-layer separation controllers on a desktop fume hood.
Huang, Rong Fung; Chen, Jia-Kun; Hsu, Ching Min; Hung, Shuo-Fu
2016-10-02
A desktop fume hood installed with an innovative design of flow boundary-layer separation controllers on the leading edges of the side plates, work surface, and corners was developed and characterized for its flow and containment leakage characteristics. The geometric features of the developed desktop fume hood included a rearward offset suction slot, two side plates, two side-plate boundary-layer separation controllers on the leading edges of the side plates, a slanted surface on the leading edge of the work surface, and two small triangular plates on the upper left and right corners of the hood face. The flow characteristics were examined using the laser-assisted smoke flow visualization technique. The containment leakages were measured by the tracer gas (sulphur hexafluoride) detection method on the hood face plane with a mannequin installed in front of the hood. The results of flow visualization showed that the smoke dispersions induced by the boundary-layer separations on the leading edges of the side plates and work surface, as well as the three-dimensional complex flows on the upper-left and -right corners of the hood face, were effectively alleviated by the boundary-layer separation controllers. The results of the tracer gas detection method with a mannequin standing in front of the hood showed that the leakage levels were negligibly small (≤0.003 ppm) at low face velocities (≥0.19 m/s).
Optimal design of distributed control and embedded systems
Çela, Arben; Li, Xu-Guang; Niculescu, Silviu-Iulian
2014-01-01
Optimal Design of Distributed Control and Embedded Systems focuses on the design of special control and scheduling algorithms based on system structural properties as well as on analysis of the influence of induced time-delay on systems performances. It treats the optimal design of distributed and embedded control systems (DCESs) with respect to communication and calculation-resource constraints, quantization aspects, and potential time-delays induced by the associated communication and calculation model. Particular emphasis is put on optimal control signal scheduling based on the system state. In order to render this complex optimization problem feasible in real time, a time decomposition is based on periodicity induced by the static scheduling is operated. The authors present a co-design approach which subsumes the synthesis of the optimal control laws and the generation of an optimal schedule of control signals on real-time networks as well as the execution of control tasks on a single processor. The a...
Optimal Tracking Controller Design for a Small Scale Helicopter
Institute of Scientific and Technical Information of China (English)
Agus Budiyono; Singgih S. Wibowo
2007-01-01
A model helicopter is more difficult to control than its full scale counterpart. This is due to its greater sensitivity to control inputs and disturbances as well as higher bandwidth of dynamics. This work is focused on designing practical tracking controller for a small scale helicopter following predefined trajectories. A tracking controller based on optimal control theory is synthesized as a part of the development of an autonomous helicopter. Some issues with regards to control constraints are addressed.The weighting between state tracking performance and control power expenditure is analyzed. Overall performance of the control design is evaluated based on its time domain histories of trajectories as well as control inputs.
Institute of Scientific and Technical Information of China (English)
Sergio VESSELLA
2005-01-01
Let Г be a portion of a C1,α boundary of an n-dimensional domain D. Let u be a solution to a second order parabolic equation in D × (-T,T) and assume that u = 0 on Г× (-T,T), 0 ∈Г. We result we prove that if u (x,t) = O (|x|k) for every t ∈ (-T,T) and every k ∈ N, then u is identically equal to zero.
An Optimized Combined Wave and Current Bottom Boundary Layer Model for Arbitrary Bed Roughness
2017-06-30
studies of shelf circulation patterns that incorporate wave-current effects in the bottom boundary layer have been conducted in the past (e.g...presence of surface waves reemphasizes the fact that wave-current effects are important on storm- dominated continental shelves. In addition to these...can be defined for / rz z1 (i.e., */ rrzz ακR1 ), where * * / )(r cw rR u z ω . The two expressions are related by * */ /r r zR zR 0 , where
Optimizing Grain Boundary Complexions to Produce Dense Pressure-Less Sintered Boron Carbide (B4C)
2008-11-14
Unlimited 18. NUMBER OF PAGES 15 19a. NAME OF RESPONSIBLE PERSON Martin P. Harmer 19b. TELEPHONE NUMBER (Include area code) 610-758-4227 Standard...American Ceramic Society, 1993. 76(11): p. 2801-8. 26. Dillon, S.J., Tang, M., Carter, W.C., and M.P. Harmer , Complexion: A New Concept for Kinetic...Engineering in Materials Science. Acta Materialia, 2007. 55: p. 6208-18. 27. Dillon, S.J. and M.P. Harmer , Multiple Grain boundary transitions in Ceramics
Modelling Driver Assitance Systems by Optimal Control
Wang, M.; Daamen, W.; Hoogendoorn, S.P.; Van Arem, B.
2012-01-01
Driver assistance systems support drivers in operating vehicles in a safe, comfortable and efficient way, and thus may induce changes in traffic flow characteristics. This paper put forward a receding horizon control framework to model driver assistance systems. The accelerations of automated vehicles are determined to optimise a cost function, assuming other vehicles driving at stationary conditions over a prediction horizon. The flexibility of the framework is demonstrated with controller d...
Rethinking optimal control of human movements
Huh, Dongsung
2012-01-01
The complex bio-mechanics of human body is capable of generating an unlimited repertoire of movements, which on one hand yields highly versatile motor behavior but on the other hand presents a formidable control problem for the brain. Understanding the computational process that allows us to easily perform various motor tasks with a high degree of coordination is of central interest to both neuroscience and robotics control. In recent decades, it became widely accepted that the observed movem...
Optimal Control Surface Layout for an Aeroservoelastic Wingbox
Stanford, Bret K.
2017-01-01
This paper demonstrates a technique for locating the optimal control surface layout of an aeroservoelastic Common Research Model wingbox, in the context of maneuver load alleviation and active utter suppression. The combinatorial actuator layout design is solved using ideas borrowed from topology optimization, where the effectiveness of a given control surface is tied to a layout design variable, which varies from zero (the actuator is removed) to one (the actuator is retained). These layout design variables are optimized concurrently with a large number of structural wingbox sizing variables and control surface actuation variables, in order to minimize the sum of structural weight and actuator weight. Results are presented that demonstrate interdependencies between structural sizing patterns and optimal control surface layouts, for both static and dynamic aeroelastic physics.
Adjoint optimal control problems for the RANS system
Attavino, A.; Cerroni, D.; Da Vià, R.; Manservisi, S.; Menghini, F.
2017-01-01
Adjoint optimal control in computational fluid dynamics has become increasingly popular recently because of its use in several engineering and research studies. However the optimal control of turbulent flows without the use of Direct Numerical Simulation is still an open problem and various methods have been proposed based on different approaches. In this work we study optimal control problems for a turbulent flow modeled with a Reynolds-Averaged Navier-Stokes system. The adjoint system is obtained through the use of a Lagrangian multiplier method by setting as objective of the control a velocity matching profile or an increase or decrease in the turbulent kinetic energy. The optimality system is solved with an in-house finite element code and numerical results are reported in order to show the validity of this approach.
Relaxed error control in shape optimization that utilizes remeshing
CSIR Research Space (South Africa)
Wilke, DN
2013-02-01
Full Text Available . These discontinuities may trap conventional optimization algorithms, which rely on both function and gradient evaluations, in local minima. This has the drawback that multiple analyses and error computations are often required per design to control the error...
Optimal False Discovery Rate Control for Dependent Data
Xie, Jichun; Cai, T. Tony; Maris, John; Li, Hongzhe
2013-01-01
This paper considers the problem of optimal false discovery rate control when the test statistics are dependent. An optimal joint oracle procedure, which minimizes the false non-discovery rate subject to a constraint on the false discovery rate is developed. A data-driven marginal plug-in procedure is then proposed to approximate the optimal joint procedure for multivariate normal data. It is shown that the marginal procedure is asymptotically optimal for multivariate normal data with a short-range dependent covariance structure. Numerical results show that the marginal procedure controls false discovery rate and leads to a smaller false non-discovery rate than several commonly used p-value based false discovery rate controlling methods. The procedure is illustrated by an application to a genome-wide association study of neuroblastoma and it identifies a few more genetic variants that are potentially associated with neuroblastoma than several p-value-based false discovery rate controlling procedures. PMID:23378870
Design of a Helicopter Stability and Control Augmentation System Using Optimal Control Theory.
technique is described for the design of multivariable feedback controllers based upon results in optimal control theory . For a specified performance...helicopter flight envelope. The results show that optimal control theory can be used to design a helicopter stability and control augmentation system