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 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, ...
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.
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.
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.
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.
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...
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.
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.
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...
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.
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.
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.
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.
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.
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.
Optimal Opinion Control: The Campaign Problem
2015-01-01
Opinion dynamics is nowadays a very common field of research. In this article we formulate and then study a novel, namely strategic perspective on such dynamics: There are the usual normal agents that update their opinions, for instance according the well-known bounded confidence mechanism. But, additionally, there is at least one strategic agent. That agent uses opinions as freely selectable strategies to get control on the dynamics: The strategic agent of our benchmark problem tries, during...
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.
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 ...
Optimal control problems related to the navigation channel engineering
Institute of Scientific and Technical Information of China (English)
朱江; 曾庆存; 郭冬建; 刘卓
1997-01-01
The navigation channel engineering poses optimal control problems of how to find the optimal way of engineering such that the water depth of the channel is maximum under certain budget constraint, or the cost of me en-gineering is minimum while certain goals are achieved. These are typical control problems of distributed system gov erned by hydraulic/sedimentation models. The problems and methods of solutions are discussed Since the models, usually complicated, are nonlinear, they can be solved by solving a series of linear problems For linear problems the solutions are given. Thus the algorithms are simplified.
Numerical methods for solving terminal optimal control problems
Gornov, A. Yu.; Tyatyushkin, A. I.; Finkelstein, E. A.
2016-02-01
Numerical methods for solving optimal control problems with equality constraints at the right end of the trajectory are discussed. Algorithms for optimal control search are proposed that are based on the multimethod technique for finding an approximate solution of prescribed accuracy that satisfies terminal conditions. High accuracy is achieved by applying a second-order method analogous to Newton's method or Bellman's quasilinearization method. In the solution of problems with direct control constraints, the variation of the control is computed using a finite-dimensional approximation of an auxiliary problem, which is solved by applying linear programming methods.
Study of optimal control problems for hybrid dynamical systems
Institute of Scientific and Technical Information of China (English)
Gao Rui; Wang Lei; Wang Yuzhen
2006-01-01
From the viewpoint of continuous systems, optimal control problem is proposed for a class of controlled Hybrid dynamical systems. Then a mathematical method- HDS minimum principle is put forward, which can solve the above problem. The HDS minimum principle is proved by means of Ekeland's variational principle.
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.
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 $\\mathbb{S}^2$.
On the optimal control problem for two regions’ macroeconomic model
Directory of Open Access Journals (Sweden)
Surkov Platon G.
2015-12-01
Full Text Available In this paper we consider a model of joint economic growth of two regions. This model bases on the classical Kobb-Douglas function and is described by a nonlinear system of differential equations. The interaction between regions is carried out by changing the balance of trade. The optimal control problem for this system is posed and the Pontryagin maximum principle is used for analysis the problem. The maximized functional represents the global welfare of regions. The numeric solution of the optimal control problem for particular regions is found. The used parameters was obtained from the basic scenario of the MERGE
Turnpike theory of continuous-time linear optimal control problems
Zaslavski, Alexander J
2015-01-01
Individual turnpike results are of great interest due to their numerous applications in engineering and in economic theory; in this book the study is focused on new results of turnpike phenomenon in linear optimal control problems. The book is intended for engineers as well as for mathematicians interested in the calculus of variations, optimal control, and in applied functional analysis. Two large classes of problems are studied in more depth. The first class studied in Chapter 2 consists of linear control problems with periodic nonsmooth convex integrands. Chapters 3-5 consist of linear control problems with autonomous nonconvex and nonsmooth integrands. Chapter 6 discusses a turnpike property for dynamic zero-sum games with linear constraints. Chapter 7 examines genericity results. In Chapter 8, the description of structure of variational problems with extended-valued integrands is obtained. Chapter 9 ends the exposition with a study of turnpike phenomenon for dynamic games with extended value integran...
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.
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.
A monotonic method for solving nonlinear optimal control problems
Salomon, Julien
2009-01-01
Initially introduced in the framework of quantum control, the so-called monotonic algorithms have shown excellent numerical results when dealing with various bilinear optimal control problems. This paper aims at presenting a unified formulation of such procedures and the intrinsic assumptions they require. In this framework, we prove the feasibility of the general algorithm. Finally, we explain how these assumptions can be relaxed.
Optimal Control Problems for Partial Differential Equations on Reticulated Domains
Kogut, Peter I
2011-01-01
In the development of optimal control, the complexity of the systems to which it is applied has increased significantly, becoming an issue in scientific computing. In order to carry out model-reduction on these systems, the authors of this work have developed a method based on asymptotic analysis. Moving from abstract explanations to examples and applications with a focus on structural network problems, they aim at combining techniques of homogenization and approximation. Optimal Control Problems for Partial Differential Equations on Reticulated Domains is an excellent reference tool for gradu
Constraint Algorithm for Extremals in Optimal Control Problems
Barbero-Linan, Maria
2007-01-01
A characterization of different kinds of extremals of optimal control problems is given if we take an open control set. A well known constraint algorithm for implicit differential equations is adapted to the study of such problems. Some necessary conditions of Pontryagin's Maximum Principle determine the primary constraint submanifold for the algorithm. Some examples in the control literature, such as subRiemannian geometry and control-affine systems, are revisited to give, in a clear geometric way, a subset where the abnormal, normal and strict abnormal extremals stand.
STOCHASTIC LINEAR QUADRATIC OPTIMAL CONTROL PROBLEMS WITH RANDOM COEFFICIENTS
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
This paper studies a stochastic linear quadratic optimal control problem (LQ problem, for short), for which the coefficients are allowed to be random and the cost functional is allowed to have a negative weight on the square of the control variable. The authors introduce the stochastic Riccati equation for the LQ problem. This is a backward SDE with a complicated nonlinearity and a singularity. The local solvability of such a backward SDE is established, which by no means is obvious. For the case of deterministic coefficients, some further discussions on the Riccati equations have been carried out. Finally, an illustrative example is presented.
Chebyshev-Legendre method for discretizing optimal control problems
Institute of Scientific and Technical Information of China (English)
ZHANG Wen; MA He-ping
2009-01-01
In this paper, a numerical method for solving the optimal control (OC) problems is presented. The method is enlightened by the Chebyshev-Legendre (CL) method for solving the partial differential equations (PDEs). The Legen-dre expansions are used to approximate both the control and the state functions. The constraints are discretized over the Chebyshev-Gauss-Lobatto (CGL) collocation points. A Legendre technique is used to approximate the integral involved in the performance index. The OC problem is changed into an equivalent nonlinear programming problem which is directly solved. The fast Legendre transform is employed to reduce the computation time. Several further illustrative examples demonstrate the efficiency of the proposed method.
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.
Structural analysis of complex ecological economic optimal control problems
Kiseleva, T.
2011-01-01
This thesis demonstrates the importance and effectiveness of methods of bifurcation theory applied to studying non-convex optimal control problems. It opens up a new methodological approach to investigation of parameterized economic models. While standard analytical methods are not efficient and
Approximated analytical solution to an Ebola optimal control problem
Hincapié-Palacio, Doracelly; Ospina, Juan; Torres, Delfim F. M.
2016-11-01
An analytical expression for the optimal control of an Ebola problem is obtained. The analytical solution is found as a first-order approximation to the Pontryagin Maximum Principle via the Euler-Lagrange equation. An implementation of the method is given using the computer algebra system Maple. Our analytical solutions confirm the results recently reported in the literature using numerical methods.
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.
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
Parareal in time intermediate targets methods for optimal control problem
Maday, Yvon; Salomon, Julien
2012-01-01
In this paper, we present a method that enables solving in parallel the Euler-Lagrange system associated with the optimal control of a parabolic equation. Our approach is based on an iterative update of a sequence of intermediate targets that gives rise to independent sub-problems that can be solved in parallel. This method can be coupled with the parareal in time algorithm. Numerical experiments show the efficiency of our method.
Lossless Convexification of Control Constraints for a Class of Nonlinear Optimal Control Problems
Blackmore, Lars; Acikmese, Behcet; Carson, John M.,III
2012-01-01
In this paper we consider a class of optimal control problems that have continuous-time nonlinear dynamics and nonconvex control constraints. We propose a convex relaxation of the nonconvex control constraints, and prove that the optimal solution to the relaxed problem is the globally optimal solution to the original problem with nonconvex control constraints. This lossless convexification enables a computationally simpler problem to be solved instead of the original problem. We demonstrate the approach in simulation with a planetary soft landing problem involving a nonlinear gravity field.
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.
New attitude penalty functions for spacecraft optimal control problems
Energy Technology Data Exchange (ETDEWEB)
Schaub, H.; Junkins, J.L. [Texas A and M Univ., College Station, TX (United States). Dept. of Aerospace Engineering; Robinett, R.D. [Sandia National Labs., Albuquerque, NM (United States)
1996-03-01
A solution of a spacecraft optimal control problem, whose cost function relies on an attitude description, usually depends on the choice of attitude coordinates used. A problem could be solved using 3-2-1 Euler angles or using classical Rodriguez parameters and yield two different ``optimal`` solutions, unless the performance index in invariant with respect to the attitude coordinate choice. Another problem arising with many attitude coordinates is that they have no sense of when a body has tumbled beyond 180{degrees} from the reference attitude. In many such cases it would be easier (i.e. cost less) to let the body complete the revolution than to force it to reverse the rotation and return to the desired attitude. This paper develops a universal attitude penalty function g() whose value is independent of the attitude coordinates chosen to represent it. Furthermore, this function will achieve its maximum value only when a principal rotation of {plus_minus}180{degrees} from the target state is performed. This will implicitly permit the g() function to sense the shortest rotational distance back to the reference state. An attitude penalty function which depends on the Modified Rodriguez Parameters (MRP) will also be presented. These recently discovered MRPs are a non-singular three-parameter set which can describe any three-attitude. This MRP penalty function is simpler than the attitude coordinate independent g() function, but retains the useful property of avoiding lengthy principal rotations of more than {plus_minus}180{degrees}.
De Groote, Friedl; Kinney, Allison L; Rao, Anil V; Fregly, Benjamin J
2016-10-01
Estimation of muscle forces during motion involves solving an indeterminate problem (more unknown muscle forces than joint moment constraints), frequently via optimization methods. When the dynamics of muscle activation and contraction are modeled for consistency with muscle physiology, the resulting optimization problem is dynamic and challenging to solve. This study sought to identify a robust and computationally efficient formulation for solving these dynamic optimization problems using direct collocation optimal control methods. Four problem formulations were investigated for walking based on both a two and three dimensional model. Formulations differed in the use of either an explicit or implicit representation of contraction dynamics with either muscle length or tendon force as a state variable. The implicit representations introduced additional controls defined as the time derivatives of the states, allowing the nonlinear equations describing contraction dynamics to be imposed as algebraic path constraints, simplifying their evaluation. Problem formulation affected computational speed and robustness to the initial guess. The formulation that used explicit contraction dynamics with muscle length as a state failed to converge in most cases. In contrast, the two formulations that used implicit contraction dynamics converged to an optimal solution in all cases for all initial guesses, with tendon force as a state generally being the fastest. Future work should focus on comparing the present approach to other approaches for computing muscle forces. The present approach lacks some of the major limitations of established methods such as static optimization and computed muscle control while remaining computationally efficient.
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).
Comments on `A discrete optimal control problem for descriptor systems'
DEFF Research Database (Denmark)
Ravn, Hans
1990-01-01
In the above-mentioned work (see ibid., vol.34, p.177-81 (1989)), necessary and sufficient optimality conditions are derived for a discrete-time optimal problem, as well as other specific cases of implicit and explicit dynamic systems. The commenter corrects a mistake and demonstrates that there ...
Optimal Control Approaches to the Aggregate Production Planning Problem
Directory of Open Access Journals (Sweden)
Yasser A. Davizón
2015-12-01
Full Text Available In the area of production planning and control, the aggregate production planning (APP problem represents a great challenge for decision makers in production-inventory systems. Tradeoff between inventory-capacity is known as the APP problem. To address it, static and dynamic models have been proposed, which in general have several shortcomings. It is the premise of this paper that the main drawback of these proposals is, that they do not take into account the dynamic nature of the APP. For this reason, we propose the use of an Optimal Control (OC formulation via the approach of energy-based and Hamiltonian-present value. The main contribution of this paper is the mathematical model which integrates a second order dynamical system coupled with a first order system, incorporating production rate, inventory level, and capacity as well with the associated cost by work force in the same formulation. Also, a novel result in relation with the Hamiltonian-present value in the OC formulation is that it reduces the inventory level compared with the pure energy based approach for APP. A set of simulations are provided which verifies the theoretical contribution of this work.
Olympio, Joris T
2011-01-01
The paper describes a continuous second-variation algorithm to solve optimal control problems where the control is defined on a closed set. A second order expansion of a Lagrangian provides linear updates of the control to construct a locally feedback optimal control of the problem. Since the process involves a backward and a forward stage, which require storing trajectories, a method has been devised to accurately store continuous solutions of ordinary differential equations. Thanks to the continuous approach, the method adapts implicitly the numerical time mesh. The novel method is demonstrated on bang-bang optimal control problems, showing the suitability of the method to identify automatically optimal switching points in the control.
Optimal Control Problem of Feeding Adaptations of Daphnia and Neural Network Simulation
Kmet', Tibor; Kmet'ov, Mria
2010-09-01
A neural network based optimal control synthesis is presented for solving optimal control problems with control and state constraints and open final time. The optimal control problem is transcribed into nonlinear programming problem, which is implemented with adaptive critic neural network [9] and recurrent neural network for solving nonlinear proprojection equations [10]. The proposed simulation methods is illustrated by the optimal control problem of feeding adaptation of filter feeders of Daphnia. Results show that adaptive critic based systematic approach and neural network solving of nonlinear equations hold promise for obtaining the optimal control with control and state constraints and open final time.
Pseudospectral Collocation Methods for the Direct Transcription of Optimal Control Problems
2003-04-01
solving optimal control problems for trajectory optimization, spacecraft attitude control, jet thruster control, missile guidance and many other... optimal control problems using a pseudospectral direct transcription method. These problems are stated here so that they may be referred to elsewhere...e.g., [7]. 2.3 Prototypical Examples Throughout this thesis two example problems are used to demonstrate various prop- erties associated with solving
Directory of Open Access Journals (Sweden)
Yaping Hu
2015-01-01
the nonsmooth convex optimization problem. First, by using Moreau-Yosida regularization, we convert the original objective function to a continuously differentiable function; then we use approximate function and gradient values of the Moreau-Yosida regularization to substitute the corresponding exact values in the algorithm. The global convergence is proved under suitable assumptions. Numerical experiments are presented to show the effectiveness of this algorithm.
Institute of Scientific and Technical Information of China (English)
ZHANG DE-TAO
2009-01-01
In this paper, we use the solutions of forward-backward stochastic differential equations to get the optimal control for backward stochastic linear quadratic optimal control problem. And we also give the linear feedback regulator for the optimal control problem by using the solutions of a group of Riccati equations.
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.
Solving the optimal attention allocation problem in manual control
Kleinman, D. L.
1976-01-01
Within the context of the optimal control model of human response, analytic expressions for the gradients of closed-loop performance metrics with respect to human operator attention allocation are derived. These derivatives serve as the basis for a gradient algorithm that determines the optimal attention that a human should allocate among several display indicators in a steady-state manual control task. Application of the human modeling techniques are made to study the hover control task for a CH-46 VTOL flight tested by NASA.
Optimal Control Problem Governed by Semilinear Parabolic Equation and its Algorithm
Institute of Scientific and Technical Information of China (English)
Chun-fa Li; Xue Yang; En-min Feng
2008-01-01
In this paper, an optimal control problem governed by semilinear parabolic equation which involves the control variable acting on forcing term and coefficients appearing in the higher order derivative terms is formulated and analyzed. The strong variation method, due originally to Mayne et al to solve the optimal control problem of a lumped parameter system, is extended to solve an optimal control problem governed by semilinear parabolic equation, a necessary condition is obtained, the strong variation algorithm for this optimal control problem is presented, and the corresponding convergence result of the algorithm is verified.
Methods of centers and methods of feasible directions for the solution of optimal control problems.
Polak, E.; Mukai, H.; Pironneau, O.
1971-01-01
Demonstration of the applicability of methods of centers and of methods of feasible directions to optimal control problems. Presented experimental results show that extensions of Frank-Wolfe (1956), Zoutendijk (1960), and Pironneau-Polak (1971) algorithms for nonlinear programming problems can be quite efficient in solving optimal control problems.
Directory of Open Access Journals (Sweden)
Sie Long Kek
2015-01-01
Full Text Available A computational approach is proposed for solving the discrete time nonlinear stochastic optimal control problem. Our aim is to obtain the optimal output solution of the original optimal control problem through solving the simplified model-based optimal control problem iteratively. In our approach, the adjusted parameters are introduced into the model used such that the differences between the real system and the model used can be computed. Particularly, system optimization and parameter estimation are integrated interactively. On the other hand, the output is measured from the real plant and is fed back into the parameter estimation problem to establish a matching scheme. During the calculation procedure, the iterative solution is updated in order to approximate the true optimal solution of the original optimal control problem despite model-reality differences. For illustration, a wastewater treatment problem is studied and the results show the efficiency of the approach proposed.
Averaging and Linear Programming in Some Singularly Perturbed Problems of Optimal Control
Energy Technology Data Exchange (ETDEWEB)
Gaitsgory, Vladimir, E-mail: vladimir.gaitsgory@mq.edu.au [Macquarie University, Department of Mathematics (Australia); Rossomakhine, Sergey, E-mail: serguei.rossomakhine@flinders.edu.au [Flinders University, Flinders Mathematical Sciences Laboratory, School of Computer Science, Engineering and Mathematics (Australia)
2015-04-15
The paper aims at the development of an apparatus for analysis and construction of near optimal solutions of singularly perturbed (SP) optimal controls problems (that is, problems of optimal control of SP systems) considered on the infinite time horizon. We mostly focus on problems with time discounting criteria but a possibility of the extension of results to periodic optimization problems is discussed as well. Our consideration is based on earlier results on averaging of SP control systems and on linear programming formulations of optimal control problems. The idea that we exploit is to first asymptotically approximate a given problem of optimal control of the SP system by a certain averaged optimal control problem, then reformulate this averaged problem as an infinite-dimensional linear programming (LP) problem, and then approximate the latter by semi-infinite LP problems. We show that the optimal solution of these semi-infinite LP problems and their duals (that can be found with the help of a modification of an available LP software) allow one to construct near optimal controls of the SP system. We demonstrate the construction with two numerical examples.
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
This article is concerned with second-order necessary and sufficient optimality conditions for optimal control problems governed by 3-dimensional Navier-Stokes equations. The periodic state constraint is considered.
Institute of Scientific and Technical Information of China (English)
2008-01-01
In this paper,we investigate the Legendre Galerkin spectral approximation of quadratic optimal control problems governed by parabolic equations.A spectral approximation scheme for the parabolic optimal control problem is presented.We obtain a posteriori error estimates of the approximated solutions for both the state and the control.
Feedback Control Method Using Haar Wavelet Operational Matrices for Solving Optimal Control Problems
Waleeda Swaidan; Amran Hussin
2013-01-01
Most of the direct methods solve optimal control problems with nonlinear programming solver. In this paper we propose a novel feedback control method for solving for solving affine control system, with quadratic cost functional, which makes use of only linear systems. This method is a numerical technique, which is based on the combination of Haar wavelet collocation method and successive Generalized Hamilton-Jacobi-Bellman equation. We formulate some new Haar wavelet oper...
A MATLAB GUI for a Legendre Pseudospectral algorithm for optimal control problems
Hall, Andrew O.
1999-01-01
Approved for public release; distribution is unlimited This implementation of a Legendre-Gauss-Lobatto Pseudospectral (LGLP) algorithm takes advantage of the MATLAB Graphical User Interface (GUI) and the Optimization Toolbox to allow an efficient implementation of a direct solution technique. Direct solutions techniques solve optimal control problems without solving for the optimality conditions. Using the LGLP method, an optimal control problem is discretized into a Nonlinear Program (NLP...
A maximum principle for smooth optimal impulsive control problems with multipoint state constraints
Dykhta, V. A.; Samsonyuk, O. N.
2009-06-01
A nonlinear optimal impulsive control problem with trajectories of bounded variation subject to intermediate state constraints at a finite number on nonfixed instants of time is considered. Features of this problem are discussed from the viewpoint of the extension of the classical optimal control problem with the corresponding state constraints. A necessary optimality condition is formulated in the form of a smooth maximum principle; thorough comments are given, a short proof is presented, and examples are discussed.
An optimal control problem for ovine brucellosis with culling.
Nannyonga, B; Mwanga, G G; Luboobi, L S
2015-01-01
A mathematical model is used to study the dynamics of ovine brucellosis when transmitted directly from infected individual, through contact with a contaminated environment or vertically through mother to child. The model developed by Aïnseba et al. [A model for ovine brucellosis incorporating direct and indirect transmission, J. Biol. Dyn. 4 (2010), pp. 2-11. Available at http://www.math.u-bordeaux1.fr/∼pmagal100p/papers/BBM-JBD09.pdf. Accessed 3 July 2012] was modified to include culling and then used to determine important parameters in the spread of human brucellosis using sensitivity analysis. An optimal control analysis was performed on the model to determine the best way to control such as a disease in the population. Three time-dependent controls to prevent exposure, cull the infected and reduce environmental transmission were used to set up to minimize infection at a minimum cost.
Feedback Control Method Using Haar Wavelet Operational Matrices for Solving Optimal Control Problems
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Waleeda Swaidan
2013-01-01
Full Text Available Most of the direct methods solve optimal control problems with nonlinear programming solver. In this paper we propose a novel feedback control method for solving for solving affine control system, with quadratic cost functional, which makes use of only linear systems. This method is a numerical technique, which is based on the combination of Haar wavelet collocation method and successive Generalized Hamilton-Jacobi-Bellman equation. We formulate some new Haar wavelet operational matrices in order to manipulate Haar wavelet series. The proposed method has been applied to solve linear and nonlinear optimal control problems with infinite time horizon. The simulation results indicate that the accuracy of the control and cost can be improved by increasing the wavelet resolution.
Debbarma, Sanjoy; Saikia, Lalit Chandra; Sinha, Nidul
2014-03-01
Present work focused on automatic generation control (AGC) of a three unequal area thermal systems considering reheat turbines and appropriate generation rate constraints (GRC). A fractional order (FO) controller named as I(λ)D(µ) controller based on crone approximation is proposed for the first time as an appropriate technique to solve the multi-area AGC problem in power systems. A recently developed metaheuristic algorithm known as firefly algorithm (FA) is used for the simultaneous optimization of the gains and other parameters such as order of integrator (λ) and differentiator (μ) of I(λ)D(µ) controller and governor speed regulation parameters (R). The dynamic responses corresponding to optimized I(λ)D(µ) controller gains, λ, μ, and R are compared with that of classical integer order (IO) controllers such as I, PI and PID controllers. Simulation results show that the proposed I(λ)D(µ) controller provides more improved dynamic responses and outperforms the IO based classical controllers. Further, sensitivity analysis confirms the robustness of the so optimized I(λ)D(µ) controller to wide changes in system loading conditions and size and position of SLP. Proposed controller is also found to have performed well as compared to IO based controllers when SLP takes place simultaneously in any two areas or all the areas. Robustness of the proposed I(λ)D(µ) controller is also tested against system parameter variations.
Han, Lanshan; Camlibel, M. Kanat; Pang, Jong-Shi; Heemels, W. P. Maurice H.
2012-01-01
This paper presents a numerical scheme for solving the continuous-time convex linear-quadratic (LQ) optimal control problem with mixed polyhedral state and control constraints. Unifying a discretization of this optimal control problem as often employed in model predictive control and that obtained
A numerical method for solving optimal control problems using state parametrization
Mehne, H.; Borzabadi, A.
2006-06-01
A numerical method for solving a special class of optimal control problems is given. The solution is based on state parametrization as a polynomial with unknown coefficients. This converts the problem to a non-linear optimization problem. To facilitate the computation of optimal coefficients, an improved iterative method is suggested. Convergence of this iterative method and its implementation for numerical examples are also given.
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.
Directory of Open Access Journals (Sweden)
Jingtao Shi
2013-01-01
Full Text Available This paper is concerned with the relationship between maximum principle and dynamic programming for stochastic recursive optimal control problems. Under certain differentiability conditions, relations among the adjoint processes, the generalized Hamiltonian function, and the value function are given. A linear quadratic recursive utility portfolio optimization problem in the financial engineering is discussed as an explicitly illustrated example of the main result.
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.
Peng, Haijun; Wang, Xinwei; Zhang, Sheng; Chen, Biaosong
2017-07-01
Nonlinear state-delayed optimal control problems have complex nonlinear characters. To solve this complex nonlinear problem, an iterative symplectic pseudospectral method based on quasilinearization techniques, the dual variational principle and pseudospectral methods is proposed in this paper. First, the proposed method transforms the original nonlinear optimal control problem into a series of linear quadratic optimal control problems. Then, a symplectic pseudospectral method is developed to solve these converted linear quadratic state-delayed optimal control problems. Coefficient matrices in the proposed method are sparse and symmetric since the dual variational principle is used, which makes the proposed method highly efficient. Converged numerical solutions with high precision can be obtained after a few iterations due to the benefit of the local pseudospectral method and quasilinearization techniques. In the numerical simulations, other numerical methods were used for comparisons. The numerical simulation results show that the proposed method is highly accurate, efficient and robust.
A Transformation Approach to Optimal Control Problems with Bounded State Variables
Hanafy, Lawrence Hanafy
1971-01-01
A technique is described and utilized in the study of the solutions to various general problems in optimal control theory, which are converted in to Lagrange problems in the calculus of variations. This is accomplished by mapping certain properties in Euclidean space onto closed control and state regions. Nonlinear control problems with a unit m cube as control region and unit n cube as state region are considered.
Deterministic Time-inconsistent Optimal Control Problems - an Essentially Cooperative Approach
Institute of Scientific and Technical Information of China (English)
Jiong-min YONG
2012-01-01
A general deterministic time-inconsistent optimal control problem is formulated for ordinary differential equations.To find a time-consistent equilibrium value function and the corresponding time-consistent equilibrium control,a non-cooperative N-person differential game (but essentially cooperative in some sense) is introduced.Under certain conditions,it is proved that the open-loop Nash equilibrium value function of the N-person differential game converges to a time-consistent equilibrium value function of the original problem,which is the value function of a time-consistent optimal control problem.Moreover,it is proved that any optimal control of the time-consistent limit problem is a time-consistent equilibrium control of the original problem.
On the Limit Matrix Obtained in the Homogenization of an Optimal Control Problem
Indian Academy of Sciences (India)
S Kesavan; M Rajesh
2002-05-01
A new formulation for the limit matrix occurring in the cost functional of an optimal control problem on homogenization is obtained. It is used to obtain an upper bound for this matrix (in the sense of positive definite matrices).
Directory of Open Access Journals (Sweden)
Mariela Olguín
2015-01-01
Full Text Available The objective of this work is to make the numerical analysis, through the finite element method with Lagrange’s triangles of type 1, of a continuous optimal control problem governed by an elliptic variational inequality where the control variable is the internal energy g. The existence and uniqueness of this continuous optimal control problem and its associated state system were proved previously. In this paper, we discretize the elliptic variational inequality which defines the state system and the corresponding cost functional, and we prove that there exist a discrete optimal control and its associated discrete state system for each positive h (the parameter of the finite element method approximation. Finally, we show that the discrete optimal control and its associated state system converge to the continuous optimal control and its associated state system when the parameter h goes to zero.
SHAPE STABILITY OF OPTIMAL CONTROL PROBLEMS IN COEFFICIENTS FOR COUPLED SYSTEM OF HAMMERSTEIN TYPE
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P. I. Kogut
2014-01-01
Full Text Available In this paper we consider an optimal control problem (OCP for the coupledsystem of a nonlinear monotone Dirichlet problem with matrix-valued L∞(Ω;RN×N-controls in coecients and a nonlinear equation of Hammerstein type, where solution nonlinearly depends on L∞ -control. Since problems of this type have no solutions in general, we make a special assumption on the coecients of the state equations and introduce the class of so-called solenoidal admissible controls. Using the direct method in calculus of variations, we prove the existence of an optimal control. We also study the stability of the optimal control problem with respect to the domain perturbation. In particular, we derive the sucient conditions of the Mosco-stability for the given class of OCPs.
The First Survey for Abilities of Wavelets in Solving Optimal Control Problems by Embedding Methods
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A. Fakharzadeh
2007-06-01
Full Text Available By a brief review on the applications of wavelets in solving optimal control problems, a multiresolution analysis for two dimensional Sobolev spaces and the square spline wavelets are considered. Regarding the density and approximation properties of these wavelets, for the first time, they are employed for solving optimal control problems by embedding method. Existence and the determination way for the solution are also discussed. Finally, the abilities of the new approach are explained by a numerical example and some comparisons
Mehmetoglu, Mustafa; Akyol, Emrah; Rose, Kenneth
2016-01-01
This note studies the global optimization of controller mappings in discrete-time stochastic control problems including Witsenhausen's celebrated 1968 counter-example. We propose a generally applicable non-convex numerical optimization method based on the concept of deterministic annealing-which is derived from information-theoretic principles and was successfully employed in several problems including vector quantization, classification, and regression. We present comparative numerical resul...
Construction of asymptotically optimal control for crisscross network from a free boundary problem
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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.
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...
Time-Inconsistent Optimal Control Problems and the Equilibrium HJB Equation
Yong, Jiongmin
2012-01-01
A general time-inconsistent optimal control problem is considered for stochastic differential equations with deterministic coefficients. Under suitable conditions, a Hamilton-Jacobi-Bellman type equation is derived for the equilibrium value function of the problem. Well-posedness and some properties of such an equation is studied, and time-consistent equilibrium strategies are constructed. As special cases, the linear-quadratic problem and a generalized Merton's portfolio problem are investigated.
Noether's Symmetry Theorem for Variational and Optimal Control Problems with Time Delay
Frederico, G. S. F.; Torres, D. F. M.
2012-01-01
We extend the DuBois-Reymond necessary optimality condition and Noether's symmetry theorem to the time delay variational setting. Both Lagrangian and Hamiltonian versions of Noether's theorem are proved, covering problems of the calculus of variations and optimal control with delays.
Direct SQP-methods for solving optimal control problems with delays
Energy Technology Data Exchange (ETDEWEB)
Goellmann, L.; Bueskens, C.; Maurer, H.
1994-12-31
The maximum principle for optimal control problems with delays leads to a boundary value problem (BVP) which is retarded in the state and advanced in the costate function. Based on shooting techniques, solution methods for this type of BVP have been proposed. In recent years, direct optimization methods have been favored for solving control problems without delays. Direct methods approximate the control and the state over a fixed mesh and solve the resulting NLP-problem with SQP-methods. These methods dispense with the costate function and have shown to be robust and efficient. In this paper, we propose a direct SQP-method for retarded control problems. In contrast to conventional direct methods, only the control variable is approximated by e.g. spline-functions. The state is computed via a high order Runge-Kutta type algorithm and does not enter explicitly the NLP-problem through an equation. This approach reduces the number of optimization variables considerably and is implementable even on a PC. Our method is illustrated by the numerical solution of retarded control problems with constraints. In particular, we consider the control of a continuous stirred tank reactor which has been solved by dynamic programming. This example illustrates the robustness and efficiency of the proposed method. Open questions concerning sufficient conditions and convergence of discretized NLP-problems are discussed.
The solution of singular optimal control problems using direct collocation and nonlinear programming
Downey, James R.; Conway, Bruce A.
1992-08-01
This paper describes work on the determination of optimal rocket trajectories which may include singular arcs. In recent years direct collocation and nonlinear programming has proven to be a powerful method for solving optimal control problems. Difficulties in the application of this method can occur if the problem is singular. Techniques exist for solving singular problems indirectly using the associated adjoint formulation. Unfortunately, the adjoints are not a part of the direct formulation. It is shown how adjoint information can be obtained from the direct method to allow the solution of singular problems.
Linearization of a Matrix Riccati Equation Associated to an Optimal Control Problem
Directory of Open Access Journals (Sweden)
Foued Zitouni
2014-01-01
Full Text Available The matrix Riccati equation that must be solved to obtain the solution to stochastic optimal control problems known as LQG homing is linearized for a class of processes. The results generalize a theorem proved by Whittle and the one-dimensional case already considered by the authors. A particular two-dimensional problem is solved explicitly.
Relaxation Methods for Hyperbolic PDE Mixed-Integer Optimal Control Problems
Hante, Falk M.
2015-01-01
We extend the convergence analysis for methods solving PDE-constrained optimal control problems containing both discrete and continuous control decisions based on relaxation and rounding strategies to the class of first order semilinear hyperbolic systems in one space dimension. The results are obtained by novel a-priori estimates for the size of the relaxation gap based on the characteristic flow, fixed-point arguments and particular regularity theory for such mixed-integer control problems....
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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.
Institute of Scientific and Technical Information of China (English)
Danping Yang; Yanzhen Chang; Wenbin Liu
2008-01-01
In this paper,we investigate a priori error estimates and superconvergence properties for a model optimal control problem of bilinear type,which includes some parameter estimation application.The state and co-state are discretized by piecewise linear functions and control is approximated by piecewise constant functions.We derive a priori error estimates and superconvergence analysis for both the control and the state approximations.We also give the optimal L2-norm error estimates and the almost optimal L8-norm estimates about the state and co-state.The results can be readily used for constructing a posteriori error estimators in adaptive finite element approximation of such optimal control problems.
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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.
Direct Method for Resolution of Optimal Control Problem with Free Initial Condition
Directory of Open Access Journals (Sweden)
Louadj Kahina
2012-01-01
Full Text Available The theory of control analyzes the proprieties of commanded systems. Problems of optimal control (OC have been intensively investigated in the world literature for over forty years. During this period, series of fundamental results have been obtained, among which should be noted the maximum principle (Pontryagin et al., 1962 and dynamic programming (Bellman, 1963. For many of the problems of the optimal control theory (OCT, adequate solutions are found (Bryson and Yu-chi, 1969, Lee and Markus, 1967, Gabasov and Kirillova, 1977, 1978, 1980. Results of the theory were taken up in various fields of science, engineering, and economics. The present paper aims at extending the constructive methods of Balashevich et al., (2000 that were developed for the problems of optimal control with the bounded initial state is not fixed are considered.
On an Optimal -Control Problem in Coefficients for Linear Elliptic Variational Inequality
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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.
Approximate dynamic programming recurrence relations for a hybrid optimal control problem
Lu, W.; Ferrari, S.; Fierro, R.; Wettergren, T. A.
2012-06-01
This paper presents a hybrid approximate dynamic programming (ADP) method for a hybrid dynamic system (HDS) optimal control problem, that occurs in many complex unmanned systems which are implemented via a hybrid architecture, regarding robot modes or the complex environment. The HDS considered in this paper is characterized by a well-known three-layer hybrid framework, which includes a discrete event controller layer, a discrete-continuous interface layer, and a continuous state layer. The hybrid optimal control problem (HOCP) is to nd the optimal discrete event decisions and the optimal continuous controls subject to a deterministic minimization of a scalar function regarding the system state and control over time. Due to the uncertainty of environment and complexity of the HOCP, the cost-to-go cannot be evaluated before the HDS explores the entire system state space; as a result, the optimal control, neither continuous nor discrete, is not available ahead of time. Therefore, ADP is adopted to learn the optimal control while the HDS is exploring the environment, because of the online advantage of ADP method. Furthermore, ADP can break the curses of dimensionality which other optimizing methods, such as dynamic programming (DP) and Markov decision process (MDP), are facing due to the high dimensions of HOCP.
A novel hybrid optimization algorithm for diferential-algebraic control problems
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F. S. Lobato
2007-09-01
Full Text Available Dynamic optimization problems can be numerically solved by direct, indirect and Hamilton-Jacobi-Bellman methods. In this paper, the differential-algebraic approach is incorporated into a hybrid method, extending the concepts of structural and differential indexes, consistent initialization analysis, index reduction and dynamic degrees of freedom to the optimal control problem. The resultant differential-algebraic optimal control problem is solved in the following steps: transformation of the original problem into a standard nonlinear programming problem that provides control and state variables, switching time estimates and costate variables profiles with the DIRCOL code; definition of the switching function and the automatically generated sequence of index-1 differential-algebraic boundary value problems from Pontryagin’s minimum principle by using the developed Otima code; and finally, application of the COLDAE code with the results of the direct method as an initial guess. The proposed hybrid method is illustrated with a pressure-constrained batch reactor optimization problem associated with the slack variable method.
Directory of Open Access Journals (Sweden)
Qinghua Zeng
2015-07-01
Full Text Available This article proposes a linear matrix inequality–based robust controller design approach to implement the synchronous design of aircraft control discipline and other disciplines, in which the variation in design parameters is treated as equivalent perturbations. Considering the complicated mapping relationships between the coefficient arrays of aircraft motion model and the aircraft design parameters, the robust controller designed is directly based on the variation in these coefficient arrays so conservative that the multidisciplinary design optimization problem would be too difficult to solve, or even if there is a solution, the robustness of design result is generally poor. Therefore, this article derives the uncertainty model of disciplinary design parameters based on response surface approximation, converts the design problem of the robust controller into a problem of solving a standard linear matrix inequality, and theoretically gives a less conservative design method of the robust controller which is based on the variation in design parameters. Furthermore, the concurrent subspace approach is applied to the multidisciplinary system with this kind of robust controller in the design loop. A multidisciplinary design optimization of a tailless aircraft as example is shown that control discipline can be synchronous optimal design with other discipline, especially this method will greatly reduce the calculated amount of multidisciplinary design optimization and make multidisciplinary design optimization results more robustness of flight performance.
Tang, Xiaojun
2016-04-01
The main purpose of this work is to provide multiple-interval integral Gegenbauer pseudospectral methods for solving optimal control problems. The latest developed single-interval integral Gauss/(flipped Radau) pseudospectral methods can be viewed as special cases of the proposed methods. We present an exact and efficient approach to compute the mesh pseudospectral integration matrices for the Gegenbauer-Gauss and flipped Gegenbauer-Gauss-Radau points. Numerical results on benchmark optimal control problems confirm the ability of the proposed methods to obtain highly accurate solutions.
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
Liu, Derong; Li, Hongliang; Wang, Ding
2015-06-01
In this paper, we establish error bounds of adaptive dynamic programming algorithms for solving undiscounted infinite-horizon optimal control problems of discrete-time deterministic nonlinear systems. We consider approximation errors in the update equations of both value function and control policy. We utilize a new assumption instead of the contraction assumption in discounted optimal control problems. We establish the error bounds for approximate value iteration based on a new error condition. Furthermore, we also establish the error bounds for approximate policy iteration and approximate optimistic policy iteration algorithms. It is shown that the iterative approximate value function can converge to a finite neighborhood of the optimal value function under some conditions. To implement the developed algorithms, critic and action neural networks are used to approximate the value function and control policy, respectively. Finally, a simulation example is given to demonstrate the effectiveness of the developed algorithms.
Institute of Scientific and Technical Information of China (English)
Yanzhen Chang; Danping Yang
2008-01-01
In this paper, we consider the finite element approximation of the distributed optimal control problems of the stationary Bénard type under the pointwise control constraint. The states and the co-states are approximated by polynomial functions of lowest-order mixed finite element space or piecewise linear functions and the control is approximated by piecewise constant functions. We give the superconvergence analysis for the control; it is proved that the approximation has a second-order rate of convergence. We further give the superconvergence analysis for the states and the co-states. Then we derive error estimates in L∞-norm and optimal error estimates in L2-norm.
Tang, Yuelong; Hua, Yuchun
2017-01-01
In this paper, a semidiscrete finite element method for solving bilinear parabolic optimal control problems is considered. Firstly, we present a finite element approximation of the model problem. Secondly, we bring in some important intermediate variables and their error estimates. Thirdly, we derive a priori error estimates of the approximation scheme. Finally, we obtain the superconvergence between the semidiscrete finite element solutions and projections of the exact solutions. A numerical example is presented to verify our theoretical results.
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.
On two speed optimization problems for ships that sail in and out of emission control areas
DEFF Research Database (Denmark)
Fagerholt, Kjetil; Psaraftis, Harilaos N.
2015-01-01
This paper deals with two speed optimization problems for ships that sail in and out of Emission Control Areas (ECAs) with strict limits on sulfur emissions. For ships crossing in and out of ECAs, such as deep-sea vessels, one of the common options for complying with these limits is to burn heavy...
Solution of Constrained Optimal Control Problems Using Multiple Shooting and ESDIRK Methods
DEFF Research Database (Denmark)
Capolei, Andrea; Jørgensen, John Bagterp
2012-01-01
In this paper, we describe a novel numerical algorithm for solution of constrained optimal control problems of the Bolza type for stiff and/or unstable systems. The numerical algorithm combines explicit singly diagonally implicit Runge-Kutta (ESDIRK) integration methods with a multiple shooting...
A new computer method for temperature measurement based on an optimal control problem
Damean, N.; Houkes, Z.; Regtien, P.P.L.
1996-01-01
A new computer method to measure extreme temperatures is presented. The method reduces the measurement of the unknown temperature to the solving of an optimal control problem, using a numerical computer. Based on this method, a new device for temperature measurement is built. It consists of a hardwa
Time-optimal control problem for the swing and the ski
Piccoli, B
1994-01-01
This paper is concerned with a class of time-optimal control problems for the swing and the ski. We first consider the motion of a man standing on a swing. For simplicity, we neglect friction and air resistance and assume that the mass of the swinger is concentrated in his baricenter B. For the ski, we use the model considered by Aldo Bressan (1991), with a special approximation of the skier. Our main concern is the existence and the structure of time-optimal controls. As first step, we introduce an auxiliary control system with control entering linearly and show the relationships between this and the original system. We then perform a detailed study of the auxiliary system, using geometric techniques. In turn this provides accurate information on the time-optimal controls for the original system.
Optimal Control Problems in Finite-Strain Elasticity by Inner Pressure and Fiber Tension
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Andreas eGünnel
2016-04-01
Full Text Available Optimal control problems for finite-strain elasticity are considered.An inner pressure or an inner fiber tension are acting as driving forces.Such internal forces are typical, for instance, for the motion of heliotropic plants, and for muscle tissue.Non-standard objective functions relevant for elasticity problems are introduced.Optimality conditions are derived on a formal basis, and a limited-memory quasi-Newton algorithm for their solution is formulated in function space.Numerical experiments confirm the expected mesh-independent performance.
Preconditioners for state-constrained optimal control problems with Moreau-Yosida penalty function
Pearson, John W.
2012-11-21
Optimal control problems with partial differential equations as constraints play an important role in many applications. The inclusion of bound constraints for the state variable poses a significant challenge for optimization methods. Our focus here is on the incorporation of the constraints via the Moreau-Yosida regularization technique. This method has been studied recently and has proven to be advantageous compared with other approaches. In this paper, we develop robust preconditioners for the efficient solution of the Newton steps associated with the fast solution of the Moreau-Yosida regularized problem. Numerical results illustrate the efficiency of our approach. © 2012 John Wiley & Sons, Ltd.
A non-standard optimal control problem arising in an economics application
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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.
Institute of Scientific and Technical Information of China (English)
Ningning YAN; Zhaojie ZHOU
2008-01-01
In this paper,we study a posteriori error estimates of the edge stabilization Galerkin method for the constrained optimal control problem governed by convection-dominated diffusion equations.The residual-type a posteriori error estimators yield both upper and lower bounds for control u measured in L2-norm and for state y and costate p measured in energy norm.Two numerical examples are presented to illustrate the effectiveness of the error estimators provided in this paper.
Parallel implementations of gradient-based iterative algorithms for optimal control problems
Energy Technology Data Exchange (ETDEWEB)
Podrazik, L.J.
1988-01-01
The primary objective of this research is to develop new parallel techniques for solving optimal control problems that occur in online real-time applications. In view of the availability of inexpensive yet powerful hardware, the use of parallel-processing techniques is proposed to satisfy both the speed constraints imposed by a real-time setting as well as the reliability requirements of an online system. Unlike previous parallel approaches to the solution of optimal control problems, the goal is to obtain an efficient solution by structuring the control algorithms to exhibit parallelism that matches the given machine architecture. In order to achieve the goal, this work reexamines optimal control problems from the perspective of their first-order optimality conditions so that the issues of parallelism and machine architecture may be considered in the forefront of the algorithm synthesis. Results include the development of an efficient parallel procedure for gradient evaluation. Embedded in the parallel-gradient evaluation procedure is a new technique for solving first-order linear recurrence systems, which is synthesized as a function of the number of available computers.
On large-scale nonlinear programming techniques for solving optimal control problems
Energy Technology Data Exchange (ETDEWEB)
Faco, J.L.D.
1994-12-31
The formulation of decision problems by Optimal Control Theory allows the consideration of their dynamic structure and parameters estimation. This paper deals with techniques for choosing directions in the iterative solution of discrete-time optimal control problems. A unified formulation incorporates nonlinear performance criteria and dynamic equations, time delays, bounded state and control variables, free planning horizon and variable initial state vector. In general they are characterized by a large number of variables, mostly when arising from discretization of continuous-time optimal control or calculus of variations problems. In a GRG context the staircase structure of the jacobian matrix of the dynamic equations is exploited in the choice of basic and super basic variables and when changes of basis occur along the process. The search directions of the bound constrained nonlinear programming problem in the reduced space of the super basic variables are computed by large-scale NLP techniques. A modified Polak-Ribiere conjugate gradient method and a limited storage quasi-Newton BFGS method are analyzed and modifications to deal with the bounds on the variables are suggested based on projected gradient devices with specific linesearches. Some practical models are presented for electric generation planning and fishery management, and the application of the code GRECO - Gradient REduit pour la Commande Optimale - is discussed.
A Real-Time Optimization Framework for the Iterative Controller Tuning Problem
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Gene A. Bunin
2013-09-01
Full Text Available We investigate the general iterative controller tuning (ICT problem, where the task is to find a set of controller parameters that optimize some user-defined performance metric when the same control task is to be carried out repeatedly. Following a repeatability assumption on the system, we show that the ICT problem may be formulated as a real-time optimization (RTO problem, thus allowing for the ICT problem to be solved in the RTO framework, which is both very flexible and comes with strong theoretical guarantees. In particular, we propose the use of a recently released RTO solver and outline a simple procedure for how this solver may be configured to solve ICT problems. The effectiveness of the proposed method is illustrated by successfully applying it to four case studies—two experimental and two simulated—that cover the tuning of model-predictive, general fixed-order and PID controllers, as well as a system of controllers working in parallel.
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.
hp-Pseudospectral method for solving continuous-time nonlinear optimal control problems
Darby, Christopher L.
2011-12-01
In this dissertation, a direct hp-pseudospectral method for approximating the solution to nonlinear optimal control problems is proposed. The hp-pseudospectral method utilizes a variable number of approximating intervals and variable-degree polynomial approximations of the state within each interval. Using the hp-discretization, the continuous-time optimal control problem is transcribed to a finite-dimensional nonlinear programming problem (NLP). The differential-algebraic constraints of the optimal control problem are enforced at a finite set of collocation points, where the collocation points are either the Legendre-Gauss or Legendre-Gauss-Radau quadrature points. These sets of points are chosen because they correspond to high-accuracy Gaussian quadrature rules for approximating the integral of a function. Moreover, Runge phenomenon for high-degree Lagrange polynomial approximations to the state is avoided by using these points. The key features of the hp-method include computational sparsity associated with low-order polynomial approximations and rapid convergence rates associated with higher-degree polynomials approximations. Consequently, the hp-method is both highly accurate and computationally efficient. Two hp-adaptive algorithms are developed that demonstrate the utility of the hp-approach. The algorithms are shown to accurately approximate the solution to general continuous-time optimal control problems in a computationally efficient manner without a priori knowledge of the solution structure. The hp-algorithms are compared empirically against local (h) and global (p) collocation methods over a wide range of problems and are found to be more efficient and more accurate. The hp-pseudospectral approach developed in this research not only provides a high-accuracy approximation to the state and control of an optimal control problem, but also provides high-accuracy approximations to the costate of the optimal control problem. The costate is approximated by
Optimal control problem for a sixth-order Cahn-Hilliard equation with nonlinear diffusion
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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.
Institute of Scientific and Technical Information of China (English)
Huaibin TANG; Zhen WU
2009-01-01
In this paper, the authors first study two kinds of stochastic differential equations (SDEs)cesses, the authors proceed to study a stochastic linear quadratic (LQ) optimal control problem with One kind of new stochastic Riccati equation that involves equality and inequality constraints is derived from the idea of square completion and its solvability is proved to be sufficient for the well-posedness and the existence of optimal control which can be of either state feedback or open-loop form of the LQ problems. Moreover, the authors obtain the existence and uniqueness of the solution to the Riccati equation for some special cases. Finally, two examples are presented to illustrate these theoretical results.
An Error Estimate for Symplectic Euler Approximation of Optimal Control Problems
Karlsson, Jesper
2015-01-01
This work focuses on numerical solutions of optimal control problems. A time discretization error representation is derived for the approximation of the associated value function. It concerns symplectic Euler solutions of the Hamiltonian system connected with the optimal control problem. The error representation has a leading-order term consisting of an error density that is computable from symplectic Euler solutions. Under an assumption of the pathwise convergence of the approximate dual function as the maximum time step goes to zero, we prove that the remainder is of higher order than the leading-error density part in the error representation. With the error representation, it is possible to perform adaptive time stepping. We apply an adaptive algorithm originally developed for ordinary differential equations. The performance is illustrated by numerical tests.
An A Posteriori Error Estimate for Symplectic Euler Approximation of Optimal Control Problems
Karlsson, Jesper
2015-01-07
This work focuses on numerical solutions of optimal control problems. A time discretization error representation is derived for the approximation of the associated value function. It concerns Symplectic Euler solutions of the Hamiltonian system connected with the optimal control problem. The error representation has a leading order term consisting of an error density that is computable from Symplectic Euler solutions. Under an assumption of the pathwise convergence of the approximate dual function as the maximum time step goes to zero, we prove that the remainder is of higher order than the leading error density part in the error representation. With the error representation, it is possible to perform adaptive time stepping. We apply an adaptive algorithm originally developed for ordinary differential equations.
Reinforcement learning solution for HJB equation arising in constrained optimal control problem.
Luo, Biao; Wu, Huai-Ning; Huang, Tingwen; Liu, Derong
2015-11-01
The constrained optimal control problem depends on the solution of the complicated Hamilton-Jacobi-Bellman equation (HJBE). In this paper, a data-based off-policy reinforcement learning (RL) method is proposed, which learns the solution of the HJBE and the optimal control policy from real system data. One important feature of the off-policy RL is that its policy evaluation can be realized with data generated by other behavior policies, not necessarily the target policy, which solves the insufficient exploration problem. The convergence of the off-policy RL is proved by demonstrating its equivalence to the successive approximation approach. Its implementation procedure is based on the actor-critic neural networks structure, where the function approximation is conducted with linearly independent basis functions. Subsequently, the convergence of the implementation procedure with function approximation is also proved. Finally, its effectiveness is verified through computer simulations.
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
Evolutionary path control strategy for solving many-objective optimization problem.
Roy, Proteek Chandan; Islam, Md Monirul; Murase, Kazuyuki; Yao, Xin
2015-04-01
The number of objectives in many-objective optimization problems (MaOPs) is typically high and evolutionary algorithms face severe difficulties in solving such problems. In this paper, we propose a new scalable evolutionary algorithm, called evolutionary path control strategy (EPCS), for solving MaOPs. The central component of our algorithm is the use of a reference vector that helps simultaneously minimizing all the objectives of an MaOP. In doing so, EPCS employs a new fitness assignment strategy for survival selection. This strategy consists of two procedures and our algorithm applies them sequentially. It encourages a population of solutions to follow a certain path reaching toward the Pareto optimal front. The essence of our strategy is that it reduces the number of nondominated solutions to increase selection pressure in evolution. Furthermore, unlike previous work, EPCS is able to apply the classical Pareto-dominance relation with the new fitness assignment strategy. Our algorithm has been tested extensively on several scalable test problems, namely five DTLZ problems with 5 to 40 objectives and six WFG problems with 2 to 13 objectives. Furthermore, the algorithm has been tested on six CEC09 problems having 2 or 3 objectives. The experimental results show that EPCS is capable of finding better solutions compared to other existing algorithms for problems with an increasing number of objectives.
Reflected BSDEs with Random Default Time and Related Mixed Optimal Stopping-control Problems
Institute of Scientific and Technical Information of China (English)
Dong-mei Guo; Xiao-ming Xu
2013-01-01
In this paper we study the one-dimensional reflected backward stochastic differential equations which are driven by Brownian motion as well as a mutually independent martingale appearing in a defaultable setting.Using a penalization method,we prove the existence and uniqueness of the solutions to these equations.As an application,we show that under proper assumptions the solution of the reflected equation is the value of the related mixed optimal stopping-control problem.
An Efficient Pseudospectral Method for Solving a Class of Nonlinear Optimal Control Problems
Emran Tohidi; Atena Pasban; Kilicman, A.; S. Lotfi Noghabi
2013-01-01
This paper gives a robust pseudospectral scheme for solving a class of nonlinear optimal control problems (OCPs) governed by differential inclusions. The basic idea includes two major stages. At the first stage, we linearize the nonlinear dynamical system by an interesting technique which is called linear combination property of intervals. After this stage, the linearized dynamical system is transformed into a multi domain dynamical system via computational interval partitioning. Moreover,...
Ito, Kazufumi; Teglas, Russell
1987-01-01
The numerical scheme based on the Legendre-tau approximation is proposed to approximate the feedback solution to the linear quadratic optimal control problem for hereditary differential systems. The convergence property is established using Trotter ideas. The method yields very good approximations at low orders and provides an approximation technique for computing closed-loop eigenvalues of the feedback system. A comparison with existing methods (based on averaging and spline approximations) is made.
Ito, K.; Teglas, R.
1984-01-01
The numerical scheme based on the Legendre-tau approximation is proposed to approximate the feedback solution to the linear quadratic optimal control problem for hereditary differential systems. The convergence property is established using Trotter ideas. The method yields very good approximations at low orders and provides an approximation technique for computing closed-loop eigenvalues of the feedback system. A comparison with existing methods (based on averaging and spline approximations) is made.
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.
Limitations in direct and indirect methods for solving optimal control problems in growth theory
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Ratković Kruna
2016-01-01
Full Text Available The focus of this paper is on a comprehensive analysis of different methods and mathematical techniques used for solving optimal control problems (OCP in growth theory. Most important methods for solving dynamic non-linear infinite-horizon growth models using optimal control theory are presented and a critical view of the limitations of different methods is given. The main problem is to determine the optimal rate of growth over time in a way that maximizes the welfare function over an infinite horizon. The welfare function depends on capital-labor ratio, the state variable, and the per-capita consumption, the control variable. Numerical methods for solving OCP are divided into two classes: direct and indirect approach. How the indirect approach can be used is given in the example of the neo-classical growth model. In order to present the indirect and the direct approach simultaneously, two endogenous growth models, one written by Romer and another by Lucas and Uzawa, are studied. Advantages and efficiency of these different approaches will be discussed. Although the indirect methods for solving OCP are still the most expanded in growth theory, it will be seen that using direct methods can also be very efficient and help to overcome problems that can occur by using the indirect approach.
SOME PROPERTIES OF THE VARIATIONAL PROBLEMS OF OPTIMAL CONTROL OF CONSUMPTION
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Alla Yu. Meyerson
2016-01-01
Full Text Available In this paper we study the General patterns of models based on variational methods in various problems of optimal control of consumption: decisionmaking in the management of the household, as well as models of the economic dynamics of the Harrod–Domar and Solow. The role of optimal control in these tasks is played by the consumption function: in the first task is a function of consumption of the household, the model of Harrod–Domar is the aggregate consumption, as in the Solow model is per capita consumption. The role of the equation of when the first task is the equation of the dynamic balance between income, expenses, and accumulated savings, the model of Harrod–Domar – equation dynamic balance between income and investment, with the assumption of proportionality of investment and derivative income, as in the Solow model the role of the equation of the relationship is played by the equation of dynamic balance between the capitallabor ratio, economic productivity and per capita consumption. In all considered processes, the optimal control problem is formulated as a maximization problem of the functional expressing the integrated discounted utility of consumption under the equity equation.
Solution of Constrained Optimal Control Problems Using Multiple Shooting and ESDIRK Methods
DEFF Research Database (Denmark)
Capolei, Andrea; Jørgensen, John Bagterp
2012-01-01
In this paper, we describe a novel numerical algorithm for solution of constrained optimal control problems of the Bolza type for stiff and/or unstable systems. The numerical algorithm combines explicit singly diagonally implicit Runge-Kutta (ESDIRK) integration methods with a multiple shooting...... algorithm. As we consider stiff systems, implicit solvers with sensitivity computation capabilities for initial value problems must be used in the multiple shooting algorithm. Traditionally, multi-step methods based on the BDF algorithm have been used for such problems. The main novel contribution...... of this paper is the use of ESDIRK integration methods for solution of the initial value problems and the corresponding sensitivity equations arising in the multiple shooting algorithm. Compared to BDF-methods, ESDIRK-methods are advantageous in multiple shooting algorithms in which restarts and frequent...
Application of DEO Method to Solving Fuzzy Multiobjective Optimal Control Problem
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Latafat A. Gardashova
2014-01-01
Full Text Available In the present paper a problem of optimal control for a single-product dynamical macroeconomic model is considered. In this model gross domestic product is divided into productive consumption, gross investment, and nonproductive consumption. The model is described by a fuzzy differential equation (FDE to take into account imprecision inherent in the dynamics that may be naturally conditioned by influence of various external factors, unforeseen contingencies of future, and so forth. The considered problems are characterized by four criteria and by several important aspects. On one hand, the problem is complicated by the presence of fuzzy uncertainty as a result of a natural imprecision inherent in information about dynamics of real-world systems. On the other hand, the number of the criteria is not small and most of them are integral criteria. Due to the above mentioned aspects, solving the considered problem by using convolution of criteria into one criterion would lead to loss of information and also would be counterintuitive and complex. We applied DEO (differential evolution optimization method to solve the considered problem.
Büskens, Christof; Maurer, Helmut
2000-08-01
Parametric nonlinear optimal control problems subject to control and state constraints are studied. Two discretization methods are discussed that transcribe optimal control problems into nonlinear programming problems for which SQP-methods provide efficient solution methods. It is shown that SQP-methods can be used also for a check of second-order sufficient conditions and for a postoptimal calculation of adjoint variables. In addition, SQP-methods lead to a robust computation of sensitivity differentials of optimal solutions with respect to perturbation parameters. Numerical sensitivity analysis is the basis for real-time control approximations of perturbed solutions which are obtained by evaluating a first-order Taylor expansion with respect to the parameter. The proposed numerical methods are illustrated by the optimal control of a low-thrust satellite transfer to geosynchronous orbit and a complex control problem from aquanautics. The examples illustrate the robustness, accuracy and efficiency of the proposed numerical algorithms.
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Emran Tohidi
2013-01-01
Full Text Available The idea of approximation by monomials together with the collocation technique over a uniform mesh for solving state-space analysis and optimal control problems (OCPs has been proposed in this paper. After imposing the Pontryagins maximum principle to the main OCPs, the problems reduce to a linear or nonlinear boundary value problem. In the linear case we propose a monomial collocation matrix approach, while in the nonlinear case, the general collocation method has been applied. We also show the efficiency of the operational matrices of differentiation with respect to the operational matrices of integration in our numerical examples. These matrices of integration are related to the Bessel, Walsh, Triangular, Laguerre, and Hermite functions.
Institute of Scientific and Technical Information of China (English)
胡云卿; 刘兴高; 薛安克
2014-01-01
This paper considers dealing with path constraints in the framework of the improved control vector it-eration (CVI) approach. Two available ways for enforcing equality path constraints are presented, which can be di-rectly incorporated into the improved CVI approach. Inequality path constraints are much more difficult to deal with, even for small scale problems, because the time intervals where the inequality path constraints are active are unknown in advance. To overcome the challenge, the l1 penalty function and a novel smoothing technique are in-troduced, leading to a new effective approach. Moreover, on the basis of the relevant theorems, a numerical algo-rithm is proposed for nonlinear dynamic optimization problems with inequality path constraints. Results obtained from the classic batch reactor operation problem are in agreement with the literature reports, and the computational efficiency is also high.
Parallel Optimization of Polynomials for Large-scale Problems in Stability and Control
Kamyar, Reza
In this thesis, we focus on some of the NP-hard problems in control theory. Thanks to the converse Lyapunov theory, these problems can often be modeled as optimization over polynomials. To avoid the problem of intractability, we establish a trade off between accuracy and complexity. In particular, we develop a sequence of tractable optimization problems --- in the form of Linear Programs (LPs) and/or Semi-Definite Programs (SDPs) --- whose solutions converge to the exact solution of the NP-hard problem. However, the computational and memory complexity of these LPs and SDPs grow exponentially with the progress of the sequence - meaning that improving the accuracy of the solutions requires solving SDPs with tens of thousands of decision variables and constraints. Setting up and solving such problems is a significant challenge. The existing optimization algorithms and software are only designed to use desktop computers or small cluster computers --- machines which do not have sufficient memory for solving such large SDPs. Moreover, the speed-up of these algorithms does not scale beyond dozens of processors. This in fact is the reason we seek parallel algorithms for setting-up and solving large SDPs on large cluster- and/or super-computers. We propose parallel algorithms for stability analysis of two classes of systems: 1) Linear systems with a large number of uncertain parameters; 2) Nonlinear systems defined by polynomial vector fields. First, we develop a distributed parallel algorithm which applies Polya's and/or Handelman's theorems to some variants of parameter-dependent Lyapunov inequalities with parameters defined over the standard simplex. The result is a sequence of SDPs which possess a block-diagonal structure. We then develop a parallel SDP solver which exploits this structure in order to map the computation, memory and communication to a distributed parallel environment. Numerical tests on a supercomputer demonstrate the ability of the algorithm to
Giordano, Nils; Mairet, Francis; Gouzé, Jean-Luc
2016-01-01
Microbial physiology exhibits growth laws that relate the macromolecular composition of the cell to the growth rate. Recent work has shown that these empirical regularities can be derived from coarse-grained models of resource allocation. While these studies focus on steady-state growth, such conditions are rarely found in natural habitats, where microorganisms are continually challenged by environmental fluctuations. The aim of this paper is to extend the study of microbial growth strategies to dynamical environments, using a self-replicator model. We formulate dynamical growth maximization as an optimal control problem that can be solved using Pontryagin’s Maximum Principle. We compare this theoretical gold standard with different possible implementations of growth control in bacterial cells. We find that simple control strategies enabling growth-rate maximization at steady state are suboptimal for transitions from one growth regime to another, for example when shifting bacterial cells to a medium supporting a higher growth rate. A near-optimal control strategy in dynamical conditions is shown to require information on several, rather than a single physiological variable. Interestingly, this strategy has structural analogies with the regulation of ribosomal protein synthesis by ppGpp in the enterobacterium Escherichia coli. It involves sensing a mismatch between precursor and ribosome concentrations, as well as the adjustment of ribosome synthesis in a switch-like manner. Our results show how the capability of regulatory systems to integrate information about several physiological variables is critical for optimizing growth in a changing environment. PMID:26958858
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Nils Giordano
2016-03-01
Full Text Available Microbial physiology exhibits growth laws that relate the macromolecular composition of the cell to the growth rate. Recent work has shown that these empirical regularities can be derived from coarse-grained models of resource allocation. While these studies focus on steady-state growth, such conditions are rarely found in natural habitats, where microorganisms are continually challenged by environmental fluctuations. The aim of this paper is to extend the study of microbial growth strategies to dynamical environments, using a self-replicator model. We formulate dynamical growth maximization as an optimal control problem that can be solved using Pontryagin's Maximum Principle. We compare this theoretical gold standard with different possible implementations of growth control in bacterial cells. We find that simple control strategies enabling growth-rate maximization at steady state are suboptimal for transitions from one growth regime to another, for example when shifting bacterial cells to a medium supporting a higher growth rate. A near-optimal control strategy in dynamical conditions is shown to require information on several, rather than a single physiological variable. Interestingly, this strategy has structural analogies with the regulation of ribosomal protein synthesis by ppGpp in the enterobacterium Escherichia coli. It involves sensing a mismatch between precursor and ribosome concentrations, as well as the adjustment of ribosome synthesis in a switch-like manner. Our results show how the capability of regulatory systems to integrate information about several physiological variables is critical for optimizing growth in a changing environment.
Trifonenkov, A. V.; Trifonenkov, V. P.
2017-01-01
This article deals with a feature of problems of calculating time-average characteristics of nuclear reactor optimal control sets. The operation of a nuclear reactor during threatened period is considered. The optimal control search problem is analysed. The xenon poisoning causes limitations on the variety of statements of the problem of calculating time-average characteristics of a set of optimal reactor power off controls. The level of xenon poisoning is limited. There is a problem of choosing an appropriate segment of the time axis to ensure that optimal control problem is consistent. Two procedures of estimation of the duration of this segment are considered. Two estimations as functions of the xenon limitation were plot. Boundaries of the interval of averaging are defined more precisely.
Geometric optimal control of the contrast imaging problem in Nuclear Magnetic Resonance
Bonnard, B; Glaser, S J; Lapert, M; Sugny, D; Zhang, Y
2012-01-01
The objective of this article is to introduce the tools to analyze the contrast imaging problem in Nuclear Magnetic Resonance. Optimal trajectories can be selected among extremal solutions of the Pontryagin Maximum Principle applied to this Mayer type optimal problem. Such trajectories are associated to the question of extremizing the transfer time. Hence the optimal problem is reduced to the analysis of the Hamiltonian dynamics related to singular extremals and their optimality status. This is illustrated by using the examples of cerebrospinal fluid / water and grey / white matter of cerebrum.
Evolution Strategies in Optimization Problems
Cruz, Pedro A F
2007-01-01
Evolution Strategies are inspired in biology and part of a larger research field known as Evolutionary Algorithms. Those strategies perform a random search in the space of admissible functions, aiming to optimize some given objective function. We show that simple evolution strategies are a useful tool in optimal control, permitting to obtain, in an efficient way, good approximations to the solutions of some recent and challenging optimal control problems.
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Yen-Liang Pan
2013-01-01
Full Text Available Deadlock prevention policies are used to solve the deadlock problems of FMSs. It is well known that the theory of regions is the efficient method for obtaining optimal (i.e., maximally permissive controllers. All legal and live maximal behaviors of Petri net models can be preserved by using marking/transition-separation instances (MTSIs or event-state-separation-problem (ESSP methods. However, they encountered great difficulties in solving all sets of inequalities that is an extremely time consuming problem. Moreover, the number of linear programming problems (LPPs of legal markings is also exponential with net size when a plant net grows exponentially. This paper proposes a novel methodology to reduce the number of MTSIs/ESSPs and LPPs. In this paper, we used the well-known reduction approach Murata (1989 to simply the construct of system such that the problem of LPPs can then be reduced. Additionally, critical ones of crucial marking/transition-separation instances (COCMTSI are developed and used in our deadlock prevention policy that allows designers to employ few MTSIs to deal with deadlocks. Experimental results indicate that the computational cost can be reduced. To our knowledge, this deadlock prevention policy is the most efficient policy to obtain maximal permissive behavior of Petri net models than past approaches.
Miele, A.; Wang, T.; Melvin, W. W.; Tzeng, C. Y.
1988-01-01
The optimal-control problem of abort-landing trajectories in the presence of low-altitude wind shear is investigated analytically. The vertical-plane Newtonian motion of a point-mass aircraft in a steady wind field is modeled, and a sequential gradient-restoration algorithm is applied. Numerical results showing the effects of wind-shear intensity, initial altitude, and power-setting rate are presented in extensive graphs and discussed in detail. Optimal trajectories for strong or severe wind shears are found to begin with a descent, followed by level flight and then an ascent after leaving the shear region.
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
Sensitivity analysis of an optimal control problem in greenhouse climate management.
Henten, van E.J.
2003-01-01
Optimal control systems are based on a performance measure to be optimised and a model description of the dynamic process to be controlled. When on-line implementation is considered, the performance of optimally controlled processes will depend on the accuracy of the model description used. Sensitiv
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G. Kondrat'ev
1999-10-01
Full Text Available In this article some ideas of Hamilton mechanics and differential-algebraic Geometry are used to exact definition of the potential function (Bellman-Lyapunov function in the optimal stabilization problem of smooth finite-dimensional systems.
Directory of Open Access Journals (Sweden)
G. Kondrat'ev
1999-12-01
Full Text Available In this article some ideas of Hamilton mechanics and differential-algebraic Geometry are used to exact definition of the potential function (Bellman-Lyapunov function in the optimal stabilization problem of smooth finite-dimensional systems.
OPTIMAL CONTROL PROBLEM FOR A PERIODIC PREDATOR-PREY MODEL WITH AGE-DEPENDENCE
Institute of Scientific and Technical Information of China (English)
无
2012-01-01
In this paper,we investigate optimal policy for periodic predator-prey system with age-dependence.Namely,we consider the model with periodic vital rates and initial distribution.The existence of optimal control strategy is discussed by Mazur's theorem and optimality condition is derived by means of normal cone.
Explicit Solution of the Average-Cost Optimality Equation for a Pest-Control Problem
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Epaminondas G. Kyriakidis
2011-01-01
Full Text Available We introduce a Markov decision process in continuous time for the optimal control of a simple symmetrical immigration-emigration process by the introduction of total catastrophes. It is proved that a particular control-limit policy is average cost optimal within the class of all stationary policies by verifying that the relative values of this policy are the solution of the corresponding optimality equation.
Balandin, DV; Kogan, MM
2004-01-01
An algorithm for checking feasibility of the robust H-infinity-control problem for systems with time-varying norm bounded uncertainty is suggested. This algorithm is an iterative procedure on each step of which an optimization problem for a linear function under convex constraints determined by LMIs
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Somayeh Nemati
2016-11-01
Full Text Available In this paper, we consider the second-kind Chebyshev polynomials (SKCPs for the numerical solution of the fractional optimal control problems (FOCPs. Firstly, an introduction of the fractional calculus and properties of the shifted SKCPs are given and then operational matrix of fractional integration is introduced. Next, these properties are used together with the Legendre-Gauss quadrature formula to reduce the fractional optimal control problem to solving a system of nonlinear algebraic equations that greatly simplifies the problem. Finally, some examples are included to confirm the efficiency and accuracy of the proposed method.
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DAHIYA, P.
2015-05-01
Full Text Available This paper presents the application of hybrid opposition based disruption operator in gravitational search algorithm (DOGSA to solve automatic generation control (AGC problem of four area hydro-thermal-gas interconnected power system. The proposed DOGSA approach combines the advantages of opposition based learning which enhances the speed of convergence and disruption operator which has the ability to further explore and exploit the search space of standard gravitational search algorithm (GSA. The addition of these two concepts to GSA increases its flexibility for solving the complex optimization problems. This paper addresses the design and performance analysis of DOGSA based proportional integral derivative (PID and fractional order proportional integral derivative (FOPID controllers for automatic generation control problem. The proposed approaches are demonstrated by comparing the results with the standard GSA, opposition learning based GSA (OGSA and disruption based GSA (DGSA. The sensitivity analysis is also carried out to study the robustness of DOGSA tuned controllers in order to accommodate variations in operating load conditions, tie-line synchronizing coefficient, time constants of governor and turbine. Further, the approaches are extended to a more realistic power system model by considering the physical constraints such as thermal turbine generation rate constraint, speed governor dead band and time delay.
Institute of Scientific and Technical Information of China (English)
2009-01-01
The paper is concerned with a stochastic optimal control problem in which the controlled system is described by a fully coupled nonlinear forward-backward stochastic differential equation driven by a Brownian motion.It is required that all admissible control processes are adapted to a given subfiltration of the filtration generated by the underlying Brownian motion.For this type of partial information control,one sufficient(a verification theorem) and one necessary conditions of optimality are proved.The control domain need to be convex and the forward diffusion coefficient of the system can contain the control variable.
Institute of Scientific and Technical Information of China (English)
MENG QingXin
2009-01-01
The paper is concerned with a stochastic optimal control problem in which the controlled system is described by a fully coupled nonlinear forward-backward stochastic differential equation driven by a Brownian motion. It is required that all admissible control processes are adapted to a given subfiltration of the filtration generated by the underlying Brownian motion. For this type of partial information control, one sufficient (a verification theorem) and one necessary conditions of optimality are proved. The control domain need to be convex and the forward diffusion coefficient of the system can contain the control variable.
Optimal Control of Mechanical Systems
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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.
Free terminal time optimal control problem for the treatment of HIV infection
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Amine Hamdache
2016-01-01
to provide the explicit formulations of the optimal controls. The corresponding optimality system with the additional transversality condition for the terminal time is derived and solved numerically using an adapted iterative method with a Runge-Kutta fourth order scheme and a gradient method routine.
最优转换控制问题的平均化%AVERAGING IN OPTIMAL SWITCHING CONTROL PROBLEMS
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
The averaging in optimal switching control problems is considered under the following two cases: the switching cost does not depend on ε and the switching cost vanishes as ε tends to zero. The value function of the original fast problem converges locally uniformly to the value function of the averaged problem under both cases. The ways of averaging turn out to be different between both cases.
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.
On two speed optimization problems for ships that sail in and out of emission control areas
DEFF Research Database (Denmark)
Fagerholt, Kjetil; Psaraftis, Harilaos N.
2015-01-01
fuel oil (HFO) outside the ECA and switch to low-sulfur fuel such as marine gas oil (MGO) inside the ECA. As the prices of these two fuels are generally very different, so may be the speeds that the ship will sail at outside and inside the ECA. The first optimization problem examined by the paper...
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Klaus Krumbiegel
2011-01-01
Full Text Available We develop sufficient optimality conditions for a Moreau-Yosidaregularized optimal control problem governed by a semilinear ellipticPDE with pointwise constraints on the state and the control. We makeuse of the equivalence of a setting of Moreau-Yosida regularization to a special setting of the virtual control concept,for which standard second order sufficient conditions have been shown. Moreover, we present a numerical example,solving a Moreau-Yosida regularized model problem with an SQP method.
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De-Lei Sheng
2014-01-01
Full Text Available This paper investigates the excess-of-loss reinsurance and investment problem for a compound Poisson jump-diffusion risk process, with the risk asset price modeled by a constant elasticity of variance (CEV model. It aims at obtaining the explicit optimal control strategy and the optimal value function. Applying stochastic control technique of jump diffusion, a Hamilton-Jacobi-Bellman (HJB equation is established. Moreover, we show that a closed-form solution for the HJB equation can be found by maximizing the insurer’s exponential utility of terminal wealth with the independence of two Brownian motions W(t and W1(t. A verification theorem is also proved to verify that the solution of HJB equation is indeed a solution of this optimal control problem. Then, we quantitatively analyze the effect of different parameter impacts on optimal control strategy and the optimal value function, which show that optimal control strategy is decreasing with the initial wealth x and decreasing with the volatility rate of risk asset price. However, the optimal value function V(t;x;s is increasing with the appreciation rate μ of risk asset.
Optimal Inventory Control Problem with Inflation-Dependent Demand Rate Under Stochastic Conditions
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A. Mirzazadeh
2012-02-01
Full Text Available The practical experiences reveal that the Supply Chain Management (SCM is under uncertain and variable conditions. One of the most important parts of SCM is inventory system management which is inherently in non-deterministic situation. The many departments of organization such as warehouse, marketing, sale, purchasing, financial, planning, production, maintenance and etc. are relevance to the inventory problem. Since 1975 a series of related papers appeared that considered the effects of inflation on the inventory system. There are a few works in the inflationary inventory researches under stochastic conditions, especially with multiple stochastic parameters. Therefore, a new mathematical model for the optimal production for an inventory control system is formulated under stochastic environment. The demand rate is a function of inflation and time value of money where the inflation and time horizon i.e., period of business, both are random in nature. In the real situation, some but not all customers will wait for backlogged items during a shortage period, such as for fashionable commodities or high-tech products. Thus, the model incorporates partial backlogging. A numerical method has been used and the numerical example has been provided for evaluation and validation of the theoretical results and some special cases of the model are discussed. The results show the importance of taking into account stochastic inflation, time horizon and demand.
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
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.
Grigoriev, I. S.; Grigoriev, K. G.
2003-05-01
The necessary first-order conditions of strong local optimality (conditions of maximum principle) are considered for the problems of optimal control over a set of dynamic systems. To derive them a method is suggested based on the Lagrange principle of removing constraints in the problems on a conditional extremum in a functional space. An algorithm of conversion from the problem of optimal control of an aggregate of dynamic systems to a multipoint boundary value problem is suggested for a set of systems of ordinary differential equations with the complete set of conditions necessary for its solution. An example of application of the methods and algorithm proposed is considered: the solution of the problem of constructing the trajectories of a spacecraft flight at a constant altitude above a preset area (or above a preset point) of a planet's surface in a vacuum (for a planet with atmosphere beyond the atmosphere). The spacecraft is launched from a certain circular orbit of a planet's satellite. This orbit is to be determined (optimized). Then the satellite is injected to the desired trajectory segment (or desired point) of a flyby above the planet's surface at a specified altitude. After the flyby the satellite is returned to the initial circular orbit. A method is proposed of correct accounting for constraints imposed on overload (mixed restrictions of inequality type) and on the distance from the planet center: extended (nonpointlike) intermediate (phase) restrictions of the equality type.
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Zuliang Lu
2014-01-01
Full Text Available The aim of this work is to investigate the discretization of general linear hyperbolic convex optimal control problems by using the mixed finite element methods. The state and costate are approximated by the k order (k≥0 Raviart-Thomas mixed finite elements and the control is approximated by piecewise polynomials of order k. By applying the elliptic projection operators and Gronwall’s lemma, we derive a priori error estimates of optimal order for both the coupled state and the control approximation.
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 Problem of Treatment for Obesity in a Closed Population
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D. Aldila
2014-01-01
Full Text Available Variety of intervention programs for controlling the obesity epidemic has been done worldwide. However, it is still not yet available a scientific tool to measure the effectiveness of those programs. This is due to the difficulty in parameterizing the human interaction and transition process of obesity. A dynamical model for simulating the interaction between healthy people, overweight people, and obese people in a randomly mixed population is discussed in here. Two scenarios of intervention programs were implemented in the model, dietary program for overweight people with healthy life campaign and treatment program for obese people. Assuming all control rates are constant, disease free equilibrium point, endemic equilibrium point, and basic reproductive ratio (ℛ0 as the epidemic indicator were shown analytically. We find that the disease free equilibrium point is locally asymptotical stable if and only if ℛ0<1. From sensitivity analysis of ℛ0, we obtain that larger rate of dietary program and treatment program will reduce ℛ0 significantly. With control rates are continuous in time, an optimal control approach was applied into the model to find the best way to minimize the number of overweight and obese people. Some numerical analysis and simulations for optimal control of the intervention were shown to support the analytical results.
Bensoussan, A.; Delfour, M. C.; Mitter, S. K.
1976-01-01
Available published results are surveyed for a special class of infinite-dimensional control systems whose evolution is characterized by a semigroup of operators of class C subscript zero. Emphasis is placed on an approach that clarifies the system-theoretic relationship among controllability, stabilizability, stability, and the existence of a solution to an associated operator equation of the Riccati type. Formulation of the optimal control problem is reviewed along with the asymptotic behavior of solutions to a general system of equations and several theorems concerning L2 stability. Examples are briefly discussed which involve second-order parabolic systems, first-order hyperbolic systems, and distributed boundary control.
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.
Class and Home Problems: Optimization Problems
Anderson, Brian J.; Hissam, Robin S.; Shaeiwitz, Joseph A.; Turton, Richard
2011-01-01
Optimization problems suitable for all levels of chemical engineering students are available. These problems do not require advanced mathematical techniques, since they can be solved using typical software used by students and practitioners. The method used to solve these problems forces students to understand the trends for the different terms…
Class and Home Problems: Optimization Problems
Anderson, Brian J.; Hissam, Robin S.; Shaeiwitz, Joseph A.; Turton, Richard
2011-01-01
Optimization problems suitable for all levels of chemical engineering students are available. These problems do not require advanced mathematical techniques, since they can be solved using typical software used by students and practitioners. The method used to solve these problems forces students to understand the trends for the different terms…
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Seyed Ali Aghayan
2013-01-01
Full Text Available A novel scheme to obtain the optimum tissue heating condition during hyperthermia treatment is proposed. To do this, the effect of the controllable overall heat transfer coefficient of the cooling system is investigated. An inverse problem by a conjugated gradient with adjoint equation is used in our model. We apply the finite difference time domain method to numerically solve the tissue temperature distribution using Pennes bioheat transfer equation. In order to provide a quantitative measurement of errors, convergence history of the method and root mean square of errors are also calculated. The effects of heat convection coefficient of water and thermal conductivity of casing layer on the control parameter are also discussed separately.
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.
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
Senses, Begum
A state-defect constraint pairing graph coarsening method is described for improving computational efficiency during the numerical factorization of large sparse Karush-Kuhn-Tucker matrices that arise from the discretization of optimal control problems via a Legendre-Gauss-Radau orthogonal collocation method. The method takes advantage of the particular sparse structure of the Karush-Kuhn-Tucker matrix that arises from the orthogonal collocation method. The state-defect constraint pairing graph coarsening method pairs each component of the state with its corresponding defect constraint and forces paired rows to be adjacent in the reordered Karush-Kuhn-Tucker matrix. Aggregate state-defect constraint pairing results are presented using a wide variety of benchmark optimal control problems where it is found that the proposed state-defect constraint pairing graph coarsening method significantly reduces both the number of delayed pivots and the number of floating point operations and increases the computational efficiency by performing more floating point operations per unit time. It is then shown that the state-defect constraint pairing graph coarsening method is less effective on Karush-Kuhn-Tucker matrices arising from Legendre-Gauss-Radau collocation when the optimal control problem contains state and control equality path constraints because such matrices may have delayed pivots that correspond to both defect and path constraints. An unweighted alternate graph coarsening method that employs maximal matching and a weighted alternate graph coarsening method that employs Hungarian algorithm on a weighting matrix are then used to attempt to further reduce the number of delayed pivots. It is found, however, that these alternate graph coarsening methods provide no further advantage over the state-defect constraint pairing graph coarsening method.
Optimization techniques for Transportation Problems
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Gauthaman.P
2017-06-01
Full Text Available This paper infers about optimization technique for various problems in transportation engineering. While for pavement engineering, maintenance is priority issue, for traffic it is signalling which is priority issue. Many optimization methods are discussed though given importance of genetic algorithm approach. While optimization techniques nearly approach practicality, research works are on for modern optimization techniques which not only adds ease of structure but also provide compatibility to modern day problems encountered in transportation engineering. Some of the modern tools are discussed to employ optimization techniques which are quite simple to use and implement once it is calibrated to the desired objective.
Solving Optimal Timing Problems Elegantly
Todorova, Tamara
2013-01-01
Few textbooks in mathematical economics cover optimal timing problems. Those which cover them do it scantly or in a rather clumsy way, making it hard for students to understand and apply the concept of optimal time in new contexts. Discussing the plentiful illustrations of optimal timing problems, we present an elegant and simple method of solving them. Whether the present value function is exponential or logarithmic, a convenient way to solve it is to convert the base to the exponential numb...
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Hamid Tikani
2016-11-01
Full Text Available In this paper, we study the problem of integrated capacitated hub location problem and seat inventory control considering concept and techniques of revenue management. We consider an airline company maximizes its revenue by utilizing the best network topology and providing proper booking limits for all itineraries and fare classes. The transportation system arises in the form of a star/star network and includes both hub-stop and non-stop flights. This problem is formulated as a two-stage stochastic integer program with mixed-integer recourse. We solve various instances carried out from the Turkish network data set. Due to the NP-hardness of the problem, we propose a hybrid optimization method, consisting of an evolutionary algorithm based on genetic algorithm and exact solution. The quality of the solutions found by the proposed meta-heuristic is compared with the original version of GA and the mathematical programming model. The results obtained by the proposed model imply that integrating hub location and seat inventory control problem would help to increase the total revenue of airline companies. Also, in the case of serving non-stop flights, the model can provide more profit by employing less number of hubs.
D'Apice, Ciro; Kogut, Peter I.
2017-07-01
We discuss the optimal control problem stated as the minimization in the L2-sense of the mismatch between the actual out-flux and a demand forecast for a hyperbolic conservation law that models a highly re-entrant production system. The output of the factory is described as a function of the work in progress and the position of the so-called push-pull point (PPP) where we separate the beginning of the factory employing a push policy from the end of the factory, which uses a pull policy.
On the nature of the optimal control problem at leaking underground fuel tank sites
Energy Technology Data Exchange (ETDEWEB)
McDowell, B
1998-12-01
In California, leaking underground fuel tank (LUFT) legislation was conceived because of concern that ''time bomb plumes'' would ultimately impact a significant portion of the state's ground and surface water resources. However, it has been found that fuel hydrocarbons (FHC) plumes are stable at relatively short distances from the source in areas of shallow groundwater. In urban areas, these shallow aquifers are not even recommended for use because they are subject to contamination from sewers, storm drains, septic fields and a variety of other sources. After the FHC source has been removed, risk to human health or the environment is insignificant in most cases. For this reason, cleanup to maximum contaminant levels (MCLs) will not significantly reduce the social damages associated with current or near-term human health or ecological risk. Based on these findings, California would be able to save significant resources that had been allocated for LUFT-site cleanup. Non-convexities in the rate of decay function and non-differentiability in the cleanup and social damage functions appear to limit the usefulness of models, such as Caputo and Wilen's (1995), that attempt to characterize the optimal cleanup path using marginal analyses. Furthermore, the effect of active remediation efforts on the natural rate of decay in stable plumes is not taken into account in their model. The imposition of deed restrictions prior to a demonstration of cleanup to MCLs is an additional conservative measure imposed by the California Regional Water Quality Control Boards (RWQCBs) to reduce the uncertainty associated with health risks to future users. These measures impose costs on society in the form of lost rents that have not been considered by regulators. By estimating the differential rents during the time to cleanup, regulators would be able to compare the costs of imposing deed restrictions with the values that society imparts to protection of future
Ardema, M. D.
1979-01-01
Singular perturbation techniques are studied for dealing with singular arc problems by analyzing a relatively low-order but otherwise general system. This system encompasses many flight mechanic problems including Goddard's problem and a version of the minimum time-to-climb problem. Boundary layer solutions are constructed which are stable and reach the outer solution in a finite time. A uniformly valid composite solution is then formed from the reduced and boundary layer solutions. The value of the approximate solution is that it is relatively easy to obtain and does not involve singular arcs. To illustrate the utility of the results, the technique is used to obtain an approximate solution of a simplified version of the aircraft minimum time-to-climb problem.
Directory of Open Access Journals (Sweden)
Hadi Mokhtari
2015-11-01
Full Text Available In this paper, the flexible job shop scheduling problem with machine flexibility and controllable process times is studied. The main idea is that the processing times of operations may be controlled by consumptions of additional resources. The purpose of this paper to find the best trade-off between processing cost and delay cost in order to minimize the total costs. The proposed model, flexible job shop scheduling with controllable processing times (FJCPT, is formulated as an integer non-linear programming (INLP model and then it is converted into an integer linear programming (ILP model. Due to NP-hardness of FJCPT, conventional analytic optimization methods are not efficient. Hence, in order to solve the problem, a Scatter Search (SS, as an efficient metaheuristic method, is developed. To show the effectiveness of the proposed method, numerical experiments are conducted. The efficiency of the proposed algorithm is compared with that of a genetic algorithm (GA available in the literature for solving FJSP problem. The results showed that the proposed SS provide better solutions than the existing GA.
Topology Optimization for Convection Problems
DEFF Research Database (Denmark)
Alexandersen, Joe
2011-01-01
This report deals with the topology optimization of convection problems.That is, the aim of the project is to develop, implement and examine topology optimization of purely thermal and coupled thermomechanical problems,when the design-dependent eects of convection are taken into consideration.......This is done by the use of a self-programmed FORTRAN-code, which builds on an existing 2D-plane thermomechanical nite element code implementing during the course `41525 FEM-Heavy'. The topology optimizationfeatures have been implemented from scratch, and allows the program to optimize elastostatic mechanical...
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%....
A Singular Differential Equation Stemming from an Optimal Control Problem in Financial Economics
Energy Technology Data Exchange (ETDEWEB)
Brunovsky, Pavol, E-mail: brunovsky@fmph.uniba.sk [Comenius University Bratislava, Department of Applied Mathematics and Statistics (Slovakia); Cerny, Ales, E-mail: ales.cerny.1@city.ac.uk [City University London, Cass Business School (United Kingdom); Winkler, Michael, E-mail: michael.winkler@uni-due.de [Universitaet Paderborn, Institut fuer Mathematik (Germany)
2013-10-15
We consider the ordinary differential equation x{sup 2} u'' = axu'+bu-c(u'-1){sup 2}, x Element-Of (0,x{sub 0}), with a Element-Of R, b Element-Of R , c>0 and the singular initial condition u(0)=0, which in financial economics describes optimal disposal of an asset in a market with liquidity effects. It is shown in the paper that if a+b<0 then no continuous solutions exist, whereas if a+b>0 then there are infinitely many continuous solutions with indistinguishable asymptotics near 0. Moreover, it is proved that in the latter case there is precisely one solution u corresponding to the choice x{sub 0}={infinity} which is such that 0{<=}u(x){<=}x for all x>0, and that this solution is strictly increasing and concave.
2012-03-01
Rao discusses the most common gradient search algorithms in [71] along with some heuristic ones that use some added randomness to direct the search... aircrews and mission planners who have interest in this type of problem. 98 Target T=Threat T x1 x2 B ou nd ar y B ou nd ar y T θ V (tf , x1(tf ), x2(tf...processing. The most valuable product to mission planners and aircrews is not the set of statistics describing expected values, variances, and covariances and
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.
Topology optimization of flow problems
DEFF Research Database (Denmark)
Gersborg, Allan Roulund
2007-01-01
of the velocity field or mixing properties. To reduce the computational complexity of the topology optimization problems the primary focus is put on the Stokes equation in 2D and in 3D. However, the thesis also contains examples with the 2D Navier-Stokes equation as well as an example with convection dominated....... Although the study of the FVM is carried out using a simple heat conduction problem, the work illuminates and discusses the technicalities of employing the FVM in connection with topology optimization. Finally, parallelized solution methods are investigated using the high performance computing facility...
Energy Technology Data Exchange (ETDEWEB)
Plekhanova, Marina V; Fedorov, Vladimir E
2011-04-30
We investigate optimal control problems for linear distributed systems which are not solved with respect to the time derivative and whose homogeneous part admits a degenerate strongly continuous solution semigroup. To this end, we first obtain theorems on the existence of a unique strong solution of the Cauchy problem. This enables us to formulate sufficient conditions for the solubility of the optimal control problems under consideration. In contrast to earlier papers on a similar topic, we substantially weaken the conditions on the quality functional with respect to the state function. The abstract results thus obtained are illustrated by an example of an optimal control problem for the linearized system of Navier-Stokes equations.
Topology optimization for transient heat transfer problems
DEFF Research Database (Denmark)
Zeidan, Said; Sigmund, Ole; Lazarov, Boyan Stefanov
The focus of this work is on passive control of transient heat transfer problems using the topology optimization (TopOpt) method [1]. The goal is to find distributions of a limited amount of phase change material (PCM), within a given design domain, which optimizes the heat energy storage [2]. Our......, TopOpt has later been extended to transient problems in mechanics and photonics (e.g. [5], [6] and [7]). In the presented approach, the optimization is gradient-based, where in each iteration the non-steady heat conduction equation is solved,using the finite element method and an appropriate time...
Optimization and geophysical inverse problems
Energy Technology Data Exchange (ETDEWEB)
Barhen, J.; Berryman, J.G.; Borcea, L.; Dennis, J.; de Groot-Hedlin, C.; Gilbert, F.; Gill, P.; Heinkenschloss, M.; Johnson, L.; McEvilly, T.; More, J.; Newman, G.; Oldenburg, D.; Parker, P.; Porto, B.; Sen, M.; Torczon, V.; Vasco, D.; Woodward, N.B.
2000-10-01
A fundamental part of geophysics is to make inferences about the interior of the earth on the basis of data collected at or near the surface of the earth. In almost all cases these measured data are only indirectly related to the properties of the earth that are of interest, so an inverse problem must be solved in order to obtain estimates of the physical properties within the earth. In February of 1999 the U.S. Department of Energy sponsored a workshop that was intended to examine the methods currently being used to solve geophysical inverse problems and to consider what new approaches should be explored in the future. The interdisciplinary area between inverse problems in geophysics and optimization methods in mathematics was specifically targeted as one where an interchange of ideas was likely to be fruitful. Thus about half of the participants were actively involved in solving geophysical inverse problems and about half were actively involved in research on general optimization methods. This report presents some of the topics that were explored at the workshop and the conclusions that were reached. In general, the objective of a geophysical inverse problem is to find an earth model, described by a set of physical parameters, that is consistent with the observational data. It is usually assumed that the forward problem, that of calculating simulated data for an earth model, is well enough understood so that reasonably accurate synthetic data can be generated for an arbitrary model. The inverse problem is then posed as an optimization problem, where the function to be optimized is variously called the objective function, misfit function, or fitness function. The objective function is typically some measure of the difference between observational data and synthetic data calculated for a trial model. However, because of incomplete and inaccurate data, the objective function often incorporates some additional form of regularization, such as a measure of smoothness
DEFF Research Database (Denmark)
Vidal, Rene Victor Valqui
1994-01-01
The paper studies the problem of determining the number and dimensions of sizes of apparel so as to maximize profits. It develops a simple one-variable bisection search algorithm that gives the optimal solution. An example is solved interactively using a Macintosh LC and Math CAD, a mathematical ...
一种求解最优控制问题的混合WNN-PSO算法%Hybrid WNN-PSO Algorithm for Optimal Control Problems
Institute of Scientific and Technical Information of China (English)
李树荣; 雷阳; 张强; 张晓东
2013-01-01
To solve optimal control problems with numerical methods, a hybrid wavelet neural network -particle swarm optimization (WNN-PSO) algorithm was developed. The first step of WNN-PSO was to parameterize the optimal control trajectory based on the non-linear approximation capability of the wavelet neural network. Then the optimal control problem was transformed into a non-linear programming problem where the decision variables are the parameters of the wavelet neural network. Lastly, the parameters of the network were optimized by the particle swarm optimization (PSO) algorithm and the global optimal solution of the NLP was obtained. Simulation study on a Bang-Bang optimal control problem and a benchmark chemical process optimal control problem shows the feasibility and effectiveness of the proposed method.%针对最优控制问题的数值求解,提出了一种混合小波神经网络粒子群(WNN-PSO)算法,算法首先利用小波神经网络的非线性逼近能力参数化最优控制轨迹,将最优控制问题转化为非线性规划(NLP)问题,其决策变量为小波神经网络的参数,然后采用粒子群(PSO)算法优化小波神经网络参数,获得NLP问题的全局最优解.针对Bang-Bang最优控制问题和一个经典的化工过程最优控制问题进行仿真研究,验证了所提出算法的可行性和有效性.
Iterative optimization in inverse problems
Byrne, Charles L
2014-01-01
Iterative Optimization in Inverse Problems brings together a number of important iterative algorithms for medical imaging, optimization, and statistical estimation. It incorporates recent work that has not appeared in other books and draws on the author's considerable research in the field, including his recently developed class of SUMMA algorithms. Related to sequential unconstrained minimization methods, the SUMMA class includes a wide range of iterative algorithms well known to researchers in various areas, such as statistics and image processing. Organizing the topics from general to more
The Duality on Vector Optimization Problems
Institute of Scientific and Technical Information of China (English)
HUANG Long-guang
2012-01-01
Duality framework on vector optimization problems in a locally convex topological vector space are established by using scalarization with a cone-strongly increasing function.The dualities for the scalar convex composed optimization problems and for general vector optimization problems are studied.A general approach for studying duality in vector optimization problems is presented.
Institute of Scientific and Technical Information of China (English)
雒志学; 王绵森
2003-01-01
An optimal harvesting problem for linear age-dependent population dynamics is investigated.By Mazur's Theorem,the existence of solutions of the optimal control problem (OH) is demonstrated.The first order necessary conditions of optimality for problem (OH) is obtained by the conception of normal cone. Finally,under suitable assumptions,the uniqueness of solutions of the optimal control problem (OH) is given.The results extend some known criteria.
Optimization in HIV screening problems
Directory of Open Access Journals (Sweden)
Lev Abolnikov
2003-01-01
Full Text Available In this article, the authors use both deterministic and stochastic approaches to the analysis of some optimization problems that arise in the group (pool HIV screening practice. Two kinds of testing policies are considered. For the first kind, group-individual testing, the optimal size of the group that should be selected for testing is found. For more general group-subgroup testing procedure the authors develop a numerical algorithm for finding the sequence of successively selected subgroups that minimizes the total cost of testing. Assuming that both arriving and testing processes have a random nature, the authors suggest a stochastic model in which the optimal size of the group in the group-individual testing procedure is found by using methods of queueing theory.
Topology optimization for acoustic problems
DEFF Research Database (Denmark)
Dühring, Maria Bayard
2006-01-01
In this paper a method to control acoustic properties in a room with topology optimization is presented. It is shown how the squared sound pressure amplitude in a certain part of a room can be minimized by distribution of material in a design domain along the ceiling in 2D and 3D. Nice 0-1 designs...
Energy Technology Data Exchange (ETDEWEB)
Addona, Davide, E-mail: d.addona@campus.unimib.it [Università degli Studi di Milano Bicocca, (MILANO BICOCCA) Dipartimento di Matematica (Italy)
2015-08-15
We obtain weighted uniform estimates for the gradient of the solutions to a class of linear parabolic Cauchy problems with unbounded coefficients. Such estimates are then used to prove existence and uniqueness of the mild solution to a semi-linear backward parabolic Cauchy problem, where the differential equation is the Hamilton–Jacobi–Bellman equation of a suitable optimal control problem. Via backward stochastic differential equations, we show that the mild solution is indeed the value function of the controlled equation and that the feedback law is verified.
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 ...
On Optimal Harvesting Problems in Random Environments
Song, Qingshuo; Zhu, Chao
2010-01-01
This paper investigates the optimal harvesting strategy for a single species living in random environments, whose growth is given by a regime-switching diffusion. Harvesting is introduced as a stochastic control. The objective is to find a harvesting strategy which maximizes the expected total discounted income from harvesting up to extinction. This is a singular stochastic control problem, with both the extinction time and harvesting policy depending on the initial condition. Consequently one no longer obtains continuity of the value function for free using the standard arguments as those in regular or singular stochastic control problems. This paper provides a sufficient condition under which the continuity of the value function is obtained. Further, we show that the value function is a viscosity solution of a coupled system of quasi-variational inequalities. A verification theorem is also established. Based upon the verification theorem, we explicitly construct an $\\varepsilon$-optimal harvesting strategy ...
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.
On Alternative Optimal Solutions to Linear Fractional Optimization Problems
Institute of Scientific and Technical Information of China (English)
ShengjiaXue
2004-01-01
The structure of the optimal solution set is derived for linear fractional optimization problems with the representation theorem of polyhedral sets．And the computational procedure in determining all optimal solutions is also given．
Stability Analysis for Stochastic Optimization Problems
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
Stochastic optimization offers a means of considering the objectives and constrains with stochastic parameters. However, it is generally difficult to solve the stochastic optimization problem by employing conventional methods for nonlinear programming when the number of random variables involved is very large. Neural network models and algorithms were applied to solve the stochastic optimization problem on the basis of the stability theory. Stability for stochastic programs was discussed. If random vector sequence converges to the random vector in the original problem in distribution, the optimal value of the corresponding approximation problems converges to the optimal value of the original stochastic optimization problem.
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 ...
About one problem of optimal stabilization of linear compound systems
Directory of Open Access Journals (Sweden)
Barseghyan V.R.
2014-12-01
Full Text Available The problem of optimal stabilization of linear compound system is investigated. Based on Lyapunov function method the method of building optimal stabilizing control action is suggested. The solution of the problem of optimal stabilization of a concrete compound system is given.
DEFF Research Database (Denmark)
Ghoreishi, Newsha; Sørensen, Jan Corfixen; Jørgensen, Bo Nørregaard
2015-01-01
compare the performance of state-of-the-art multi-objective evolutionary algorithms to solve a non-linear multi-objective multi-issue optimisation problem found in Greenhouse climate control. The chosen algorithms in the study includes NSGAII, eNSGAII, eMOEA, PAES, PESAII and SPEAII. The performance...
Some Undecidable Problems on Approximability of NP Optimization Problems
Institute of Scientific and Technical Information of China (English)
黄雄
1996-01-01
In this paper some undecidable problems on approximability of NP optimization problems are investigated.In particular,the following problems are all undecidable:(1) Given an NP optimization problem,is it approximable in polynomial time?(2)For any polynomial-time computable function r(n),given a polynomial time approximable NP optimization problem,has it a polynomial-time approximation algorithm with approximation performance ratio r(n) (r(n)-approximable)?(3)For any polynomial-time computable functions r(n),r'(n),where r'(n)
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
Anita, Sebastian; Capasso, Vincenzo
2011-01-01
Combining control theory and modeling, this textbook introduces and builds on methods for simulating and tackling concrete problems in a variety of applied sciences. Emphasizing "learning by doing," the authors focus on examples and applications to real-world problems. An elementary presentation of advanced concepts, proofs to introduce new ideas, and carefully presented MATLAB(R) programs help foster an understanding of the basics, but also lead the way to new, independent research. With minimal prerequisites and exercises in each chapter, this work serves as an excellent textbook a
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.
Generalized Benders’ Decomposition for topology optimization problems
DEFF Research Database (Denmark)
Munoz Queupumil, Eduardo Javier; Stolpe, Mathias
2011-01-01
This article considers the non-linear mixed 0–1 optimization problems that appear in topology optimization of load carrying structures. The main objective is to present a Generalized Benders’ Decomposition (GBD) method for solving single and multiple load minimum compliance (maximum stiffness......–1 semi definite programming formulation of the considered problem. Several ways to accelerate the method are suggested and an implementation is described. Finally, a set of truss topology optimization problems are numerically solved to global optimality....
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.
Interaction Prediction Optimization in Multidisciplinary Design Optimization Problems
Directory of Open Access Journals (Sweden)
Debiao Meng
2014-01-01
Full Text Available The distributed strategy of Collaborative Optimization (CO is suitable for large-scale engineering systems. However, it is hard for CO to converge when there is a high level coupled dimension. Furthermore, the discipline objectives cannot be considered in each discipline optimization problem. In this paper, one large-scale systems control strategy, the interaction prediction method (IPM, is introduced to enhance CO. IPM is utilized for controlling subsystems and coordinating the produce process in large-scale systems originally. We combine the strategy of IPM with CO and propose the Interaction Prediction Optimization (IPO method to solve MDO problems. As a hierarchical strategy, there are a system level and a subsystem level in IPO. The interaction design variables (including shared design variables and linking design variables are operated at the system level and assigned to the subsystem level as design parameters. Each discipline objective is considered and optimized at the subsystem level simultaneously. The values of design variables are transported between system level and subsystem level. The compatibility constraints are replaced with the enhanced compatibility constraints to reduce the dimension of design variables in compatibility constraints. Two examples are presented to show the potential application of IPO for MDO.
Ant colony optimization in continuous problem
Institute of Scientific and Technical Information of China (English)
YU Ling; LIU Kang; LI Kaishi
2007-01-01
Based on the analysis of the basic ant colony optimization and optimum problem in a continuous space,an ant colony optimization (ACO) for continuous problem is constructed and discussed. The algorithm is efficient and beneficial to the study of the ant colony optimization in a continuous space.
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...
Masud, M A; Kim, Byul Nim; Kim, Yongkuk
Dengue viruses (DENV) are transmitted to humans by the bite of Aedes mosquitoes. It is known that dengue virus infection in Aedes aegypti female mosquitoes makes a change in the feeding behavior of the infected mosquitoes. In this study, using the forces of infection, we incorporated the effect of changes in the feeding behavior of mosquitoes into the standard vector-borne SIR-SI model. It has been proved that both a single-strain model and a two-strain model exhibit forward bifurcations. Moreover, optimal implementations of control with specific prevention measures for dengue transmission are analyzed. As a result we found that more implementation of controls on the secondary infection of humans should be considered for the behavioral changes in feeding of the infected mosquitoes. Copyright © 2017 Elsevier B.V. All rights reserved.
Uecker, Hannes
2015-01-01
p2pOC is an add-on toolbox to the Matlab package pde2path. It is aimed at the numerical solution of optimal control (OC) problems with an infinite time horizon for parabolic systems of PDE over 1D or 2D spatial domains. The basic idea is to treat the OC problem via the associated canonical system in two steps. First we use pde2path to find branches of stationary solutions of the canonical system, also called canonical steady states (CSS). In a second step we use the results and the spatial di...
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.
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.
非线性椭圆型种群模型的最优控制问题%On the Optimal Control Problem of a Nonlinear Elliptic Population System
Institute of Scientific and Technical Information of China (English)
贾超华; 冯德兴
2005-01-01
The optimal control problem for a nonlinear elliptic population system is considered.First, under certain hypotheses, the existence and uniqueness of coexistence state solutions are shown. Then the existence of the optimal control is given and the optimality system is established.
Multiple optimal solutions to a sort of nonlinear optimization problem
Institute of Scientific and Technical Information of China (English)
Xue Shengjia
2007-01-01
The optimization problem is considered in which the objective function is pseudolinear(both pseudoconvex and pseudoconcave) and the constraints are linear. The general expression for the optimal solutions to the problem is derived with the representation theorem of polyhedral sets, and the uniqueness condition of the optimal solution and the computational procedures to determine all optimal solutions ( ifthe uniqueness condition is not satisfied ) are provided. Finally, an illustrative example is also given.
On Optimizing the Satisfiability (SAT) Problem
Institute of Scientific and Technical Information of China (English)
GU Jun; GU Qianping; DU Dingzhu
1999-01-01
The satisfiability(SAT) problem is abasic problem in computing theory. Presently, an active area of researchon SAT problem is to design efficient optimization algorithms forfinding a solution for a satisfiable CNF formula. A newformulation, the Universal SAT problem model, which transforms the SAT problem on Boolean space into an optimization problem on real spacehas been developed. Many optimization techniques,such as the steepest descent method, Newton's method, and thecoordinate descent method, can be used to solve the Universal SAT problem. In this paper, we prove that, when the initial solution issufficiently close to the optimal solution, the steepest descent methodhas a linear convergence ratio β<1, Newton's method has aconvergence ratio of order two, and the convergence ratio of thecoordinate descent method is approximately (1-β/m) for the Universal SAT problem with m variables. An algorithm based on the coordinate descent method for the Universal SAT problem is alsopresented in this paper.
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.
Evolutionary computation for dynamic optimization problems
Yao, Xin
2013-01-01
This book provides a compilation on the state-of-the-art and recent advances of evolutionary computation for dynamic optimization problems. The motivation for this book arises from the fact that many real-world optimization problems and engineering systems are subject to dynamic environments, where changes occur over time. Key issues for addressing dynamic optimization problems in evolutionary computation, including fundamentals, algorithm design, theoretical analysis, and real-world applications, are presented. "Evolutionary Computation for Dynamic Optimization Problems" is a valuable reference to scientists, researchers, professionals and students in the field of engineering and science, particularly in the areas of computational intelligence, nature- and bio-inspired computing, and evolutionary computation.
Usage of the particle swarm optimization in problems of mechanics
Directory of Open Access Journals (Sweden)
Hajžman M.
2016-06-01
Full Text Available This paper deals with the optimization method called particle swarm optimization and its usage in mechanics. Basic versions of the method is introduced and several improvements and modifications are applied for better convergence of the algorithms. The performance of the optimization algorithm implemented in an original in-house software is investigated by means of three basic and one complex problems of mechanics. The goal of the first problem is to find optimal parameters of a dynamic absorber of vibrations. The second problem is about the tunning of eigenfrequencies of beam bending vibrations. The third problem is to optimize parameters of a clamped beam with various segments. The last complex problem is the optimization of a tilting mechanism with multilevel control. The presented results show that the particle swarm optimization can be efficiently used in mechanical tasks.
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...
Ant Colony Optimization and Hypergraph Covering Problems
Pat, Ankit
2011-01-01
Ant Colony Optimization (ACO) is a very popular metaheuristic for solving computationally hard combinatorial optimization problems. Runtime analysis of ACO with respect to various pseudo-boolean functions and different graph based combinatorial optimization problems has been taken up in recent years. In this paper, we investigate the runtime behavior of an MMAS*(Max-Min Ant System) ACO algorithm on some well known hypergraph covering problems that are NP-Hard. In particular, we have addressed the Minimum Edge Cover problem, the Minimum Vertex Cover problem and the Maximum Weak- Independent Set problem. The influence of pheromone values and heuristic information on the running time is analysed. The results indicate that the heuristic information has greater impact towards improving the expected optimization time as compared to pheromone values. For certain instances of hypergraphs, we show that the MMAS* algorithm gives a constant order expected optimization time when the dominance of heuristic information is ...
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
求解最优控制问题的微分变换方法%The Differential Transform Method for Solving Optimal Control Problems
Institute of Scientific and Technical Information of China (English)
李炳杰; 张国华; 吕园
2011-01-01
针对无约束最优控制问题,建立求其近似解析解的微分变换法.对哈密顿正则方程组中状态方程、协态方程和控制方程构造基于初值的微分变换形式或基于终端的微分变换形式,将最优性条件化为相应的代数方程,得到最优控制问题的近似解析解.在特定条件下,对结构复杂的非线性最优控制问题,依据插值逼近原理,结合微分变换法,可构建离散型代数方程组得到其近似解析解.利用微分变换法将微分方程初边值问题和泛函优化问题构成的复杂系统化为易于求解的代数方程形式,简单可行,易于实现.最后,通过算例验证方法的有效性.%The differential transform method used for solving the approximation analytic solution of the unconstrained optimal control problem is established. According to the state equation, costate equation and governing equation in the set of Hamilton regular equations, we first construct the differential transform form based on initial value or terminal station, by which the optimality condition is transformed into a corresponding algebraic equation, furthermore, the approximation analytic solution of the optimal control problem is obtained. In addition, to the nonlinear optimal control problem which is complex in structure, in particular condition, the discreteness set of algebraic equations can be constructed in light of the principle of approximation by interpolation and the differential transform method to obtain its approximation analytic solution. By using this method, the initial -boundary value problem of the differential equation and the complex system of the functional optimization problems are converted into algebraic equations which facilitate getting the solution, also are simple, feasible and easy to realize. Finally, the effectiveness of this method is verified by numerical examples.
Constrained Graph Optimization: Interdiction and Preservation Problems
Energy Technology Data Exchange (ETDEWEB)
Schild, Aaron V [Los Alamos National Laboratory
2012-07-30
The maximum flow, shortest path, and maximum matching problems are a set of basic graph problems that are critical in theoretical computer science and applications. Constrained graph optimization, a variation of these basic graph problems involving modification of the underlying graph, is equally important but sometimes significantly harder. In particular, one can explore these optimization problems with additional cost constraints. In the preservation case, the optimizer has a budget to preserve vertices or edges of a graph, preventing them from being deleted. The optimizer wants to find the best set of preserved edges/vertices in which the cost constraints are satisfied and the basic graph problems are optimized. For example, in shortest path preservation, the optimizer wants to find a set of edges/vertices within which the shortest path between two predetermined points is smallest. In interdiction problems, one deletes vertices or edges from the graph with a particular cost in order to impede the basic graph problems as much as possible (for example, delete edges/vertices to maximize the shortest path between two predetermined vertices). Applications of preservation problems include optimal road maintenance, power grid maintenance, and job scheduling, while interdiction problems are related to drug trafficking prevention, network stability assessment, and counterterrorism. Computational hardness results are presented, along with heuristic methods for approximating solutions to the matching interdiction problem. Also, efficient algorithms are presented for special cases of graphs, including on planar graphs. The graphs in many of the listed applications are planar, so these algorithms have important practical implications.
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 Mathematical Optimization Problem in Bioinformatics
Heyer, Laurie J.
2008-01-01
This article describes the sequence alignment problem in bioinformatics. Through examples, we formulate sequence alignment as an optimization problem and show how to compute the optimal alignment with dynamic programming. The examples and sample exercises have been used by the author in a specialized course in bioinformatics, but could be adapted…
A Mathematical Optimization Problem in Bioinformatics
Heyer, Laurie J.
2008-01-01
This article describes the sequence alignment problem in bioinformatics. Through examples, we formulate sequence alignment as an optimization problem and show how to compute the optimal alignment with dynamic programming. The examples and sample exercises have been used by the author in a specialized course in bioinformatics, but could be adapted…
Metaheuristic optimization of acoustic inverse problems.
van Leijen, A.V.; Rothkrantz, L.; Groen, F.
2011-01-01
Swift solving of geoacoustic inverse problems strongly depends on the application of a global optimization scheme. Given a particular inverse problem, this work aims to answer the questions how to select an appropriate metaheuristic search strategy, and how to configure it for optimal performance.
Metaheuristic optimization of acoustic inverse problems.
van Leijen, A.V.; Rothkrantz, L.; Groen, F.
2011-01-01
Swift solving of geoacoustic inverse problems strongly depends on the application of a global optimization scheme. Given a particular inverse problem, this work aims to answer the questions how to select an appropriate metaheuristic search strategy, and how to configure it for optimal performance. F
Topology optimization of wave-propagation problems
DEFF Research Database (Denmark)
Jensen, Jakob Søndergaard; Sigmund, Ole
2006-01-01
Topology optimization is demonstrated as a useful tool for systematic design of wave-propagation problems. We illustrate the applicability of the method for optical, acoustic and elastic devices and structures.......Topology optimization is demonstrated as a useful tool for systematic design of wave-propagation problems. We illustrate the applicability of the method for optical, acoustic and elastic devices and structures....
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...
Institute of Scientific and Technical Information of China (English)
贾继红
2007-01-01
This paper made a study of Wolfe duality for optimization problems with parameters in Banach spaces. In Invex-convexlike hypothesis, weak duality theorem and strong duality theorem for Wolfe duality were obtained. For application, the optimal control theory was also dealt with.%研究了Banach空间中参数优化问题的对偶问题,在不变类凸假设下,获得了Wolfe对偶的弱对偶定理和强对偶定理.作为应用,研究了一类最优控制问题的Wolfe对偶.
Directory of Open Access Journals (Sweden)
Seyed Mohsen Mousavi
2014-01-01
Full Text Available A multi-item multiperiod inventory control model is developed for known-deterministic variable demands under limited available budget. Assuming the order quantity is more than the shortage quantity in each period, the shortage in combination of backorder and lost sale is considered. The orders are placed in batch sizes and the decision variables are assumed integer. Moreover, all unit discounts for a number of products and incremental quantity discount for some other items are considered. While the objectives are to minimize both the total inventory cost and the required storage space, the model is formulated into a fuzzy multicriteria decision making (FMCDM framework and is shown to be a mixed integer nonlinear programming type. In order to solve the model, a multiobjective particle swarm optimization (MOPSO approach is applied. A set of compromise solution including optimum and near optimum ones via MOPSO has been derived for some numerical illustration, where the results are compared with those obtained using a weighting approach. To assess the efficiency of the proposed MOPSO, the model is solved using multi-objective genetic algorithm (MOGA as well. A large number of numerical examples are generated at the end, where graphical and statistical approaches show more efficiency of MOPSO compared with MOGA.
Mousavi, Seyed Mohsen; Niaki, S T A; Bahreininejad, Ardeshir; Musa, Siti Nurmaya
2014-01-01
A multi-item multiperiod inventory control model is developed for known-deterministic variable demands under limited available budget. Assuming the order quantity is more than the shortage quantity in each period, the shortage in combination of backorder and lost sale is considered. The orders are placed in batch sizes and the decision variables are assumed integer. Moreover, all unit discounts for a number of products and incremental quantity discount for some other items are considered. While the objectives are to minimize both the total inventory cost and the required storage space, the model is formulated into a fuzzy multicriteria decision making (FMCDM) framework and is shown to be a mixed integer nonlinear programming type. In order to solve the model, a multiobjective particle swarm optimization (MOPSO) approach is applied. A set of compromise solution including optimum and near optimum ones via MOPSO has been derived for some numerical illustration, where the results are compared with those obtained using a weighting approach. To assess the efficiency of the proposed MOPSO, the model is solved using multi-objective genetic algorithm (MOGA) as well. A large number of numerical examples are generated at the end, where graphical and statistical approaches show more efficiency of MOPSO compared with MOGA.
Problem Solving through an Optimization Problem in Geometry
Poon, Kin Keung; Wong, Hang-Chi
2011-01-01
This article adapts the problem-solving model developed by Polya to investigate and give an innovative approach to discuss and solve an optimization problem in geometry: the Regiomontanus Problem and its application to football. Various mathematical tools, such as calculus, inequality and the properties of circles, are used to explore and reflect…
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.
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
Minimal Controllability Problems
Olshevsky, Alex
2013-01-01
Given a linear system, we consider the problem of finding a small set of variables to affect with an input so that the resulting system is controllable. We show that this problem is NP-hard; indeed, we show that even approximating the minimum number of variables that need to be affected within a multiplicative factor of $c \\log n$ is NP-hard for some positive $c$. On the positive side, we show it is possible to find sets of variables matching this inapproximability barrier in polynomial time....
Optimality conditions for the numerical solution of optimization problems with PDE constraints :
Energy Technology Data Exchange (ETDEWEB)
Aguilo Valentin, Miguel Alejandro; Ridzal, Denis
2014-03-01
A theoretical framework for the numerical solution of partial di erential equation (PDE) constrained optimization problems is presented in this report. This theoretical framework embodies the fundamental infrastructure required to e ciently implement and solve this class of problems. Detail derivations of the optimality conditions required to accurately solve several parameter identi cation and optimal control problems are also provided in this report. This will allow the reader to further understand how the theoretical abstraction presented in this report translates to the application.
Solving the drift control problem
Directory of Open Access Journals (Sweden)
Melda Ormeci Matoglu
2015-12-01
Full Text Available We model the problem of managing capacity in a build-to-order environment as a Brownian drift control problem. We formulate a structured linear program that models a practical discretization of the problem and exploit a strong relationship between relative value functions and dual solutions to develop a functional lower bound for the continuous problem from a dual solution to the discrete problem. Refining the discretization proves a functional strong duality for the continuous problem. The linear programming formulation is so badly scaled, however, that solving it is beyond the capabilities of standard solvers. By demonstrating the equivalence between strongly feasible bases and deterministic unichain policies, we combinatorialize the pivoting process and by exploiting the relationship between dual solutions and relative value functions, develop a mechanism for solving the LP without ever computing its coefficients. Finally, we exploit the relationship between relative value functions and dual solutions to develop a scheme analogous to column generation for refining the discretization so as to drive the gap between the discrete approximation and the continuous problem to zero quickly while keeping the LP small. Computational studies show our scheme is much faster than simply solving a regular discretization of the problem both in terms of finding a policy with a low average cost and in terms of providing a lower bound on the optimal average cost.
Institute of Scientific and Technical Information of China (English)
崔鹏; 张承慧
2007-01-01
The finite time horizon indefinite linear quadratic(LQ) optimal control problem for singular linear discrete time-varying systems is discussed. Indefinite LQ optimal control problem for singular systems can be transformed to that for standard state-space systems under a reasonable assumption. It is shown that the indefinite LQ optimal control problem is dual to that of projection for backward stochastic systems. Thus, the optimal LQ controller can be obtained by computing the gain matrices of Kalman filter.Necessary and sufficient conditions guaranteeing a unique solution for the indefinite LQ problem are given. An explicit solution for the problem is obtained in terms of the solution of Riccati difference equations.
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
Binary Cockroach Swarm Optimization for Combinatorial Optimization Problem
Directory of Open Access Journals (Sweden)
Ibidun Christiana Obagbuwa
2016-09-01
Full Text Available The Cockroach Swarm Optimization (CSO algorithm is inspired by cockroach social behavior. It is a simple and efficient meta-heuristic algorithm and has been applied to solve global optimization problems successfully. The original CSO algorithm and its variants operate mainly in continuous search space and cannot solve binary-coded optimization problems directly. Many optimization problems have their decision variables in binary. Binary Cockroach Swarm Optimization (BCSO is proposed in this paper to tackle such problems and was evaluated on the popular Traveling Salesman Problem (TSP, which is considered to be an NP-hard Combinatorial Optimization Problem (COP. A transfer function was employed to map a continuous search space CSO to binary search space. The performance of the proposed algorithm was tested firstly on benchmark functions through simulation studies and compared with the performance of existing binary particle swarm optimization and continuous space versions of CSO. The proposed BCSO was adapted to TSP and applied to a set of benchmark instances of symmetric TSP from the TSP library. The results of the proposed Binary Cockroach Swarm Optimization (BCSO algorithm on TSP were compared to other meta-heuristic algorithms.
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 ...
Optimization and inverse problems in electromagnetism
Wiak, Sławomir
2003-01-01
From 12 to 14 September 2002, the Academy of Humanities and Economics (AHE) hosted the workshop "Optimization and Inverse Problems in Electromagnetism". After this bi-annual event, a large number of papers were assembled and combined in this book. During the workshop recent developments and applications in optimization and inverse methodologies for electromagnetic fields were discussed. The contributions selected for the present volume cover a wide spectrum of inverse and optimal electromagnetic methodologies, ranging from theoretical to practical applications. A number of new optimal and inverse methodologies were proposed. There are contributions related to dedicated software. Optimization and Inverse Problems in Electromagnetism consists of three thematic chapters, covering: -General papers (survey of specific aspects of optimization and inverse problems in electromagnetism), -Methodologies, -Industrial Applications. The book can be useful to students of electrical and electronics engineering, computer sci...
On the Ramified Optimal Allocation Problem
Xia, Qinglan
2011-01-01
This paper proposes an optimal allocation problem with ramified transport technology in a spatial economy. Ramified transportation is used to model the transport economy of scale in group transportation observed widely in both nature and efficiently designed transport systems of branching structures. The ramified allocation problem aims at finding an optimal allocation plan as well as an associated optimal allocation path to minimize overall cost of transporting commodity from factories to households. This problem differentiates itself from existing ramified transportation literature in that the distribution of production among factories is not fixed but endogenously determined as observed in many allocation practices. It's shown that due to the transport economy of scale in ramified transportation, each optimal allocation plan corresponds equivalently to an optimal assignment map from households to factories. This optimal assignment map provides a natural partition of both households and allocation paths. We...
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...
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
解决最优控制问题的准梯度方法%Quasigradient Methods for Solving Optimal Control Problems
Institute of Scientific and Technical Information of China (English)
王玲; 李建国; 斯洛齐克
1999-01-01
In this paper,the nonlinear optimal control problem connected with the ordinary differential system is considered,Two modifications to the standard gradient procedures are constructed.The presented methods are based on the qualitative approximations of the cost functional.For linear-quadratic problems,the modifications have the property of the nonlocal improvement in contrast to the standard gradient procedures.Some results relating to the convergence of the new methods are proved.%讨论非线性最优控制问题构造的标准梯度方法的两种改进方法.文中的方法是以罚函数的有效近似为基础,与标准梯度方法相比,该方法对于非线性二次问题具有非局部的特点,同时给出相关收敛结果.
Hybrid intelligent optimization methods for engineering problems
Pehlivanoglu, Yasin Volkan
quantification studies, we improved new mutation strategies and operators to provide beneficial diversity within the population. We called this new approach as multi-frequency vibrational GA or PSO. They were applied to different aeronautical engineering problems in order to study the efficiency of these new approaches. These implementations were: applications to selected benchmark test functions, inverse design of two-dimensional (2D) airfoil in subsonic flow, optimization of 2D airfoil in transonic flow, path planning problems of autonomous unmanned aerial vehicle (UAV) over a 3D terrain environment, 3D radar cross section minimization problem for a 3D air vehicle, and active flow control over a 2D airfoil. As demonstrated by these test cases, we observed that new algorithms outperform the current popular algorithms. The principal role of this multi-frequency approach was to determine which individuals or particles should be mutated, when they should be mutated, and which ones should be merged into the population. The new mutation operators, when combined with a mutation strategy and an artificial intelligent method, such as, neural networks or fuzzy logic process, they provided local and global diversities during the reproduction phases of the generations. Additionally, the new approach also introduced random and controlled diversity. Due to still being population-based techniques, these methods were as robust as the plain GA or PSO algorithms. Based on the results obtained, it was concluded that the variants of the present multi-frequency vibrational GA and PSO were efficient algorithms, since they successfully avoided all local optima within relatively short optimization cycles.
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...
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.
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.
Vector Broadcast Channels: Optimal Threshold Selection Problem
Samarasinghe, Tharaka; Evans, Jamie
2011-01-01
Threshold feedback policies are well known and provably rate-wise optimal selective feedback techniques for communication systems requiring partial channel state information (CSI). However, optimal selection of thresholds at mobile users to maximize information theoretic data rates subject to feedback constraints is an open problem. In this paper, we focus on the optimal threshold selection problem, and provide a solution for this problem for finite feedback systems. Rather surprisingly, we show that using the same threshold values at all mobile users is not always a rate-wise optimal feedback strategy, even for a system with identical users experiencing statistically the same channel conditions. By utilizing the theory of majorization, we identify an underlying Schur-concave structure in the rate function and obtain sufficient conditions for a homogenous threshold feedback policy to be optimal. Our results hold for most fading channel models, and we illustrate an application of our results to familiar Raylei...
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.
Geoengineering as an optimization problem
Energy Technology Data Exchange (ETDEWEB)
Ban-Weiss, George A; Caldeira, Ken, E-mail: georgebw@stanford.edu [Department of Global Ecology, Carnegie Institution for Science, 260 Panama Street, Stanford, CA 94305 (United States)
2010-07-15
There is increasing evidence that Earth's climate is currently warming, primarily due to emissions of greenhouse gases from human activities, and Earth has been projected to continue warming throughout this century. Scientists have begun to investigate the potential for geoengineering options for reducing surface temperatures and whether such options could possibly contribute to environmental risk reduction. One proposed method involves deliberately increasing aerosol loading in the stratosphere to scatter additional sunlight to space. Previous modeling studies have attempted to predict the climate consequences of hypothetical aerosol additions to the stratosphere. These studies have shown that this method could potentially reduce surface temperatures, but could not recreate a low-CO{sub 2} climate in a high-CO{sub 2} world. In this study, we attempt to determine the latitudinal distribution of stratospheric aerosols that would most closely achieve a low-CO{sub 2} climate despite high CO{sub 2} levels. Using the NCAR CAM3.1 general circulation model, we find that having a stratospheric aerosol loading in polar regions higher than that in tropical regions leads to a temperature distribution that is more similar to the low-CO{sub 2} climate than that yielded by a globally uniform loading. However, such polar weighting of stratospheric sulfate tends to degrade the degree to which the hydrological cycle is restored, and thus does not markedly contribute to improved recovery of a low-CO{sub 2} climate. In the model, the optimal latitudinally varying aerosol distributions diminished the rms zonal mean land temperature change from a doubling of CO{sub 2} by 94% and the rms zonal mean land precipitation minus evaporation change by 74%. It is important to note that this idealized study represents a first attempt at optimizing the engineering of climate using a general circulation model; uncertainties are high and not all processes that are important in reality are
An optimal hostage rescue problem
Shi, Fengbo
2000-01-01
We propose the following mathematical model of optinal reacue problems concerning hostage.Suppose i persons are taken as hostages at any given point in time t,and we have to make a decision on attempting either rescue or no resuce. Let p be the probability of a hostage being killed in a rescue attempt,and let s be the probability of criminal(s) surrendering up to the following point in time if no rescue attempt is made.Futher,let g and r be the probabilities of a hostage being,respectively,ki...
Institute of Scientific and Technical Information of China (English)
李树荣; 张强; 雷阳; 张晓东
2011-01-01
A control vector parameterization（CVP）based numerical approach is proposed for free time optimal control problems.By using a time-scaling factor,free time optimal control problem is converted into a fixed time one,and the final time is defined as an optimization parameter.Based on CVP method,the resulted optimal control problem is reformulated as a nonlinear programming（NLP）problem.By constructing the Hamiltonian functions of objective and constraint functions, the adjoint functions are solved to obtain the gradients of objective and constraint functions.The numerical solution is obtained by using the sequential quadratic programming（SQP）method.For the control switched optimal control problems, a mesh refinement strategy is presented to improve the optimal solution.A simulation on a fed-batch reactor optimal control problem shows the effectiveness of the proposed approach.%针对自由时间最优控制问题,提出一种控制向量参数化（CVP）方法.通过引入时间尺度因子,将自由时间最优控制问题转化为固定时间问题,并将终端时刻作为优化参数.基于CVP方法,最优控制问题被转化为一个非线性规划（NLP）问题.建立目标和约束函数的Hamiltonian函数,通过求解伴随方程获得目标和约束函数的梯度,采用序列二次规划（SQP）方法获得问题的数值解.对于控制有切换结构的优化问题,给出了一种网格精细化策略,以提高控制质量.补料分批反应器最优控制问题的仿真实验验证了所提出方法的有效性.
A Problem-Oriented Mathematical Optimization Course
Wenger, Robert B.; Rhyner, Charles R.
1977-01-01
This article describes a one-semester junior and senior level course in applied mathematical optimization for undergraduates which provides the opportunity to test models by doing numerical experiments and to learn to use computer subroutines for solving optimization problems. (MN)
Test problem construction for single-objective bilevel optimization.
Sinha, Ankur; Malo, Pekka; Deb, Kalyanmoy
2014-01-01
In this paper, we propose a procedure for designing controlled test problems for single-objective bilevel optimization. The construction procedure is flexible and allows its user to control the different complexities that are to be included in the test problems independently of each other. In addition to properties that control the difficulty in convergence, the procedure also allows the user to introduce difficulties caused by interaction of the two levels. As a companion to the test problem construction framework, the paper presents a standard test suite of 12 problems, which includes eight unconstrained and four constrained problems. Most of the problems are scalable in terms of variables and constraints. To provide baseline results, we have solved the proposed test problems using a nested bilevel evolutionary algorithm. The results can be used for comparison, while evaluating the performance of any other bilevel optimization algorithm. The code related to the paper may be accessed from the website http://bilevel.org .
An improved group search optimizer for mechanical design optimization problems
Institute of Scientific and Technical Information of China (English)
Hai Shen; Yunlong Zhu; Ben Niu; Q.H. Wu
2009-01-01
This paper presents an improved group search optimizer (iGSO) for solving mechanical design optimization problems.In the pro-posed algorithm,subpopulations and a co-operation evolutionary strategy were adopted to improve the global search capability and convergence performance.The iGSO is evaluated on two optimization problems of classical mechanical design:spring and pressure vessel.The experimental results are analyzed in comparison with those reported in the literatures.The results show that iGSO has much better convergence performance and is easier to implement in comparison with other existing evolutionary algorithms.
Directory of Open Access Journals (Sweden)
William Margulies
2004-11-01
Full Text Available In this paper, we study a specific stochastic differential equation depending on a parameter and obtain a representation of its probability density function in terms of Jacobi Functions. The equation arose in a control problem with a quadratic performance criteria. The quadratic performance is used to eliminate the control in the standard Hamilton-Jacobi variational technique. The resulting stochastic differential equation has a noise amplitude which complicates the solution. We then solve Kolmogorov's partial differential equation for the probability density function by using Jacobi Functions. A particular value of the parameter makes the solution a Martingale and in this case we prove that the solution goes to zero almost surely as time tends to infinity.
An optimal design problem in wave propagation
DEFF Research Database (Denmark)
Bellido, J.C.; Donoso, Alberto
2007-01-01
We consider an optimal design problem in wave propagation proposed in Sigmund and Jensen (Roy. Soc. Lond. Philos. Trans. Ser. A 361:1001-1019, 2003) in the one-dimensional situation: Given two materials at our disposal with different elastic Young modulus and different density, the problem consists...... of finding the best distributions of the two initial materials in a rod in order to minimize the vibration energy in the structure under periodic loading of driving frequency Omega. We comment on relaxation and optimality conditions, and perform numerical simulations of the optimal configurations. We prove...
Shape flows for spectral optimization problems
Bucur, Dorin; Stefanelli, Ulisse
2011-01-01
We consider a general formulation of gradient flow evolution for problems whose natural framework is the one of metric spaces. The applications we deal with are concerned with the evolution of {\\it capacitary measures} with respect to the $\\gamma$-convergence dissipation distance and with the evolution of domains in spectral optimization problems.
Variable Expansion Techniques for Decomposable Optimization Problems
2011-03-05
meration or dynamic programming. Recall the edge partition problem studied by Taskin et al. above in reference 7. (Z. Caner Taskin was supported by the...Stochastic Integer Program- ming, August 2009 August 2009. 12 2. Z. Caner Taskin, Algorithms for Solving Multi-Level Optimization Problems with Dis
Topology optimization of fluid mechanics problems
DEFF Research Database (Denmark)
Gersborg-Hansen, Allan
While topology optimization for solid continuum structures have been studied for about 20 years and for the special case of trusses for many more years, topology optimization of fluid mechanics problems is more recent. Borrvall and Petersson [1] is the seminal reference for topology optimization...... with respect to minimizing the energy loss, characteristic properties of the velocity field or mixing properties. To reduce the computational complexity of the topology optimization problems the primary focus is put on the Stokes equation in 2D and in 3D. However, the the talk also contains examples with the 2......D Navier-Stokes equation as well as an example with convection dominated transport in 2D Stokes flow. Using Stokes flow limits the range of applications; nonetheless, the present work gives a proof-of-concept for the application of the method within fluid mechanics problems and it remains...
1988-01-01
measure on the Borel sets of U x [0,*)) random variable m(-) is an admissible relaxed control if ff’f(s,,)m( dsda ) is progressively measurable for each...anticipativc and tt f(s,a~m( dsda ) = ds f(s,a)m,(da) for all t w.p.l. Sometimes we use the ’feedback’ relaxed control (which we write as mx(-)) which is a...controls. An admissible relaxed contol m(.) for (2.1) is also a measure valued random variable (as above) but f;f(s,a)m( dsda ) is progressively measurable
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.
Belief Propagation Algorithm for Portfolio Optimization Problems.
Shinzato, Takashi; Yasuda, Muneki
2015-01-01
The typical behavior of optimal solutions to portfolio optimization problems with absolute deviation and expected shortfall models using replica analysis was pioneeringly estimated by S. Ciliberti et al. [Eur. Phys. B. 57, 175 (2007)]; however, they have not yet developed an approximate derivation method for finding the optimal portfolio with respect to a given return set. In this study, an approximation algorithm based on belief propagation for the portfolio optimization problem is presented using the Bethe free energy formalism, and the consistency of the numerical experimental results of the proposed algorithm with those of replica analysis is confirmed. Furthermore, the conjecture of H. Konno and H. Yamazaki, that the optimal solutions with the absolute deviation model and with the mean-variance model have the same typical behavior, is verified using replica analysis and the belief propagation algorithm.
Belief Propagation Algorithm for Portfolio Optimization Problems.
Directory of Open Access Journals (Sweden)
Takashi Shinzato
Full Text Available The typical behavior of optimal solutions to portfolio optimization problems with absolute deviation and expected shortfall models using replica analysis was pioneeringly estimated by S. Ciliberti et al. [Eur. Phys. B. 57, 175 (2007]; however, they have not yet developed an approximate derivation method for finding the optimal portfolio with respect to a given return set. In this study, an approximation algorithm based on belief propagation for the portfolio optimization problem is presented using the Bethe free energy formalism, and the consistency of the numerical experimental results of the proposed algorithm with those of replica analysis is confirmed. Furthermore, the conjecture of H. Konno and H. Yamazaki, that the optimal solutions with the absolute deviation model and with the mean-variance model have the same typical behavior, is verified using replica analysis and the belief propagation algorithm.
Topology optimization of Channel flow problems
DEFF Research Database (Denmark)
Gersborg-Hansen, Allan; Sigmund, Ole; Haber, R. B.
2005-01-01
]. Further, the inclusion of inertia effects significantly alters the physics, enabling solutions of new classes of optimization problems, such as velocity--driven switches, that are not addressed by the earlier method. Specifically, we determine optimal layouts of channel flows that extremize a cost...... sensitivities. Our target application is optimal layout design of channels in fluid network systems. Using concepts borrowed from topology optimization of compliant mechanisms in solid mechanics, we introduce a method for the synthesis of fluidic components, such as switches, diodes, etc....
Optimal control of hydroelectric facilities
Zhao, Guangzhi
challenging problem of optimizing a sequence of two hydro dams sharing the same river system. The complexity of this problem is magnified and we just scratch its surface here. The thesis concludes with suggestions for future work in this fertile area. Keywords: dynamic programming, hydroelectric facility, optimization, optimal control, switching cost, turbine efficiency.
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...
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.
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.
Better relaxations of classical discrete optimization problems.
Energy Technology Data Exchange (ETDEWEB)
Lancia, Giuseppe; Konjevod, Goran; Carr, Robert D.; Parehk, Ojas
2008-08-01
A mathematical program is an optimization problem expressed as an objective function of multiple variables subject to set of constraints. When the optimization problem has specific structure, the problem class usually has a special name. A linear program is the optimization of a linear objective function subject to linear constraints. An integer program is a linear program where some of the variables must take only integer values. A semidefinite program is a linear program where the variables are arranged in a matrix and for all feasible solutions, this matrix must be positive semidefinite. There are general-purpose solvers for each of these classes of mathematical program. There are usually many ways to express a problem as a correct, say, linear program. However, equivalent formulations can have significantly different practical tractability. In this poster, we present new formulations for two classic discrete optimization problems, maximum cut (max cut) and the graphical traveling salesman problem (GTSP), that are significantly stronger, and hence more computationally tractable, than any previous formulations of their class. Both partially answer longstanding open theoretical questions in polyhedral combinatorics.
Rahmah, Z.; Subartini, B.; Djauhari, E.; Anggriani, N.; Supriatna, A. K.
2017-03-01
Tuberculosis (TB) is a disease that is infected by the bacteria Mycobacterium tuberculosis. The World Health Organization (WHO) recommends to implement the Baccilus Calmete Guerin (BCG) vaccine in toddler aged two to three months to be protected from the infection. This research explores the numerical simulation of forward-backward difference approximation method on the model of TB transmission considering this vaccination program. The model considers five compartments of sub-populations, i.e. susceptible, vaccinated, exposed, infected, and recovered human sub-populations. We consider here the vaccination as a control variable. The results of the simulation showed that vaccination can indeed reduce the number of infected human population.
A simple convex optimization problem with many applications
DEFF Research Database (Denmark)
Vidal, Rene Victor Valqui
1994-01-01
This paper presents an algorithm for the solution of a simple convex optimization problem. This problem is a generalization of several other optimization problems which have applications to resource allocation, optimal capacity expansion, and vehicle scheduling. The algorithm is based...
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...
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.
Topology Optimization for Transient Wave Propagation Problems
DEFF Research Database (Denmark)
Matzen, René
as for vectorial elastic wave propagation problems using finite element analysis [P2], [P4]. The concept is implemented in a parallel computing code that includes efficient techniques for performing gradient based topology optimization. Using the developed computational framework the thesis considers four...... new technology, by designing new materials and their layout. The thesis presents a general framework for applying topology optimization in the design of material layouts for transient wave propagation problems. In contrast to the high level of modeling in the frequency domain, time domain topology...
Trajectory metaheuristic algorithms to optimize problems combinatorics
Directory of Open Access Journals (Sweden)
Natalia Alancay
2016-12-01
Full Text Available The application of metaheuristic algorithms to optimization problems has been very important during the last decades. The main advantage of these techniques is their flexibility and robustness, which allows them to be applied to a wide range of problems. In this work we concentrate on metaheuristics based on Simulated Annealing, Tabu Search and Variable Neighborhood Search trajectory whose main characteristic is that they start from a point and through the exploration of the neighborhood vary the current solution, forming a trajectory. By means of the instances of the selected combinatorial problems, a computational experimentation is carried out that illustrates the behavior of the algorithmic methods to solve them. The main objective of this work is to perform the study and comparison of the results obtained for the selected trajectories metaheuristics in its application for the resolution of a set of academic problems of combinatorial optimization.
Solving global optimization problems on GPU cluster
Barkalov, Konstantin; Gergel, Victor; Lebedev, Ilya
2016-06-01
The paper contains the results of investigation of a parallel global optimization algorithm combined with a dimension reduction scheme. This allows solving multidimensional problems by means of reducing to data-independent subproblems with smaller dimension solved in parallel. The new element implemented in the research consists in using several graphic accelerators at different computing nodes. The paper also includes results of solving problems of well-known multiextremal test class GKLS on Lobachevsky supercomputer using tens of thousands of GPU cores.
Shape Optimization Problems with Internal Constraint
Bucur, Dorin; Velichkov, Bozhidar
2011-01-01
We consider shape optimization problems with internal inclusion constraints, of the form $$\\min\\big\\{J(\\Omega)\\ :\\ \\Dr\\subset\\Omega\\subset\\R^d,\\ |\\Omega|=m\\big\\},$$ where the set $\\Dr$ is fixed, possibly unbounded, and $J$ depends on $\\Omega$ via the spectrum of the Dirichlet Laplacian. We analyze the existence of a solution and its qualitative properties, and rise some open questions.
Modelling Robust Design Problems via Conic Optimization
Chaerani, D.
2006-01-01
This thesis deals with optimization problems with uncertain data. Uncertainty here means that the data is not known exactly at the time when its solution has to be determined. In many models the uncertainty is ignored and a representative nominal value of the data is used. The uncertainty may be due
Solving the Travelling Salesman Problem Using the Ant Colony Optimization
Directory of Open Access Journals (Sweden)
Zuzana Čičková
2011-12-01
Full Text Available In this article, we study a possibility of solving the well-known Travelling Salesman Problem (TSP, which ranges among NP-hard problems, and offer a theoretical overview of some methods used for solving this problem. We discuss the Ant Colony Optimization (ACO, which belongs to the group of evolutionary techniques and presents the approach used in the application of ACO to the TSP. We study the impact of some control parameters by implementing this algorithm. The quality of the solution is compared with the optimal solution.
Minimal Time Problem with Impulsive Controls
Energy Technology Data Exchange (ETDEWEB)
Kunisch, Karl, E-mail: karl.kunisch@uni-graz.at [University of Graz, Institute for Mathematics and Scientific Computing (Austria); Rao, Zhiping, E-mail: zhiping.rao@ricam.oeaw.ac.at [Austrian Academy of Sciences, Radon Institute of Computational and Applied Mathematics (Austria)
2017-02-15
Time optimal control problems for systems with impulsive controls are investigated. Sufficient conditions for the existence of time optimal controls are given. A dynamical programming principle is derived and Lipschitz continuity of an appropriately defined value functional is established. The value functional satisfies a Hamilton–Jacobi–Bellman equation in the viscosity sense. A numerical example for a rider-swing system is presented and it is shown that the reachable set is enlargered by allowing for impulsive controls, when compared to nonimpulsive controls.
Institute of Scientific and Technical Information of China (English)
雷阳; 李树荣; 张强; 张晓东
2011-01-01
The traditional uniform control vector parameterization method can not obtain accurate optimal control policy when solving optimal control problems with fixed final time. For this reason, a non-uniform control vector parameterization approach was proposed. Firstly, the given time interval was divided into several time stages of varying lengths which were defined as new optimization parameters. Secondly, the original optimal control problem was transformed into a uniform parameterization problem by introducing a time-scaling factor. Finally, the adjoint equations were solved to obtain the gradients by constructing the Hamilton functions of objective and constraint functions. The numerical solution was obtained by sequential quadratic programming method. Simulation results on two optimal control problems of chemical process show the effectiveness of the proposed method.%传统的均匀参数化方法在求解固定终端时刻最优控制问题时,不能精确地逼近最优控制轨迹.针对这一问题,提出一种非均匀控制向量参数化的数值解法.首先将控制时域离散化为不同长度的时间段,各时间段长度作为新的优化参数；然后引入时间尺度因子,将非均匀参数化的最优控制问题转化为标准化时域上的均匀参数化问题；最后建立目标和约束函数的Hamilton函数,通过求解伴随方程计算梯度,采用序列二次规划方法获得数值解.针对两个经典的化工过程最优控制问题进行仿真研究,仿真结果验证了所提出算法的有效性.
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
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.
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.
Institute of Scientific and Technical Information of China (English)
李国栋; 刘兴高
2015-01-01
控制向量参数化方法是求解最优控制问题的一种常用数值方法。它通过离散化控制时域，将控制向量近似地表示成一组参数化的函数。离散化后的时间网格通常是固定的，其划分会影响到最优控制问题数值求解的精度和效率。为了同时优化控制参数和时间网格节点，提出了一种时间节点可变的控制向量参数化方法。推导出了最优控制性能指标对时间参数的导数与对时间分段长度导数之间的关系，得到了性能指标的梯度表达式。用两个经典最优控制实例对所提出的方法进行了测试，结果表明所提出方法能够更好地逼近最优控制轨迹。%Control vector parameterization (CVP) is a frequently used numerical method for solving optimal control problems, where the control vector is approximated by a group of parametric functions through time discretization. Usually, the discretized time grid is fixed, and its partition will affect accuracy and performance of the numerical solution of optimal control problem. To optimize both the control parameters and the time grid nodes, a CVP method with variable time nodes was proposed. Based on the derived relationship between the gradients of time nodes and the ones of interval lengths, the gradient equations for parameters were presented. The proposed method was demonstrated to have better approximation ability for the optimal control trajectories on two classic optimal control problems.
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.
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...
TSP based Evolutionary optimization approach for the Vehicle Routing Problem
Kouki, Zoulel; Chaar, Besma Fayech; Ksouri, Mekki
2009-03-01
Vehicle Routing and Flexible Job Shop Scheduling Problems (VRP and FJSSP) are two common hard combinatorial optimization problems that show many similarities in their conceptual level [2, 4]. It was proved for both problems that solving techniques like exact methods fail to provide good quality solutions in a reasonable amount of time when dealing with large scale instances [1, 5, 14]. In order to overcome this weakness, we decide in the favour of meta heuristics and we focalize on evolutionary algorithms that have been successfully used in scheduling problems [1, 5, 9]. In this paper we investigate the common properties of the VRP and the FJSSP in order to provide a new controlled evolutionary approach for the CVRP optimization inspired by the FJSSP evolutionary optimization algorithms introduced in [10].
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.
Distributed Algorithms for Optimal Power Flow Problem
Lam, Albert Y S; Tse, David
2011-01-01
Optimal power flow (OPF) is an important problem for power generation and it is in general non-convex. With the employment of renewable energy, it will be desirable if OPF can be solved very efficiently so its solution can be used in real time. With some special network structure, e.g. trees, the problem has been shown to have a zero duality gap and the convex dual problem yields the optimal solution. In this paper, we propose a primal and a dual algorithm to coordinate the smaller subproblems decomposed from the convexified OPF. We can arrange the subproblems to be solved sequentially and cumulatively in a central node or solved in parallel in distributed nodes. We test the algorithms on IEEE radial distribution test feeders, some random tree-structured networks, and the IEEE transmission system benchmarks. Simulation results show that the computation time can be improved dramatically with our algorithms over the centralized approach of solving the problem without decomposition, especially in tree-structured...
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
Directory of Open Access Journals (Sweden)
Ahmet Demir
2017-01-01
Full Text Available In the fields which require finding the most appropriate value, optimization became a vital approach to employ effective solutions. With the use of optimization techniques, many different fields in the modern life have found solutions to their real-world based problems. In this context, classical optimization techniques have had an important popularity. But after a while, more advanced optimization problems required the use of more effective techniques. At this point, Computer Science took an important role on providing software related techniques to improve the associated literature. Today, intelligent optimization techniques based on Artificial Intelligence are widely used for optimization problems. The objective of this paper is to provide a comparative study on the employment of classical optimization solutions and Artificial Intelligence solutions for enabling readers to have idea about the potential of intelligent optimization techniques. At this point, two recently developed intelligent optimization algorithms, Vortex Optimization Algorithm (VOA and Cognitive Development Optimization Algorithm (CoDOA, have been used to solve some multidisciplinary optimization problems provided in the source book Thomas' Calculus 11th Edition and the obtained results have compared with classical optimization solutions.
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.
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.
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.
Hybrid Predictive Control for Dynamic Transport Problems
Núñez, Alfredo A; Cortés, Cristián E
2013-01-01
Hybrid Predictive Control for Dynamic Transport Problems develops methods for the design of predictive control strategies for nonlinear-dynamic hybrid discrete-/continuous-variable systems. The methodology is designed for real-time applications, particularly the study of dynamic transport systems. Operational and service policies are considered, as well as cost reduction. The control structure is based on a sound definition of the key variables and their evolution. A flexible objective function able to capture the predictive behaviour of the system variables is described. Coupled with efficient algorithms, mainly drawn from the area of computational intelligence, this is shown to optimize performance indices for real-time applications. The framework of the proposed predictive control methodology is generic and, being able to solve nonlinear mixed-integer optimization problems dynamically, is readily extendable to other industrial processes. The main topics of this book are: ●hybrid predictive control (HPC) ...
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
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.
Properties of solutions of optimization problems for set functions
Directory of Open Access Journals (Sweden)
Slawomir Dorosiewicz
2001-01-01
Full Text Available A definition of a special class of optimization problems with set functions is given. The existence of optimal solutions and first-order optimality conditions are proved. This case of optimal problems can be transformed to standard mixed problems of mathematical programming in Euclidean space. It makes possible the applications of various algorithms for these optimization problems for finding conditional extrema of set functions.
Directory of Open Access Journals (Sweden)
Ioannis Athanasopoulos
1984-01-01
Full Text Available In an open bounded region of n-space occupied by a homogeneous and isotropic medium, we control the temperature through the boundary. The normal derivative of the temperature (which measures the appropriate heat flux is restricted to be nonnegative. This gives rise to a free boundary in space-time separating the areas of positive and zero heat flux. Under a natural monotonicity condition, the free boundary is the graph of a function of space. This function is shown to be locally Lipschitz. Moreover for n=2 the time derivative of the temperature is proven to be continuous across the free boundary.
Institute of Scientific and Technical Information of China (English)
彭海军; 高强; 吴志刚; 钟万勰
2011-01-01
针对非线性最优控制导出的Hamiltonian系统两点边值问题,提出一种以离散区段右端状态和左端协态为混合独立变量的数值求解方法,将非线性Hamiltonian系统两点边值问题的求解通过混合独立变量变分原理转化为非线性方程组求解.所提出的算法综合了求解最优控制的“直接法”和“间接法”的特征,既满足最优控制理论的一阶必要条件,又不需要对协态初值的准确猜测,避免了求解大规模非线性规划问题.通过两个航天控制算例讨论了本文算法的精度和效率等问题.与近年来在航空航天控制中备受关注的高斯伪谱方法相比较,本文算法无论是在精度还是效率上都具有明显的优势.%The nonlinear optimal control problem is transformed into the Hamiltonian two point boundary value problem (TPBVP), and a numerical method is proposed based on the dual variational principle. The nonlinear Hamiltonian TPBVP is transformed into a system of nonlinear equations by using the dual variational principle and by taking the left costate and the right state as independent variables. The proposed algorithm has the feature of both "direct method" and "indirect method" for solving optimal control problem, I.e., it satisfies the first-order necessary condition of optimal control theory, and it needs no precise initial guess for costate variables and avoids the solving of large scale nonlinear programming problem. The accuracy and efficiency of the proposed method are discussed by numerical simulations in aerospace control. Comparison between the proposed algorithm and the famous Gauss pseudo-spectral method in aeronautics and astronautics control shows that the proposed algorithm has obvious advantages on accuracy and efficiency.
Optimal Planning and Problem-Solving
Clemet, Bradley; Schaffer, Steven; Rabideau, Gregg
2008-01-01
CTAEMS MDP Optimal Planner is a problem-solving software designed to command a single spacecraft/rover, or a team of spacecraft/rovers, to perform the best action possible at all times according to an abstract model of the spacecraft/rover and its environment. It also may be useful in solving logistical problems encountered in commercial applications such as shipping and manufacturing. The planner reasons around uncertainty according to specified probabilities of outcomes using a plan hierarchy to avoid exploring certain kinds of suboptimal actions. Also, planned actions are calculated as the state-action space is expanded, rather than afterward, to reduce by an order of magnitude the processing time and memory used. The software solves planning problems with actions that can execute concurrently, that have uncertain duration and quality, and that have functional dependencies on others that affect quality. These problems are modeled in a hierarchical planning language called C_TAEMS, a derivative of the TAEMS language for specifying domains for the DARPA Coordinators program. In realistic environments, actions often have uncertain outcomes and can have complex relationships with other tasks. The planner approaches problems by considering all possible actions that may be taken from any state reachable from a given, initial state, and from within the constraints of a given task hierarchy that specifies what tasks may be performed by which team member.
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.
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.
Linux software for large topology optimization problems
DEFF Research Database (Denmark)
evolving product, which allows a parallel solution of the PDE, it lacks the important feature that the matrix-generation part of the computations is localized to each processor. This is well-known to be critical for obtaining a useful speedup on a Linux cluster and it motivates the search for a COMSOL......-like package for large topology optimization problems. One candidate for such software is developed for Linux by Sandia Nat’l Lab in the USA being the Sundance system. Sundance also uses a symbolic representation of the PDE and a scalable numerical solution is achieved by employing the underlying Trilinos...
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.
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.
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
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.
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.
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...
Particle Swarm Optimization for Structural Design Problems
Directory of Open Access Journals (Sweden)
Hamit SARUHAN
2010-02-01
Full Text Available The aim of this paper is to employ the Particle Swarm Optimization (PSO technique to a mechanical engineering design problem which is minimizing the volume of a cantilevered beam subject to bending strength constraints. Mechanical engineering design problems are complex activities which are computing capability are more and more required. The most of these problems are solved by conventional mathematical programming techniques that require gradient information. These techniques have several drawbacks from which the main one is becoming trapped in local optima. As an alternative to gradient-based techniques, the PSO does not require the evaluation of gradients of the objective function. The PSO algorithm employs the generation of guided random positions when they search for the global optimum point. The PSO which is a nature inspired heuristics search technique imitates the social behavior of bird flocking. The results obtained by the PSO are compared with Mathematical Programming (MP. It is demonstrated that the PSO performed and obtained better convergence reliability on the global optimum point than the MP. Using the MP, the volume of 2961000 mm3 was obtained while the beam volume of 2945345 mm3 was obtained by the PSO.
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
Ideology and problems of systems and economic optimization of NPPs
Directory of Open Access Journals (Sweden)
A.V. Klimenko
2016-06-01
Problems of systems optimization of components of the NFEC system as the functional of NPP optimization are identified. The task of optimization of complex systems refers to the most complex class of degenerate optimization problems [1]. No theory of degenerate optimization problems exists as of the present moment, although specifically these problems are real. Degenerate optimization problems should not be associated with degenerate matrices. Degenerate optimization problems deal with non-singular matrices having inverse matrices and, consequently, having solutions. However, the nature of these problems is such, that these solutions are degenerate (one or more components of the basis vector of the solution are equal to zero. The problem of convergence in the optimization of arbitrary component of the NFEC system to locally optimal plan coordinated with locally optimal plans for other components of the NFEC system is one of the main problems of degenerate optimization problems. Appearance of iterating loops during internal iterations in the process of optimization of plans for separate component of the NFEC system is not less important for problems of this class. This feature requires including incorporation of additional algorithms for exiting from the loops in the optimization algorithms.
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.
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.
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
Chemical Reaction Optimization for Max Flow Problem
Directory of Open Access Journals (Sweden)
Reham Barham
2016-08-01
Full Text Available This study presents an algorithm for MaxFlow problem using "Chemical Reaction Optimization algorithm (CRO". CRO is a recently established meta-heuristics algorithm for optimization, inspired by the nature of chemical reactions. The main concern is to find the best maximum flow value at which the flow can be shipped from the source node to the sink node in a flow network without violating any capacity constraints in which the flow of each edge remains within the upper bound value of the capacity. The proposed MaxFlow-CRO algorithm is presented, analyzed asymptotically and experimental test is conducted. Asymptotic runtime is derived theoretically. The algorithm is implemented using JAVA programming language. Results show a good performance with a complexity of O(I E2, for I iterations and E edges. The number of iterations I in the algorithm, is an important factor that will affect the results obtained. As number of iterations is increased, best possible max-Flow value is obtained.
Optimization methods for activities selection problems
Mahad, Nor Faradilah; Alias, Suriana; Yaakop, Siti Zulaika; Arshad, Norul Amanina Mohd; Mazni, Elis Sofia
2017-08-01
Co-curriculum activities must be joined by every student in Malaysia and these activities bring a lot of benefits to the students. By joining these activities, the students can learn about the time management and they can developing many useful skills. This project focuses on the selection of co-curriculum activities in secondary school using the optimization methods which are the Analytic Hierarchy Process (AHP) and Zero-One Goal Programming (ZOGP). A secondary school in Negeri Sembilan, Malaysia was chosen as a case study. A set of questionnaires were distributed randomly to calculate the weighted for each activity based on the 3 chosen criteria which are soft skills, interesting activities and performances. The weighted was calculated by using AHP and the results showed that the most important criteria is soft skills. Then, the ZOGP model will be analyzed by using LINGO Software version 15.0. There are two priorities to be considered. The first priority which is to minimize the budget for the activities is achieved since the total budget can be reduced by RM233.00. Therefore, the total budget to implement the selected activities is RM11,195.00. The second priority which is to select the co-curriculum activities is also achieved. The results showed that 9 out of 15 activities were selected. Thus, it can concluded that AHP and ZOGP approach can be used as the optimization methods for activities selection problem.
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.)
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.
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.
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).
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...
Mathematical programming methods for large-scale topology optimization problems
DEFF Research Database (Denmark)
Rojas Labanda, Susana
, and at the same time, reduce the number of function evaluations. Nonlinear optimization methods, such as sequential quadratic programming and interior point solvers, have almost not been embraced by the topology optimization community. Thus, this work is focused on the introduction of this kind of second......This thesis investigates new optimization methods for structural topology optimization problems. The aim of topology optimization is finding the optimal design of a structure. The physical problem is modelled as a nonlinear optimization problem. This powerful tool was initially developed...... for the classical minimum compliance problem. Two of the state-of-the-art optimization algorithms are investigated and implemented for this structural topology optimization problem. A Sequential Quadratic Programming (TopSQP) and an interior point method (TopIP) are developed exploiting the specific mathematical...
Institute of Scientific and Technical Information of China (English)
吴臻; 王向荣
2003-01-01
给出一类布朗运动和泊松过程混合驱动的正倒向随机微分方程解的存在唯一性结果,应用这一结果研究带有随机跳跃干扰的线性二次随机最优控制问题,并得到最优控制的显式形式,可以证明最优控制是唯一的.然后,引入和研究一类推广的黎卡提方程系统,讨论该方程系统的可解性并由该方程的解得到带有随机跳跃干扰的线性二次随机最优控制问题最优的线性反馈.%One kind of existence and uniqueness result of forward-backward stochastic differential equations with Brownian motion and Poisson process is given. The result is applied to get the explicit form of the optimal control for linear quadratic stochastic optimal control problem with random jumps. The optimal control can be proved to be unique. One kind of generalized Riccati equation system is introduced and its solvability is discussed. The linear feedback regulator for the optimal control problem with random jump is given by the solution of the generalized Riccati equation system
Enhanced Bee Colony Algorithm for Complex Optimization Problems
Directory of Open Access Journals (Sweden)
S.Suriya
2012-01-01
Full Text Available Optimization problems are considered to be one kind of NP hard problems. Usually heuristic approaches are found to provide solutions for NP hard problems. There are a plenty of heuristic algorithmsavailable to solve optimization problems namely: Ant Colony Optimization, Particle Swarm Optimization, Bee Colony Optimization, etc. The basic Bee Colony algorithm, a population based search algorithm, is analyzed to be a novel tool for complex optimization problems. The algorithm mimics the food foraging behavior of swarmsof honey bees. This paper deals with a modified fitness function of Bee Colony algorithm. The effect of problem dimensionality on the performance of the algorithms will be investigated. This enhanced Bee Colony Optimization will be evaluated based on the well-known benchmark problems. The testing functions like Rastrigin, Rosenbrock, Ackley, Griewank and Sphere are used to evaluavate the performance of the enhanced Bee Colony algorithm. The simulation will be developed on MATLAB.
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...
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.
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...
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.
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.
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.
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.
SolveDB: Integrating Optimization Problem Solvers Into SQL Databases
DEFF Research Database (Denmark)
Siksnys, Laurynas; Pedersen, Torben Bach
2016-01-01
Many real-world decision problems involve solving optimization problems based on data in an SQL database. Traditionally, solving such problems requires combining a DBMS with optimization software packages for each required class of problems (e.g. linear and constraint programming) -- leading...... to workflows that are cumbersome, complex, inefficient, and error-prone. In this paper, we present SolveDB - a DBMS for optimization applications. SolveDB supports solvers for different problem classes and offers seamless data management and optimization problem solving in a pure SQL-based setting. This allows...... for much simpler and more effective solutions of database-based optimization problems. SolveDB is based on the 3-level ANSI/SPARC architecture and allows formulating, solving, and analysing solutions of optimization problems using a single so-called solve query. SolveDB provides (1) an SQL-based syntax...
Intrinsic Optimal Control for Mechanical Systems on Lie Group
Directory of Open Access Journals (Sweden)
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.
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.
Convergence rates of symplectic pontryagin approximations in optimal control theory
Sandberg, Mattias; Szepessy, Anders
2006-01-01
Many inverse problems for differential equations can be formulated as optimal control problems. It is well known that inverse problems often need to be regularized to obtain good approximations. This work presents a systematic method to regularize and to establish error estimates for approximations to some control problems in high dimension, based on symplectic approximation of the Hamiltonian system for the control problem. In particular the work derives error estimates and constructs regul...
Quantum speed problem: Theoretical hints for control
Lisboa, Alexandre Coutinho; Piqueira, José Roberto Castilho
2016-06-01
The transition time between states plays an important role in designing quantum devices as they are very sensitive to environmental influences. Decoherence phenomenon is responsible for possible destructions of the entanglement that is a fundamental requirement to implement quantum information processing systems. If the time between states is minimized, the decoherence effects can be reduced, thus, it is advantageous to the designer to develop expressions for time performance measures. Quantum speed limit (QSL) problem has been studied from the theoretical point of view, providing general results. Considering the implementation of quantum control systems, as the decoherence phenomenon is unavoidable, it is important to apply these general results to particular cases, developing expressions and performance measures, to assist control engineering designers. Here, a minimum time performance measure is defined for quantum control problems, for time-independent or time-dependent Hamiltonians, and applied to some practical examples, providing hints that may be useful for researchers pursuing optimization strategies for quantum control systems.
Group Search Optimizer for the Mobile Location Management Problem
Directory of Open Access Journals (Sweden)
Dan Wang
2014-01-01
Full Text Available We propose a diversity-guided group search optimizer-based approach for solving the location management problem in mobile computing. The location management problem, which is to find the optimal network configurations of management under the mobile computing environment, is considered here as an optimization problem. The proposed diversity-guided group search optimizer algorithm is realized with the aid of diversity operator, which helps alleviate the premature convergence problem of group search optimizer algorithm, a successful optimization algorithm inspired by the animal behavior. To address the location management problem, diversity-guided group search optimizer algorithm is exploited to optimize network configurations of management by minimizing the sum of location update cost and location paging cost. Experimental results illustrate the effectiveness of the proposed approach.
Group Search Optimizer for the Mobile Location Management Problem
Wang, Dan; Xiong, Congcong; Huang, Wei
2014-01-01
We propose a diversity-guided group search optimizer-based approach for solving the location management problem in mobile computing. The location management problem, which is to find the optimal network configurations of management under the mobile computing environment, is considered here as an optimization problem. The proposed diversity-guided group search optimizer algorithm is realized with the aid of diversity operator, which helps alleviate the premature convergence problem of group search optimizer algorithm, a successful optimization algorithm inspired by the animal behavior. To address the location management problem, diversity-guided group search optimizer algorithm is exploited to optimize network configurations of management by minimizing the sum of location update cost and location paging cost. Experimental results illustrate the effectiveness of the proposed approach. PMID:25180199
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...
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 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...
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...
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.
Optimization, Randomized Approximability, and Boolean Constraint Satisfaction Problems
Yamakami, Tomoyuki
2011-01-01
We give a unified treatment to optimization problems that can be expressed in the form of nonnegative-real-weighted Boolean constraint satisfaction problems. Creignou, Khanna, Sudan, Trevisan, and Williamson studied the complexity of approximating their optimal solutions whose optimality is measured by the sums of outcomes of constraints. To explore a wider range of optimization constraint satisfaction problems, following an early work of Marchetti-Spaccamela and Romano, we study the case where the optimality is measured by products of constraints' outcomes. We completely classify those problems into three categories: PO problems, NPO-hard problems, and intermediate problems that lie between the former two categories. To prove this trichotomy theorem, we analyze characteristics of nonnegative-real-weighted constraints using a variant of the notion of T-constructibility developed earlier for complex-weighted counting constraint satisfaction problems.
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
Directory of Open Access Journals (Sweden)
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 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.
Algorithmic Aspects of Several Data Transfer Service Optimization Problems
Andreica, Mugurel Ionut; Ionescu, Florin; Andreica, Cristina Teodora
2009-01-01
Optimized data transfer services are highly demanded nowadays, due to the large amounts of data which are frequently being produced and accessed. In this paper we consider several data transfer service optimization problems (optimal server location in path networks, optimal packet sequencing and minimum makespan packet scheduling), for which we provide novel algorithmic solutions.
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...
Particle Swarm Optimization with Genetic Operators for Vehicle Routing Problem
Directory of Open Access Journals (Sweden)
P. V. PURANIK
2012-07-01
Full Text Available Vehicle Routing Problem (VRP is to find shortest route thereby minimizing total cost. VRP is a NP-hard and Combinatorial optimization problem. Such problems increase exponentially with the problem size. Various derivative based optimization techniques are employed for optimization. Derivative based optimization techniques are difficult to evaluate. Therefore parallel search algorithm emerged to solve VRP. In this work, a particle swarm optimization (PSO algorithm and Genetic algorithm (GA with crossover and mutation operator are applied to two typical functions to deal with the problem of VRP efficiently using MATLAB software. Before solving VRP, optimization of functions using PSO and GA are checked. In this paper capacitate VRP with time window (CVRPTW is proposed. The computational result shows generation of input for VRP, optimization of Rastrigin function, Rosenbrock function using PSO and GA.
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...
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.
Topology optimization problems with design-dependent sets of constraints
DEFF Research Database (Denmark)
Schou, Marie-Louise Højlund
Topology optimization is a design tool which is used in numerous fields. It can be used whenever the design is driven by weight and strength considerations. The basic concept of topology optimization is the interpretation of partial differential equation coefficients as effective material...... structural topology optimization problems. For such problems a stress constraint for an element should only be present in the optimization problem when the structural design variable corresponding to this element has a value greater than zero. We model the stress constrained topology optimization problem...... using both discrete and continuous design variables. Using discrete design variables is the natural modeling frame. However, we cannot solve real-size problems with the technological limits of today. Using continuous design variables makes it possible to also study topology optimization problems...
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.
Replica analysis for the duality of the portfolio optimization problem
Shinzato, Takashi
2016-11-01
In the present paper, the primal-dual problem consisting of the investment risk minimization problem and the expected return maximization problem in the mean-variance model is discussed using replica analysis. As a natural extension of the investment risk minimization problem under only a budget constraint that we analyzed in a previous study, we herein consider a primal-dual problem in which the investment risk minimization problem with budget and expected return constraints is regarded as the primal problem, and the expected return maximization problem with budget and investment risk constraints is regarded as the dual problem. With respect to these optimal problems, we analyze a quenched disordered system involving both of these optimization problems using the approach developed in statistical mechanical informatics and confirm that both optimal portfolios can possess the primal-dual structure. Finally, the results of numerical simulations are shown to validate the effectiveness of the proposed method.
some notes on discount factor restrictions for dynamic optimization problems
Gerhard Sorger
2008-01-01
We consider dynamic optimization problems on one-dimensional state spaces. Un- der standard smoothness and convexity assumptions, the optimal solutions are characterized by an optimal policy function h mapping the state space into itself. There exists an extensive literature on the relation between the size of the discount factor of the dynamic optimization problem on the one hand and the properties of the dynamical system xt+1 = h(xt) on the other hand. The purpose of this paper is to survey...
Overview: Applications of numerical optimization methods to helicopter design problems
Miura, H.
1984-01-01
There are a number of helicopter design problems that are well suited to applications of numerical design optimization techniques. Adequate implementation of this technology will provide high pay-offs. There are a number of numerical optimization programs available, and there are many excellent response/performance analysis programs developed or being developed. But integration of these programs in a form that is usable in the design phase should be recognized as important. It is also necessary to attract the attention of engineers engaged in the development of analysis capabilities and to make them aware that analysis capabilities are much more powerful if integrated into design oriented codes. Frequently, the shortcoming of analysis capabilities are revealed by coupling them with an optimization code. Most of the published work has addressed problems in preliminary system design, rotor system/blade design or airframe design. Very few published results were found in acoustics, aerodynamics and control system design. Currently major efforts are focused on vibration reduction, and aerodynamics/acoustics applications appear to be growing fast. The development of a computer program system to integrate the multiple disciplines required in helicopter design with numerical optimization technique is needed. Activities in Britain, Germany and Poland are identified, but no published results from France, Italy, the USSR or Japan were found.
LDRD Final Report: Global Optimization for Engineering Science Problems
Energy Technology Data Exchange (ETDEWEB)
HART,WILLIAM E.
1999-12-01
For a wide variety of scientific and engineering problems the desired solution corresponds to an optimal set of objective function parameters, where the objective function measures a solution's quality. The main goal of the LDRD ''Global Optimization for Engineering Science Problems'' was the development of new robust and efficient optimization algorithms that can be used to find globally optimal solutions to complex optimization problems. This SAND report summarizes the technical accomplishments of this LDRD, discusses lessons learned and describes open research issues.
An Effective Hybrid Optimization Algorithm for Capacitated Vehicle Routing Problem
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
Capacitated vehicle routing problem (CVRP) is an important combinatorial optimization problem. However, it is quite difficult to achieve an optimal solution with the traditional optimization methods owing to the high computational complexity. A hybrid algorithm was developed to solve the problem, in which an artificial immune clonal algorithm (AICA) makes use of the global search ability to search the optimal results and simulated annealing (SA) algorithm employs certain probability to avoid becoming trapped in a local optimum. The results obtained from the computational study show that the proposed algorithm is a feasible and effective method for capacitated vehicle routing problem.
Directory of Open Access Journals (Sweden)
Mykola Bokalo
2017-03-01
Full Text Available We consider an optimal control problem for systems described by a Fourier problem for parabolic equations. We prove the existence of solutions, and obtain necessary conditions of the optimal control in the case of final observation when the control functions occur in the coefficients.
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.
Particle swarm optimization - Genetic algorithm (PSOGA) on linear transportation problem
Rahmalia, Dinita
2017-08-01
Linear Transportation Problem (LTP) is the case of constrained optimization where we want to minimize cost subject to the balance of the number of supply and the number of demand. The exact method such as northwest corner, vogel, russel, minimal cost have been applied at approaching optimal solution. In this paper, we use heurisitic like Particle Swarm Optimization (PSO) for solving linear transportation problem at any size of decision variable. In addition, we combine mutation operator of Genetic Algorithm (GA) at PSO to improve optimal solution. This method is called Particle Swarm Optimization - Genetic Algorithm (PSOGA). The simulations show that PSOGA can improve optimal solution resulted by PSO.
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....
Institute of Scientific and Technical Information of China (English)
Xu Zhang; En-min Feng
2004-01-01
This paper studies the two-dimensional layout optimization problem.An optimization model with performance constraints is presented.The layout problem is partitioned intofinite subproblems in terms of graph theory,in such a way of that each subproblem overcomes its on-o inature optimal variable.A minimax problem is constructed that is locally equivalent to each subproblem.By using this minimax problem,we present the optimality function for every subproblem and prove that the first order necessary optimality condition is satisfied at a point if and only if this point is a zero of optimality function.
An optimization method for the problems of thermal cloaking of material bodies
Alekseev, G. V.; Levin, V. A.
2016-11-01
Inverse heat-transfer problems related to constructing special thermal devices such as cloaking shells, thermal-illusion or thermal-camouflage devices, and heat-flux concentrators are studied. The heatdiffusion equation with a variable heat-conductivity coefficient is used as the initial heat-transfer model. An optimization method is used to reduce the above inverse problems to the respective control problem. The solvability of the above control problem is proved, an optimality system that describes necessary extremum conditions is derived, and a numerical algorithm for solving the control problem is proposed.
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...
ISOGEOMETRIC SHAPE OPTIMIZATION FOR ELECTROMAGNETIC SCATTERING PROBLEMS
DEFF Research Database (Denmark)
Nguyen, D. M.; Evgrafov, Anton; Gravesen, Jens
2012-01-01
We consider the benchmark problem of magnetic energy density enhancement in a small spatial region by varying the shape of two symmetric conducting scatterers. We view this problem as a prototype for a wide variety of geometric design problems in electromagnetic applications. Our approach...
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 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.
APPLYING PARTICLE SWARM OPTIMIZATION TO JOB-SHOP SCHEDULING PROBLEM
Institute of Scientific and Technical Information of China (English)
Xia Weijun; Wu Zhiming; Zhang Wei; Yang Genke
2004-01-01
A new heuristic algorithm is proposed for the problem of finding the minimum makespan in the job-shop scheduling problem. The new algorithm is based on the principles of particle swarm optimization (PSO). PSO employs a collaborative population-based search, which is inspired by the social behavior of bird flocking. It combines local search (by self experience) and global search (by neighboring experience), possessing high search efficiency. Simulated annealing (SA) employs certain probability to avoid becoming trapped in a local optimum and the search process can be controlled by the cooling schedule. By reasonably combining these two different search algorithms, a general, fast and easily implemented hybrid optimization algorithm, named HPSO, is developed. The effectiveness and efficiency of the proposed PSO-based algorithm are demonstrated by applying it to some benchmark job-shop scheduling problems and comparing results with other algorithms in literature. Comparing results indicate that PSO-based algorithm is a viable and effective approach for the job-shop scheduling problem.
Advances in bio-inspired computing for combinatorial optimization problems
Pintea, Camelia-Mihaela
2013-01-01
Advances in Bio-inspired Combinatorial Optimization Problems' illustrates several recent bio-inspired efficient algorithms for solving NP-hard problems.Theoretical bio-inspired concepts and models, in particular for agents, ants and virtual robots are described. Large-scale optimization problems, for example: the Generalized Traveling Salesman Problem and the Railway Traveling Salesman Problem, are solved and their results are discussed.Some of the main concepts and models described in this book are: inner rule to guide ant search - a recent model in ant optimization, heterogeneous sensitive a
Analysis and optimization of delays in networked control systems
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
The minimization problem of time delays in networked control system (NCS) is concered, which is a hot area of such research field. First, some analysis and comments on time-delayed NCS model listed in previous work are given.Then, time delay minimization problem based on average behavior of network queuing delay is presented. Under fixed routing scheme and certain optimization performance indexes, the delay minimization problem is translated into convex optimization problem. And the solution of the delay minimization problems is attained through optimized allocation of flow rates among network links.
Implementation of Travelling Salesman Problem Using ant Colony Optimization
Directory of Open Access Journals (Sweden)
Gaurav Singh,
2014-04-01
Full Text Available Within the Artificial Intelligence community, there is great need for fast and accurate traversal algorithms, specifically those that find a path from a start to goal with minimum cost. Cost can be distance, time, money, energy, etc. Travelling salesman problem (TSP is a combinatorial optimization problem. TSP is the most intensively studied problem in the area of optimization. Ant colony optimization (ACO is a population-based metaheuristic that can be used to find approximate solutions to difficult optimization problems. There have been many efforts in the past to provide time efficient solutions for the problem, both exact and approximate. This paper demonstrates the implementation of TSP using ant colony optimization(ACO.The solution to this problem enjoys wide applicability in a variety of practical fields.TSP in its purest form has several applications such as planning, logistics, and manufacture of microchips, military and traffic.
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.
Solving semi-infinite optimization problems with interior point techniques
Stein, Oliver; Still, Georg
2003-01-01
We introduce a new numerical solution method for semi-infinite optimization problems with convex lower level problems. The method is based on a reformulation of the semi-infinite problem as a Stackelberg game and the use of regularized nonlinear complementarity problem functions. This approach leads
Solving semi-infinite optimization problems with interior point techniques
Stein, Oliver; Still, Georg J.
2003-01-01
We introduce a new numerical solution method for semi-infinite optimization problems with convex lower level problems. The method is based on a reformulation of the semi-infinite problem as a Stackelberg game and the use of regularized nonlinear complementarity problem functions. This approach leads
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.
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.
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.
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.
The study of cuckoo optimization algorithm for production planning problem
Akbarzadeh, Afsane; Shadkam, Elham
2015-01-01
Constrained Nonlinear programming problems are hard problems, and one of the most widely used and common problems for production planning problem to optimize. In this study, one of the mathematical models of production planning is survey and the problem solved by cuckoo algorithm. Cuckoo Algorithm is efficient method to solve continues non linear problem. Moreover, mentioned models of production planning solved with Genetic algorithm and Lingo software and the results will compared. The Cucko...
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...
Degenerate optimization problems and competitiveness of NPPs
Directory of Open Access Journals (Sweden)
A.V. Klimenko
2016-12-01
Since, as it was demonstrated by the performed systems optimization calculations of power generation in Russia, the examined options of NPPs with fast reactors (SVBR-100, BN-1200 (three-circuit, BREST-1200 appeared to be included not into all optimal plans, there is a place for certain doubts that the chosen parameters of the NPPs and the associated nuclear fuel cycles (NFCs are not competitive although strenuous multi-parameter research in this direction is ongoing during already several decades.
Metaheuristic Optimization: Algorithm Analysis and Open Problems
2012-01-01
Metaheuristic algorithms are becoming an important part of modern optimization. A wide range of metaheuristic algorithms have emerged over the last two decades, and many metaheuristics such as particle swarm optimization are becoming increasingly popular. Despite their popularity, mathematical analysis of these algorithms lacks behind. Convergence analysis still remains unsolved for the majority of metaheuristic algorithms, while efficiency analysis is equally challenging. In this paper, we i...
An optimization approach for the satisfiability problem
Directory of Open Access Journals (Sweden)
S. Noureddine
2015-01-01
Full Text Available We describe a new approach for solving the satisfiability problem by geometric programming. We focus on the theoretical background and give details of the algorithmic procedure. The algorithm is provably efficient as geometric programming is in essence a polynomial problem. The correctness of the algorithm is discussed. The version of the satisfiability problem we study is exact satisfiability with only positive variables, which is known to be NP-complete.
Frequency response as a surrogate eigenvalue problem in topology optimization
DEFF Research Database (Denmark)
Andreassen, Erik; Ferrari, Federico; Sigmund, Ole
2017-01-01
This article discusses the use of frequency response surrogates for eigenvalue optimization problems in topology optimization that may be used to avoid solving the eigenvalue problem. The motivation is to avoid complications that arise from multiple eigenvalues and the computational complexity as...
Ant Colony Optimization and the Minimum Cut Problem
DEFF Research Database (Denmark)
Kötzing, Timo; Lehre, Per Kristian; Neumann, Frank
2010-01-01
Ant Colony Optimization (ACO) is a powerful metaheuristic for solving combinatorial optimization problems. With this paper we contribute to the theoretical understanding of this kind of algorithm by investigating the classical minimum cut problem. An ACO algorithm similar to the one that was prov...
Optimization problems for fast AAM fitting in-the-wild
Tzimiropoulos, Georgios; Pantic, Maja
2013-01-01
We describe a very simple framework for deriving the most-well known optimization problems in Active Appearance Models (AAMs), and most importantly for providing efficient solutions. Our formulation results in two optimization problems for fast and exact AAM fitting, and one new algorithm which has
Applications of Fitzpatrick functions for solving optimization problems
Nashed, Z.; Raykov, I.
2012-10-01
This paper presents applications of Fitzparick functions to optimization problems. The main purpose of the present work is to introduce applications of the Fitzpatrick functions, involving their specific properties as the maximal monotonicity, or the proper, convex and lower semi-continuity, for solving optimization problems.
Applications of Fitzpatrick functions for solving optimization problems II
Nashed, Z.; Raykov, I.
2015-10-01
This paper is a continuation of the paper [8] and presents more applications of Fitzpatrick functions for solving optimization problems. The main purpose of the present work is to introduce some new properties of Fitzpatrick functions useful for solving optimization problems, using also their already presented specific properties, as the maximal monotonicity, proper, convex and lower semi-continuity.
Institute of Scientific and Technical Information of China (English)
徐少兵; 李升波; 成波
2014-01-01
伪谱法通过全局插值多项式参数化状态和控制变量，将最优控制问题(OCP)转化为非线性规划问题(NLP)进行求解，是一类具有更高求解效率的直接法。总结Legendre伪谱法转化Bolza型最优控制问题的基本框架，推导OCP伴随变量与NLP问题KKT乘子的映射关系，建立基于拟牛顿法的LGL配点数值计算方法，并针对非光滑系统，进一步研究分段伪谱逼近策略。基于上述理论开发通用OCP求解器，并对3个典型最优控制问题进行求解，结果表明了所提出方法和求解器的有效性。%The pseudo-spectral method approximates control and state variables through global interpolation polynomials, then discrete the optimal control problem(OCP) to a nonlinear programming problem(NLP) effectively. It’s a kind of direct method with higher solving efficiency. The basic framework of the Legendre pseudo-spectral method converting the Bolza OCP into NLP is summarized, and the mapping between the costates of OCP and the KKT multiplier to NLP is derived. Furthermore, a numerical method is elaborated based on the quasi-Newton method in order to calculate the LGL collocation accurately. The multiphase strategy is also being introduced for non-smooth systems. Finally, a universal optimal control solver POPS(pseudo-spectral optimal control problem solver) is developed based on the Legendre pseudo-spectral method in Matlab. Three typical optimal control problems are solved by using the solver POPS, and the results show the effectiveness of the proposed method and solver POPS.
Artificial bee colony algorithm for constrained possibilistic portfolio optimization problem
Chen, Wei
2015-07-01
In this paper, we discuss the portfolio optimization problem with real-world constraints under the assumption that the returns of risky assets are fuzzy numbers. A new possibilistic mean-semiabsolute deviation model is proposed, in which transaction costs, cardinality and quantity constraints are considered. Due to such constraints the proposed model becomes a mixed integer nonlinear programming problem and traditional optimization methods fail to find the optimal solution efficiently. Thus, a modified artificial bee colony (MABC) algorithm is developed to solve the corresponding optimization problem. Finally, a numerical example is given to illustrate the effectiveness of the proposed model and the corresponding algorithm.
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
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.
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.
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....
Directory of Open Access Journals (Sweden)
K. Lenin
2013-03-01
Full Text Available Reactive Power Optimization is a complex combinatorial optimization problem involving non-linear function having multiple local minima, non-linear and discontinuous constrains. This paper presents Attractive and repulsive Particle Swarm Optimization (ARPSO and Random Virus Algorithm (RVA in trying to overcome the Problem of premature convergence. RVA and ARPSO is applied to Reactive Power Optimization problem and is evaluated on standard IEEE 30Bus System. The results show that RVA prevents premature convergence to high degree but still keeps a rapid convergence. It gives best solution when compared to Attractive and repulsive Particle Swarm Optimization (ARPSO and Particle Swarm Optimization (PSO.
Optimal Component Lumping: problem formulation and solution techniques
DEFF Research Database (Denmark)
Lin, Bao; Leibovici, Claude F.; Jørgensen, Sten Bay
2008-01-01
to determine the lumping scheme. Given an objective function defined with a linear weighting rule, an optimal lumping problem is formulated as a mixed integer nonlinear programming (MINLP) problem both in discrete and in continuous settings. A reformulation of the original problem is also presented, which...... significantly reduces the number of independent variables. The application to a system with 144 components demonstrates that the optimal lumping problem can be efficiently solved with a stochastic optimization method, Tabu Search (TS) algorithm. The case study also reveals that the discrete formulation...
Optimal control theory applications to management science and economics
Sethi, Suresh P
2006-01-01
Optimal control methods are used to determine the best ways to control a dynamic system. This book applies theoretical work to business management problems developed from the authors' research and classroom instruction. The thoroughly revised new edition has been refined with careful attention to the text and graphic material presentation. Chapters cover a range of topics including finance, production and inventory problems, marketing problems, machine maintenance and replacement, problems of optimal consumption of natural resources, and applications of control theory to economics. The book in
Topology optimization of coated structures and material interface problems
DEFF Research Database (Denmark)
Clausen, Anders; Aage, Niels; Sigmund, Ole
2015-01-01
This paper presents a novel method for including coated structures and prescribed material interface properties into the minimum compliance topology optimization problem. Several elements of the method are applicable to a broader range of interface problems. The approach extends the standard SIMP...... method by including the normalized norm of the spatial gradient of the design field into the material interpolation function, enforcing coating material at interfaces by attributing particular properties. The length scales of the base structure and the coating are separated by introducing a two......-step filtering/projection approach. The modeled coating thickness is derived analytically, and the coating is shown to be accurately controlled and applied in a highly uniform manner over the structure. An alternative interpretation of the model is to perform single-material design for additive manufacturing...
Topology optimization of coated structures and material interface problems
DEFF Research Database (Denmark)
Clausen, Anders; Aage, Niels; Sigmund, Ole
2015-01-01
This paper presents a novel method for including coated structures and prescribed material interface properties into the minimum compliance topology optimization problem. Several elements of the method are applicable to a broader range of interface problems. The approach extends the standard SIMP...... method by including the normalized norm of the spatial gradient of the design field into the material interpolation function, enforcing coating material at interfaces by attributing particular properties. The length scales of the base structure and the coating are separated by introducing a two......-step filtering/projection approach. The modeled coating thickness is derived analytically, and the coating is shown to be accurately controlled and applied in a highly uniform manner over the structure. An alternative interpretation of the model is to perform single-material design for additive manufacturing...
OPTIMIZATION OF CAPACITATED VEHICLE ROUTING PROBLEM USING PSO
Directory of Open Access Journals (Sweden)
S.R.VENKATESAN
2011-10-01
Full Text Available This paper presents solution techniques for Capacitated Vehicle Routing Problem (CVRP using metaheuristics. Capacitated Vehicle Routing Problem is divided into set of customers called cluster, and find optimum travel distance of vehicle route. The CVRP is a combinatorial optimization problem; particle swarm optimization(PSO technique is adapted in this paper to solve this problem. The main problem is divided into subprograms/clusters and each subprogram is treated as travelling salesman problem and solved by usingparticle swarm optimization techniques (PSO. This paper presents a sweep, Clark and wright algorithm to form the clusters. This model is then solved by using a particle swarm optimization (PSO method to find optimum travel distance of vehicle route. Our analysis suggests that the proposed model enables users to establish route to serve all given customers with minimum distance of vehicles and maximum capacity.
Unconstrained Optimization Reformulations of Equilibrium Problems
Institute of Scientific and Technical Information of China (English)
Li Ping ZHANG; Ji Ye HAN
2009-01-01
We generalize the D-gap function developed in the literature for variational inequalities to a general equilibrium problem (EP). Through the D-gap function,the equilibrium problem is cast as an unconstrained minimization problem. We give conditions under which any stationary point of the D-gap function is a solution of EP and conditions under which it provides a global error bound for EP. Finally,these results are applied to box-constrained EP and then weaker conditions are established to obtain the desired results for box-constrained EP.
Improved Ant Colony Optimization for Seafood Product Delivery Routing Problem
Directory of Open Access Journals (Sweden)
Baozhen Yao
2014-02-01
Full Text Available This paper deals with a real-life vehicle delivery routing problem, which is a seafood product delivery routing problem. Considering the features of the seafood product delivery routing problem, this paper formulated this problem as a multi-depot open vehicle routing problem. Since the multi-depot open vehicle routing problem is a very complex problem, a method is used to reduce the complexity of the problem by changing the multi-depot open vehicle routing problem into an open vehicle routing problem with a dummy central depot in this paper. Then, ant colony optimization is used to solve the problem. To improve the performance of the algorithm, crossover operation and some adaptive strategies are used. Finally, the computational results for the benchmark problems of the multi-depot vehicle routing problem indicate that the proposed ant colony optimization is an effective method to solve the multi-depot vehicle routing problem. Furthermore, the computation results of the seafood product delivery problem from Dalian, China also suggest that the proposed ant colony optimization is feasible to solve the seafood product delivery routing problem.
A General Theory of Markovian Time Inconsistent Stochastic Control Problems
DEFF Research Database (Denmark)
Björk, Tomas; Murgochi, Agatha
We develop a theory for stochastic control problems which, in various ways, are time inconsistent in the sense that they do not admit a Bellman optimality principle. We attach these problems by viewing them within a game theoretic framework, and we look for Nash subgame perfect equilibrium points...... examples of time inconsistency in the literature are easily seen to be special cases of the present theory. We also prove that for every time inconsistent problem, there exists an associated time consistent problem such that the optimal control and the optimal value function for the consistent problem....... For a general controlled Markov process and a fairly general objective functional we derive an extension of the standard Hamilton-Jacobi-Bellman equation, in the form of a system of on-linear equations, for the determination for the equilibrium strategy as well as the equilibrium value function. All known...
Moments of random sums and Robbins' problem of optimal stopping
Gnedin, Alexander
2011-01-01
Robbins' problem of optimal stopping asks one to minimise the expected {\\it rank} of observation chosen by some nonanticipating stopping rule. We settle a conjecture regarding the {\\it value} of the stopped variable under the rule optimal in the sense of the rank, by embedding the problem in a much more general context of selection problems with the nonanticipation constraint lifted, and with the payoff growing like a power function of the rank.
Remarks on a benchmark nonlinear constrained optimization problem
Institute of Scientific and Technical Information of China (English)
Luo Yazhong; Lei Yongjun; Tang Guojin
2006-01-01
Remarks on a benchmark nonlinear constrained optimization problem are made. Due to a citation error, two absolutely different results for the benchmark problem are obtained by independent researchers. Parallel simulated annealing using simplex method is employed in our study to solve the benchmark nonlinear constrained problem with mistaken formula and the best-known solution is obtained, whose optimality is testified by the Kuhn-Tucker conditions.
Optimization Problems in Supply Chain Management
D. Romero Morales (Dolores)
2000-01-01
textabstractMaria Dolores Romero Morales was born on Augustus 5th, 1971, in Sevilla (Spain). She studied Mathematics at University of Sevilla from 1989 to 1994 and specialized in Statistics and Operations Research. She wrote her Master's thesis on Global Optimization in Location Theory under the sup
Problem optimalnih kartografskih projekcija : Problem of the optimal cartographic projections
Directory of Open Access Journals (Sweden)
Krešimir Frankić
2014-12-01
Full Text Available Kartografske projekcije primjenjuju se za grafičko prikazivanje teritorija u sitnom mjerilu. Pravilnim izborom projekcije smanjuju se deformacije prikazanog teritorija, koji je omeđen graničnom linijom. U većini slučajeva ta granična linija nije neka matematički definirana krivulja, koja se najlakše prikazuje u obliku zatvorenog poligona. Optimalne kartografske projekcije, slijedeći neki definirani kriterij, trebale bi utvrditi konstante projekcije s najmanjim mogućim deformacijama. Airy-Kavrajski kriterij vodi direktno do optimizacije Euklidske norme, a to znači do metode najmanjih kvadrata. Brzi moderni kompjutori omogućuju jednostavnu optimizaciju bilo koje analitički definirane projekcije za teritorije čija granica se aproksimira konačnim nizom individualnih točaka. : Cartographic projections are basis for the graphical representation of various territories in small scale mapping. Proper selection of projection reduces the deformation of the presented territory, which is bounded by a boundary line. In most cases, this border line is not a mathematically defined curve, which is most easily displayed in the form of a closed polygon. The optimal cartographic projections based on a selected criterion of quality are those whose constants lead to the smallest value of the criterion. In the presented work it is recommended to use Airy-Kavrajski criterion whose minimization is actually minimization of the second Euclidean norm. The solution of optimal projections of various classes is reduced to the method of least squares. Fast modern computers enable the optimization of an arbitrary territory by evaluating the selected criterion in a finite number of points.
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.
Improved extremal optimization for the asymmetric traveling salesman problem
Chen, Yu-Wang; Zhu, Yao-Jia; Yang, Gen-Ke; Lu, Yong-Zai
2011-11-01
This paper presents an improved extremal optimization (IEO) algorithm for solving the asymmetric traveling salesman problem (ATSP). At each update step, the IEO algorithm proceeds through two main steps: extremal dynamics and cooperative optimization. As an improvement of extremal optimization (EO), the IEO provides a general combinatorial optimization framework by emphasizing the step of cooperative optimization. In the paper, an effective cooperative optimization strategy with combination of greedy search and random walk is designed in terms of the microscopic characteristics of the ATSP solutions. Simulation results on a set of benchmark ATSP instances show that the proposed IEO algorithm provides satisfactory performance on computational effectiveness and efficiency.
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
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
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.
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.
Higher-order techniques for some problems of nonlinear control
Directory of Open Access Journals (Sweden)
Sarychev Andrey V.
2002-01-01
Full Text Available A natural first step when dealing with a nonlinear problem is an application of some version of linearization principle. This includes the well known linearization principles for controllability, observability and stability and also first-order optimality conditions such as Lagrange multipliers rule or Pontryagin's maximum principle. In many interesting and important problems of nonlinear control the linearization principle fails to provide a solution. In the present paper we provide some examples of how higher-order methods of differential geometric control theory can be used for the study nonlinear control systems in such cases. The presentation includes: nonlinear systems with impulsive and distribution-like inputs; second-order optimality conditions for bang–bang extremals of optimal control problems; methods of high-order averaging for studying stability and stabilization of time-variant control systems.
Multiobjective optimization design of a fractional order PID controller for a gun control system.
Gao, Qiang; Chen, Jilin; Wang, Li; Xu, Shiqing; Hou, Yuanlong
2013-01-01
Motion control of gun barrels is an ongoing topic for the development of gun control equipments possessing excellent performances. In this paper, a typical fractional order PID control strategy is employed for the gun control system. To obtain optimal parameters of the controller, a multiobjective optimization scheme is developed from the loop-shaping perspective. To solve the specified nonlinear optimization problem, a novel Pareto optimal solution based multiobjective differential evolution algorithm is proposed. To enhance the convergent rate of the optimization process, an opposition based learning method is embedded in the chaotic population initialization process. To enhance the robustness of the algorithm for different problems, an adapting scheme of the mutation operation is further employed. With assistance of the evolutionary algorithm, the optimal solution for the specified problem is selected. The numerical simulation results show that the control system can rapidly follow the demand signal with high accuracy and high robustness, demonstrating the efficiency of the proposed controller parameter tuning method.
Near Optimal Decentralized H-infinity Control: Bounded vs. Unbounded Controller Order
DEFF Research Database (Denmark)
Stoustrup, Jakob; Niemann, H.H.
1997-01-01
It is shown that for a class of decentralized control problems there does not exist a sequence of controllers of bounded order which obtains near optimal control. Neither does there exist an infinite dimensional optimal controller. Using the insight of the line of proof of these results, a heuris...
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. ...
Topology optimization problems with design-dependent sets of constraints
DEFF Research Database (Denmark)
Schou, Marie-Louise Højlund
Topology optimization is a design tool which is used in numerous fields. It can be used whenever the design is driven by weight and strength considerations. The basic concept of topology optimization is the interpretation of partial differential equation coefficients as effective material...... properties and designing through changing these coefficients. For example, consider a continuous structure. Then the basic concept is to represent this structure by small pieces of material that are coinciding with the elements of a finite element model of the structure. This thesis treats stress constrained...... structural topology optimization problems. For such problems a stress constraint for an element should only be present in the optimization problem when the structural design variable corresponding to this element has a value greater than zero. We model the stress constrained topology optimization problem...
The Uniqueness of Optimal Solution for Linear Programming Problem
Institute of Scientific and Technical Information of China (English)
QuanlingWei; HongYan; JunWang
2004-01-01
This paper investigates an old problem in operations research, the uniqueness of the optimal solution to a linear programming problem. We discuss the problem on a general polyhedron, give some equivalent conditions for uniqueness testing. In addition, we discuss the implementation issues for linear programming based decision making procedures,which motivated this research.
Portfolio optimization and the random magnet problem
Rosenow, B.; Plerou, V.; Gopikrishnan, P.; Stanley, H. E.
2002-08-01
Diversification of an investment into independently fluctuating assets reduces its risk. In reality, movements of assets are mutually correlated and therefore knowledge of cross-correlations among asset price movements are of great importance. Our results support the possibility that the problem of finding an investment in stocks which exposes invested funds to a minimum level of risk is analogous to the problem of finding the magnetization of a random magnet. The interactions for this "random magnet problem" are given by the cross-correlation matrix C of stock returns. We find that random matrix theory allows us to make an estimate for C which outperforms the standard estimate in terms of constructing an investment which carries a minimum level of risk.
A Decomposition Algorithm for Optimal Control of Distributed Energy System
DEFF Research Database (Denmark)
Sokoler, Leo Emil; Edlund, Kristian; Standardi, Laura
2013-01-01
In economic model predictive control of distributed energy systems, the constrained optimal control problem can be expressed as a linear program with a block-angular structure. In this paper, we present an efficient Dantzig-Wolfe decomposition algorithm specifically tailored to problems...
Newtonian Nonlinear Dynamics for Complex Linear and Optimization Problems
Vázquez, Luis
2013-01-01
Newtonian Nonlinear Dynamics for Complex Linear and Optimization Problems explores how Newton's equation for the motion of one particle in classical mechanics combined with finite difference methods allows creation of a mechanical scenario to solve basic problems in linear algebra and programming. The authors present a novel, unified numerical and mechanical approach and an important analysis method of optimization. This book also: Presents mechanical method for determining matrix singularity or non-independence of dimension and complexity Illustrates novel mathematical applications of classical Newton’s law Offers a new approach and insight to basic, standard problems Includes numerous examples and applications Newtonian Nonlinear Dynamics for Complex Linear and Optimization Problems is an ideal book for undergraduate and graduate students as well as researchers interested in linear problems and optimization, and nonlinear dynamics.
Constraint Optimization for Highly Constrained Logistic Problems
DEFF Research Database (Denmark)
Mochnacs, Maria Kinga; Tanaka, Meang Akira; Nyborg, Anders
This report investigates whether propagators combined with branch and bound algorithm are suitable for solving the storage area stowage problem within reasonable time. The approach has not been attempted before and experiments show that the implementation was not capable of solving the storage ar...
Present-day Problems and Methods of Optimization in Mechatronics
Directory of Open Access Journals (Sweden)
Tarnowski Wojciech
2017-06-01
Full Text Available It is justified that design is an inverse problem, and the optimization is a paradigm. Classes of design problems are proposed and typical obstacles are recognized. Peculiarities of the mechatronic designing are specified as a proof of a particle importance of optimization in the mechatronic design. Two main obstacles of optimization are discussed: a complexity of mathematical models and an uncertainty of the value system, in concrete case. Then a set of non-standard approaches and methods are presented and discussed, illustrated by examples: a fuzzy description, a constraint-based iterative optimization, AHP ranking method and a few MADM functions in Matlab.
A Numerical Embedding Method for Solving the Nonlinear Optimization Problem
Institute of Scientific and Technical Information of China (English)
田保锋; 戴云仙; 孟泽红; 张建军
2003-01-01
A numerical embedding method was proposed for solving the nonlinear optimization problem. By using the nonsmooth theory, the existence and the continuation of the following path for the corresponding homotopy equations were proved. Therefore the basic theory for the algorithm of the numerical embedding method for solving the non-linear optimization problem was established. Based on the theoretical results, a numerical embedding algorithm was designed for solving the nonlinear optimization problem, and prove its convergence carefully. Numerical experiments show that the algorithm is effective.
Infinite Horizon Discrete Time Control Problems for Bounded Processes
Directory of Open Access Journals (Sweden)
Hayek Naïla
2008-01-01
Full Text Available We establish Pontryagin Maximum Principles in the strong form for infinite horizon optimal control problems for bounded processes, for systems governed by difference equations. Results due to Ioffe and Tihomirov are among the tools used to prove our theorems. We write necessary conditions with weakened hypotheses of concavity and without invertibility, and we provide new results on the adjoint variable. We show links between bounded problems and nonbounded ones. We also give sufficient conditions of optimality.
Infinite Horizon Discrete Time Control Problems for Bounded Processes
Directory of Open Access Journals (Sweden)
2009-03-01
Full Text Available We establish Pontryagin Maximum Principles in the strong form for infinite horizon optimal control problems for bounded processes, for systems governed by difference equations. Results due to Ioffe and Tihomirov are among the tools used to prove our theorems. We write necessary conditions with weakened hypotheses of concavity and without invertibility, and we provide new results on the adjoint variable. We show links between bounded problems and nonbounded ones. We also give sufficient conditions of optimality.
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.
Optimization and optimality test for the Max-Cut Problem
Hohmann, Chr.; Kern, Walter
1990-01-01
We show that the following two problems are polynomially equivalent: 1. Given a (weighted) graphG, and a cutC ofG, decide whetherC is maximal or not. 2. Given a (weighted) graphG, and a cutC ofG, decide whetherC is maximal or not, and in case it is not, find a better solutionC′. As a consequence, an
Finite Volumes Discretization of Topology Optimization Problems
DEFF Research Database (Denmark)
Evgrafov, Anton; Gregersen, Misha Marie; Sørensen, Mads Peter
such a mature and versatile technique for discretiz- ing partial dierential equations in the form of conservation laws of varying types. Advantages of FVMs include the simplicity of implementation, their local conservation properties, and the ease of coupling various PDEs in a multi-physics setting. In fact...... attractive, as all involved PDEs on a given domain are discretized using the same and the low- est possible number of degrees of freedom. In spite of their numerous favourable advantages, FVMs have seen very little adoption within the topology optimization community, where the absolute majority of numerical...
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.
Checking for Optimal Solutions in Some NP-Complete Problems
Bauer, Michel; Orland, Henri
2005-09-01
For some weighted NP-complete problems, checking whether a proposed solution is optimal is a nontrivial task. Such is the case for the traveling salesman problem, or the spin-glass problem in three dimensions. In this Letter, we consider the weighted tripartite matching problem, a well known NP-complete problem. We write mean-field finite temperature equations for this model and derive their zero temperature limit. We show that any solution of the zero temperature equations provides an exact absolute ground state of the system. As a consequence, we propose a criterion which can be checked in polynomial time, and such that given a putative optimal solution, if the criterion is satisfied, then the solution is indeed optimal. This criterion is generalized to a class of variants of the multiple traveling salesmen problems.
OPTIMIZATION PROBLEMS ON SUBURBAN TRANSPORT SYSTEMS
T. M. Grigorovа
2015-01-01
The paper considers problems that permit to solve such issue as organization of transport service for suburban population with due account of passenger transport fatigue which is considered as one of subconscious criteria for selection of a travel mode. Improvement of transportation process entails an increase in demand for such service. Demands predetermine transport supply and situation on the market depends on supply-and-demand balance. The paper presents an analysis of approaches to the...
Optimization problems related to zigzag pocket machining
Energy Technology Data Exchange (ETDEWEB)
Arkin, E.M.; Held, M.; Smith, C.L. [State Univ. of New York, Stony Brook, NY (United States)
1996-12-31
A fundamental problem of manufacturing is to produce mechanical parts from billets by clearing areas within specified boundaries from the material. Based on a graph-theoretical formulation, the algorithmic handling of one particular machining problem {open_quote}zigzag pocket machining{close_quote} is investigated. We present a linear-time algorithm that ensures that no region of the pocket is machined repeatedly, thereby attempting to minimize the number of tool retractions required. This problem is shown to be NP-hard for pockets with holes. Our algorithm is a provable good in the sense that the machining path generated for a pocket with h holes requires at most 5. OPT+ 6 - h retractions, where OPT is the (unknown) minimum number of retractions required by any algorithm. The algorithm has been implemented, and practical tests for pockets without holes clearly showed that one can expect an approximation factor of about 1.5 for practical examples, rather than the factor 5 as proved by our analysis.
Efficient differential evolution algorithms for multimodal optmal control problems
Lopez Cruz, I.L.; Willigenburg, van L.G.; Straten, van G.
2003-01-01
Many methods for solving optimal control problems, whether direct or indirect, rely upon gradient information and therefore may converge to a local optimum. Global optimisation methods like Evolutionary algorithms, overcome this problem. In this work it is investigated how well novel and easy to und
Gradient Gene Algorithm: a Fast Optimization Method to MST Problem
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
The extension of Minimum Spanning Tree(MST) problem is an NP hardproblem which does not exit a polynomial time algorithm. In this paper, a fast optimizat ion method on MST problem--the Gradient Gene Algorithm is introduced. Compar ed with other evolutionary algorithms on MST problem, it is more advanced: firstly, very simple and easy to realize; then, efficient and accurate; finally general on other combination optimization problems.
Comparison of optimal design methods in inverse problems
Banks, H. T.; Holm, K.; Kappel, F.
2011-07-01
Typical optimal design methods for inverse or parameter estimation problems are designed to choose optimal sampling distributions through minimization of a specific cost function related to the resulting error in parameter estimates. It is hoped that the inverse problem will produce parameter estimates with increased accuracy using data collected according to the optimal sampling distribution. Here we formulate the classical optimal design problem in the context of general optimization problems over distributions of sampling times. We present a new Prohorov metric-based theoretical framework that permits one to treat succinctly and rigorously any optimal design criteria based on the Fisher information matrix. A fundamental approximation theory is also included in this framework. A new optimal design, SE-optimal design (standard error optimal design), is then introduced in the context of this framework. We compare this new design criterion with the more traditional D-optimal and E-optimal designs. The optimal sampling distributions from each design are used to compute and compare standard errors; the standard errors for parameters are computed using asymptotic theory or bootstrapping and the optimal mesh. We use three examples to illustrate ideas: the Verhulst-Pearl logistic population model (Banks H T and Tran H T 2009 Mathematical and Experimental Modeling of Physical and Biological Processes (Boca Raton, FL: Chapman and Hall/CRC)), the standard harmonic oscillator model (Banks H T and Tran H T 2009) and a popular glucose regulation model (Bergman R N, Ider Y Z, Bowden C R and Cobelli C 1979 Am. J. Physiol. 236 E667-77 De Gaetano A and Arino O 2000 J. Math. Biol. 40 136-68 Toffolo G, Bergman R N, Finegood D T, Bowden C R and Cobelli C 1980 Diabetes 29 979-90).
Solution of transient optimization problems by using an algorithm based on nonlinear programming
Teren, F.
1977-01-01
A new algorithm is presented for solution of dynamic optimization problems which are nonlinear in the state variables and linear in the control variables. It is shown that the optimal control is bang-bang. A nominal bang-bang solution is found which satisfies the system equations and constraints, and influence functions are generated which check the optimality of the solution. Nonlinear optimization (gradient search) techniques are used to find the optimal solution. The algorithm is used to find a minimum time acceleration for a turbofan engine.
Solution of transient optimization problems by using an algorithm based on nonlinear programming
Teren, F.
1977-01-01
A new algorithm is presented for solution of dynamic optimization problems which are nonlinear in the state variables and linear in the control variables. It is shown that the optimal control is bang-bang. A nominal bang-bang solution is found which satisfies the system equations and constraints, and influence functions are generated which check the optimality of the solution. Nonlinear optimization (gradient search) techniques are used to find the optimal solution. The algorithm is used to find a minimum time acceleration for a turbofan engine.
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.
Topology Optimization of Large Scale Stokes Flow Problems
DEFF Research Database (Denmark)
Aage, Niels; Poulsen, Thomas Harpsøe; Gersborg-Hansen, Allan
2008-01-01
This note considers topology optimization of large scale 2D and 3D Stokes flow problems using parallel computations. We solve problems with up to 1.125.000 elements in 2D and 128.000 elements in 3D on a shared memory computer consisting of Sun UltraSparc IV CPUs.......This note considers topology optimization of large scale 2D and 3D Stokes flow problems using parallel computations. We solve problems with up to 1.125.000 elements in 2D and 128.000 elements in 3D on a shared memory computer consisting of Sun UltraSparc IV CPUs....
Embedded Optimal Control of Robot Manipulators with Passive Joints
Directory of Open Access Journals (Sweden)
Alberto Olivares
2015-01-01
Full Text Available This paper studies the optimal control problem for planar underactuated robot manipulators with two revolute joints and brakes at the unactuated joints in the presence of gravity. The presence of a brake at an unactuated joint gives rise to two operating modes for that joint: free and braked. As a consequence, there exist two operating modes for a robot manipulator with one unactuated joint and four operating modes for a manipulator with two unactuated joints. Since these systems can change dynamics, they can be regarded as switched dynamical systems. The optimal control problem for these systems is solved using the so-called embedding approach. The main advantages of this technique are that assumptions about the number of switches are not necessary, integer or binary variables do not have to be introduced to model switching decisions between modes, and the optimal switching times between modes are not unknowns of the optimal control problem. As a consequence, the resulting problem is a classical continuous optimal control problem. In this way, a general method for the solution of optimal control problems for switched dynamical systems is obtained. It is shown in this paper that it can deal with nonintegrable differential constraints.
Topology optimization of 3D Stokes flow problems
DEFF Research Database (Denmark)
Gersborg-Hansen, Allan
to different flow problems. However, this research has focused on 2D fluid modelling, which limits the practical impact of the computed designs. The explanation of the limitation is that the finite size domain used in topology optimization problems ensures that the velocity components couples, even for Stokes......Topology optimization has been applied to a multitude of physical systems and is now a mature technology used in industrial practice, see [1] for an overview. Borrvall and Petersson [2] introduced topology optimization of Stokes flow problems which initiated works on extending topology optimization...... flow [3]. Furthermore, it is questionable if such a coupling can be captured by a 2D model especially in non-trivial geometries as typically seen in topology design. This statement is widely accepted in the fluid mechanics community, i.e. that planar fluid models are useful for academic test problems...
Institute of Scientific and Technical Information of China (English)
王江峰; 伍贻兆; Périaux J
2004-01-01
对比了进化算法(基因算法)与确定性算法(共轭梯度法)在优化控制问题中的优化效率.两种方法都与分散式优化策略-Nash对策进行了结合,并成功地应用于优化控制问题.计算模型采用绕NACA0012翼型的位流流场.区域分裂技术的引用使得全局流场被分裂为多个带有重叠区的子流场,使用4种不同的方法进行当地流场解的耦合,这些算法可以通过当地的流场解求得全局流场解.数值计算结果的对比表明,进化算法可以得到与共轭梯度法相同的计算结果,并且进化算法的不依赖梯度信息的特性使其在复杂问题及非线性问题中具有广泛的应用前景.%The comparison for optimization efficiency between evolutionary algorithms (Genetic Algorithms, GAs) and deterministic algorithms (Conjugate Gradient, CG) is presented. Both two different methods are combined with Nash strategy-decentralized optimization strategy in Game Theory-and implemented into an optimal control problem using a technique DDM (Domain Decomposition Method). The problem consists in simulating the perfect potential flow field around a NACA0012 airfoil with the technique DDM, the global calculation domain is then split into sub-domains with overlaps, the accord of local solutions on interfaces is obtained using four different algorithms which permit the resolution of global problem via local sub-problems on sub-domains and their interfaces. Comparable numerical results are obtained by different algorithms and show that the property of independence of gradient makes GAs based algorithms serious and robust research tools for great dimension problems or non-linear problems.
Institute of Scientific and Technical Information of China (English)
秦廷华; 马和平
2012-01-01
提出一种解常微分方程最优控制问题的自适应拟谱方法.对状态函数和控制函数使用不同次数的多项式逼近.设计了一个自适应算法决定不同的次数,并给出了理论分析.数值算例比较了本文方法与一种常用的拟谱方法.%An adaptive pseudospectral method is proposed to solve optimal control problems governed by ordinary differential equations. The polynomials approximating the state and control functions can have the different degrees. An adaptive algorithm is designed in order to determine the different degrees, and theoretical analysis is given. The proposed method is compared with a widely applied pseudo spectral method by numerical example.
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.
An approximation scheme for optimal control of Volterra integral equations
Belbas, S. A.
2006-01-01
We present and analyze a new method for solving optimal control problems for Volterra integral equations, based on approximating the controlled Volterra integral equations by a sequence of systems of controlled ordinary differential equations. The resulting approximating problems can then be solved by dynamic programming methods for ODE controlled systems. Other, straightforward versions of dynamic programming, are not applicable to Volterra integral equations. We also derive the connection b...
Topology optimization of vibration and wave propagation problems
DEFF Research Database (Denmark)
Jensen, Jakob Søndergaard
2007-01-01
The method of topology optimization is a versatile method to determine optimal material layouts in mechanical structures. The method relies on, in principle, unlimited design freedom that can be used to design materials, structures and devices with significantly improved performance and sometimes...... novel functionality. This paper addresses basic issues in simulation and topology design of vibration and wave propagation problems. Steady-state and transient wave propagation problems are addressed and application examples for both cases are presented....
Modified constrained differential evolution for solving nonlinear global optimization problems
2013-01-01
Nonlinear optimization problems introduce the possibility of multiple local optima. The task of global optimization is to find a point where the objective function obtains its most extreme value while satisfying the constraints. Some methods try to make the solution feasible by using penalty function methods, but the performance is not always satisfactory since the selection of the penalty parameters for the problem at hand is not a straightforward issue. Differential evolut...
Existence and approximation results for shape optimization problems in rotordynamics
Strauß, Frank; Heuveline, Vincent; Schweizer, Ben
2006-01-01
We consider a shape optimization problem in rotordynamics where the mass of a rotor is minimized subject to constraints on the natural frequencies. Our analysis is based on a class of rotors described by a Rayleigh beam model including effects of rotary inertia and gyroscopic moments. The solution of the equation of motion leads to a generalized eigenvalue problem. The governing operators are non-symmetric due to the gyroscopic terms. We prove the existence of solutions for the optimization p...
Fuzzy Inspired Hybrid Genetic Approach to Optimize Travelling Salesman Problem
Directory of Open Access Journals (Sweden)
Bindu
2012-06-01
Full Text Available One of the category of algorithm Problems are basically exponential problems. These problems are basically exponential problems and take time to find the solution. In the present work we are optimising one of the common NP complete problem called Travelling Salesman Problem. In our work we have defined a genetic approach by combining fuzzy approach along with genetics. In this work we have implemented the modified DPX crossover to improve genetic approach. The work is implemented in MATLAB environment and obtained results shows the define approach has optimized the existing genetic algorithm results
CONVEXIFICATION AND CONCAVIFICATION METHODS FOR SOME GLOBAL OPTIMIZATION PROBLEMS
Institute of Scientific and Technical Information of China (English)
WU Zhiyou; ZHANG Liansheng; BAI Fusheng; YANG Xinmin
2004-01-01
In this paper, firstly, we propose several convexification and concavification transformations to convert a strictly monotone function into a convex or concave function,then we propose several convexification and concavification transformations to convert a non-convex and non-concave objective function into a convex or concave function in the programming problems with convex or concave constraint functions, and propose several convexification and concavification transformations to convert a non-monotone objective function into a convex or concave function in some programming problems with strictly monotone constraint functions. Finally, we prove that the original programming problem can be converted into an equivalent concave minimization problem, or reverse convex programming problem or canonical D.C. Programming problem. Then the global optimal solution of the original problem can be obtained by solving the converted concave minimization problem, or reverse convex programming problem or canonical D.C. Programming problem using the existing algorithms about them.
Issues related to topology optimization of snap-through problems
DEFF Research Database (Denmark)
Lindgaard, Esben; Dahl, Jonas
2012-01-01
This work focuses on issues related to topology optimization of static geometrically nonlinear structures experiencing snap-through behaviour. Different compliance and buckling criterion functions are studied and applied to topology optimization of a point loaded curved beam problem with the aim ...
A Decision Support System for Solving Multiple Criteria Optimization Problems
Filatovas, Ernestas; Kurasova, Olga
2011-01-01
In this paper, multiple criteria optimization has been investigated. A new decision support system (DSS) has been developed for interactive solving of multiple criteria optimization problems (MOPs). The weighted-sum (WS) approach is implemented to solve the MOPs. The MOPs are solved by selecting different weight coefficient values for the criteria…
Topology optimization problems for reflection and dissipation of elastic waves
DEFF Research Database (Denmark)
Jensen, Jakob Søndergaard
2007-01-01
This paper is devoted to topology optimization problems for elastic wave propagation. The objective of the study is to maximize the reflection or the dissipation in a finite slab of material for pressure and shear waves in a range of frequencies. The optimized designs consist of two or three mate...
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.
borealis - A generalized global update algorithm for Boolean optimization problems
Zhu, Zheng; Katzgraber, Helmut G
2016-01-01
Optimization problems with Boolean variables that fall into the nondeterministic polynomial (NP) class are of fundamental importance in computer science, mathematics, physics and industrial applications. Most notably, solving constraint-satisfaction problems, which are related to spin-glass-like Hamiltonians in physics, remains a difficult numerical task. As such, there has been great interest in designing efficient heuristics to solve these computationally difficult problems. Inspired by parallel tempering Monte Carlo in conjunction with the rejection-free isoenergetic cluster algorithm developed for Ising spin glasses, we present a generalized global update optimization heuristic that can be applied to different NP-complete problems with Boolean variables. The global cluster updates allow for a wide-spread sampling of phase space, thus considerably speeding up optimization. By carefully tuning the pseudo-temperature (needed to randomize the configurations) of the problem, we show that the method can efficie...
Optimal Solutions for the Temporal Precedence Problem
DEFF Research Database (Denmark)
Brodal, Gerth Stølting; Makris, Christos; Sioutas, Spyros;
2002-01-01
a in the structure, while the operation precedes (a,b) returns true iff element a was inserted before element b temporally. In [11] a solution was provided to the problem with worst-case time complexity O (log log n ) per operation and O(n log log n) space, where n is the number of elements inserted. It was also...... demonstrated that the precedes operation has a lower bound of Ω (log log n ) for the Pure Pointer Machine model of computation. In this paper we present two simple solutions with linear space and worst-case constant insertion time. In addition, we describe two algorithms that can handle the precedes (a...
Optimal control of switched linear systems based on Migrant Particle Swarm Optimization algorithm
Xie, Fuqiang; Wang, Yongji; Zheng, Zongzhun; Li, Chuanfeng
2009-10-01
The optimal control problem for switched linear systems with internally forced switching has more constraints than with externally forced switching. Heavy computations and slow convergence in solving this problem is a major obstacle. In this paper we describe a new approach for solving this problem, which is called Migrant Particle Swarm Optimization (Migrant PSO). Imitating the behavior of a flock of migrant birds, the Migrant PSO applies naturally to both continuous and discrete spaces, in which definitive optimization algorithm and stochastic search method are combined. The efficacy of the proposed algorithm is illustrated via a numerical example.
Numerical solution of control problems governed by nonlinear differential equations
Energy Technology Data Exchange (ETDEWEB)
Heinkenschloss, M. [Virginia Polytechnic Institute and State Univ., Blacksburg, VA (United States)
1994-12-31
In this presentation the author investigates an iterative method for the solution of optimal control problems. These problems are formulated as constrained optimization problems with constraints arising from the state equation and in the form of bound constraints on the control. The method for the solution of these problems uses the special structure of the problem arising from the bound constraint and the state equation. It is derived from SQP methods and projected Newton methods and combines the advantages of both methods. The bound constraint is satisfied by all iterates using a projection, the nonlinear state equation is satisfied in the limit. Only a linearized state equation has to be solved in every iteration. The solution of the linearized problems are done using multilevel methods and GMRES.
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
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.
Global Optimization Problems in Optimal Design of Experiments in Regression Models
Boer, E.P.J.; Hendrix, E.M.T.
2000-01-01
In this paper we show that optimal design of experiments, a specific topic in statistics, constitutes a challenging application field for global optimization. This paper shows how various structures in optimal design of experiments problems determine the structure of corresponding challenging global
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.
Phase optimization problems applications in wave field theory
Bulatsyk, Olena O; Topolyuk, Yury P; Bulatsyk, Olena; Voitovich, Nikolai N
2010-01-01
This is the only book available in English language to consider inverse and optimization problems in which phase field distributions are used as optimizing functions. The mathematical technique used relates to nonlinear integral equations, with numerical methods developed and applied to concrete problems. Written by a team of outstanding and renowned experts in the field, this monograph will appeal to all those dealing with the investigation, design, and optimization of electromagnetic and acoustic radiating and transmitting devices and systems, while also being of interest to mathematicians w
Upper Hölder continuity of parametric vector optimization problems
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Xian-Fu Hu
2016-11-01
Full Text Available Abstract This paper is concerned with upper Hölder continuity and Hölder calmness of a perturbed vector optimization problem. We establish some new sufficient conditions for upper Hölder continuity and Hölder calmness of the perturbed solution mappings and the perturbed optimal value mappings of a vector optimization problem under the case that the objective function and the feasible set are, respectively, perturbed by parameters. Our results generalize and extend the corresponding ones of Li and Li (Appl. Math. Comput. 232:908-918, 2014.
Directory of Open Access Journals (Sweden)
Harish Garg
2013-01-01
systems by utilizing uncertain, limited, and imprecise data. In many practical situations where reliability enhancement is involved, the decision making is complicated because of the presence of several mutually conflicting objectives. Moreover, data collected or available for the systems are vague, ambiguous, qualitative, and imprecise in nature due to various practical constraints and hence create some difficulties in optimizing the design problems. To handle these problems, this work presents an interactive method for solving the fuzzy multiobjective optimization decision-making problem, which can be used for the optimization decision making of the reliability with two or more objectives. Based on the preference of the decision makers toward the objectives, fuzzy multi-objective optimization problem is converted into crisp optimization problem and then solved with evolutionary algorithm. The proposed approach has been applied to the decomposition unit of a urea fertilizer plant situated in the northern part of India producing 1500–2000 metric tons per day.
Strong Duality and Optimality Conditions for Generalized Equilibrium Problems
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D. H. Fang
2013-01-01
Full Text Available We consider a generalized equilibrium problem involving DC functions. By using the properties of the epigraph of the conjugate functions, some sufficient and/or necessary conditions for the weak and strong duality results and optimality conditions for generalized equilibrium problems are provided.
Multiplier methods for optimization problems with Lipschitzian derivatives
Izmailov, A. F.; Kurennoy, A. S.
2012-12-01
Optimization problems for which the objective function and the constraints have locally Lipschitzian derivatives but are not assumed to be twice differentiable are examined. For such problems, analyses of the local convergence and the convergence rate of the multiplier (or the augmented Lagrangian) method and the linearly constraint Lagrangian method are given.
Reverse convex problems: an approach based on optimality conditions
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Ider Tseveendorj
2006-01-01
Full Text Available We present some results concerning reverse convex problems. Global optimality conditions for the problems with a nonsmooth reverse convex constraint are established and convergence of an algorithm in the case of linear program with an additional quadratic reverse convex constraint is studied.
Moments of random sums and Robbins' problem of optimal stopping
Gnedin, A.V.; Iksanov, A.
2011-01-01
Robbins' problem of optimal stopping is that of minimising the expected rank of an observation chosen by some nonanticipating stopping rule. We settle a conjecture regarding the value of the stopped variable under the rule that yields the minimal expected rank, by embedding the problem in a much