WorldWideScience

Sample records for singular linear system

  1. Synchronization and Control of Linearly Coupled Singular Systems

    Directory of Open Access Journals (Sweden)

    Fang Qingxiang

    2013-01-01

    Full Text Available The synchronization and control problem of linearly coupled singular systems is investigated. The uncoupled dynamical behavior at each node is general and can be chaotic or, otherwise the coupling matrix is not assumed to be symmetrical. Some sufficient conditions for globally exponential synchronization are derived based on Lyapunov stability theory. These criteria, which are in terms of linear matrix inequality (LMI, indicate that the left and right eigenvectors corresponding to eigenvalue zero of the coupling matrix play key roles in the stability analysis of the synchronization manifold. The controllers are designed for state feedback control and pinning control, respectively. Finally, a numerical example is provided to illustrate the effectiveness of the proposed conditions.

  2. Slowly growing solutions of singular linear functional differential systems

    Czech Academy of Sciences Publication Activity Database

    Pylypenko, V.; Rontó, András

    2012-01-01

    Roč. 285, 5-6 (2012), s. 727-743 ISSN 0025-584X Institutional support: RVO:67985840 Keywords : functional differential equation * singular Cauchy problem * slowly growing solution Subject RIV: BA - General Mathematics Impact factor: 0.576, year: 2012 http://onlinelibrary.wiley.com/doi/10.1002/ mana .201000014/abstract

  3. Stability Analysis for Fractional-Order Linear Singular Delay Differential Systems

    Directory of Open Access Journals (Sweden)

    Hai Zhang

    2014-01-01

    Full Text Available We investigate the delay-independently asymptotic stability of fractional-order linear singular delay differential systems. Based on the algebraic approach, the sufficient conditions are presented to ensure the asymptotic stability for any delay parameter. By applying the stability criteria, one can avoid solving the roots of transcendental equations. An example is also provided to illustrate the effectiveness and applicability of the theoretical results.

  4. Finite-Time Stability Analysis of Discrete-Time Linear Singular Systems

    Directory of Open Access Journals (Sweden)

    Songlin Wo

    2014-01-01

    Full Text Available The finite-time stability (FTS problem of discrete-time linear singular systems (DTLSS is considered in this paper. A necessary and sufficient condition for FTS is obtained, which can be expressed in terms of matrix inequalities. Then, another form of the necessary and sufficient condition for FTS is also given by using matrix-null space technology. In order to solve the stability problem expediently, a sufficient condition for FTS is given via linear matrix inequality (LMI approach; this condition can be expressed in terms of LMIs. Finally, an illustrating example is also given to show the effectiveness of the proposed method.

  5. Finite-Time Robust H∞ Control for Uncertain Linear Continuous-Time Singular Systems with Exogenous Disturbances

    Directory of Open Access Journals (Sweden)

    Songlin Wo

    2018-01-01

    Full Text Available Singular systems arise in a great deal of domains of engineering and can be used to solve problems which are more difficult and more extensive than regular systems to solve. Therefore, in this paper, the definition of finite-time robust H∞ control for uncertain linear continuous-time singular systems is presented. The problem we address is to design a robust state feedback controller which can deal with the singular system with time-varying norm-bounded exogenous disturbance, such that the singular system is finite-time robust bounded (FTRB with disturbance attenuation γ. Sufficient conditions for the existence of solutions to this problem are obtained in terms of linear matrix equalities (LMIs. When these LMIs are feasible, the desired robust controller is given. A detailed solving method is proposed for the restricted linear matrix inequalities. Finally, examples are given to show the validity of the methodology.

  6. Singular Linear Differential Equations in Two Variables

    NARCIS (Netherlands)

    Braaksma, B.L.J.; Put, M. van der

    2008-01-01

    The formal and analytic classification of integrable singular linear differential equations has been studied among others by R. Gerard and Y. Sibuya. We provide a simple proof of their main result, namely: For certain irregular systems in two variables there is no Stokes phenomenon, i.e. there is no

  7. On preconditioning techniques for dense linear systems arising from singular boundary integral equations

    Energy Technology Data Exchange (ETDEWEB)

    Chen, Ke [Univ. of Liverpool (United Kingdom)

    1996-12-31

    We study various preconditioning techniques for the iterative solution of boundary integral equations, and aim to provide a theory for a class of sparse preconditioners. Two related ideas are explored here: singularity separation and inverse approximation. Our preliminary conclusion is that singularity separation based preconditioners perform better than approximate inverse based while it is desirable to have both features.

  8. Detection of Singularities in Fingerprint Images Using Linear Phase Portraits

    Science.gov (United States)

    Ram, Surinder; Bischof, Horst; Birchbauer, Josef

    abstract The performance of fingerprint recognition depends heavily on the reliable extraction of singularities. Common algorithms are based on a Poinc’are Index estimation. These algorithms are only robust when certain heuristics and rules are applied. In this chapter we present a model-based approach for the detection of singular points. The presented method exploits the geometric nature of linear differential equation systems. Our method is robust against noise in the input image and is able to detect singularities even if they are partly occluded. The algorithm proceeds by fitting linear phase portraits at each location of a sliding window and then analyses its parameters. Using a well-established mathematical background, our algorithm is able to decide if a singular point is existent. Furthermore, the parameters can be used to classify the type of the singular point into whorls, deltas and loops.

  9. Dissipative control for singular impulsive dynamical systems

    Directory of Open Access Journals (Sweden)

    Li Yang

    2012-04-01

    Full Text Available The aim of this work is to study the dissipative control problem for singular impulsive dynamical systems. We start by introducing the impulse to the singular systems, and give the definition of the dissipation for singular impulsive dynamical systems. Then we discuss the dissipation of singular impulsive dynamical systems, we obtain some sufficient and necessary conditions for dissipation of these systems by solving some linear matrix inequalities (LMIs. By using this method, we design a state feedback controller to make the closed-loop system dissipative. At last, we testify the feasibility of the method by a numerical example.

  10. Linear systems

    CERN Document Server

    Bourlès, Henri

    2013-01-01

    Linear systems have all the necessary elements (modeling, identification, analysis and control), from an educational point of view, to help us understand the discipline of automation and apply it efficiently. This book is progressive and organized in such a way that different levels of readership are possible. It is addressed both to beginners and those with a good understanding of automation wishing to enhance their knowledge on the subject. The theory is rigorously developed and illustrated by numerous examples which can be reproduced with the help of appropriate computation software. 60 exe

  11. On linear viscoelasticity within general fractional derivatives without singular kernel

    Directory of Open Access Journals (Sweden)

    Gao Feng

    2017-01-01

    Full Text Available The Riemann-Liouville and Caputo-Liouville fractional derivatives without singular kernel are proposed as mathematical tools to describe the mathematical models in line viscoelasticity in the present article. The fractional mechanical models containing the Maxwell and Kelvin-Voigt elements are graphically discussed with the Laplace transform. The results are accurate and efficient to reveal the complex behaviors of the real materials.

  12. Bifurcation for non linear ordinary differential equations with singular perturbation

    Directory of Open Access Journals (Sweden)

    Safia Acher Spitalier

    2016-10-01

    Full Text Available We study a family of singularly perturbed ODEs with one parameter and compare their solutions to the ones of the corresponding reduced equations. The interesting characteristic here is that the reduced equations have more than one solution for a given set of initial conditions. Then we consider how those solutions are organized for different values of the parameter. The bifurcation associated to this situation is studied using a minimal set of tools from non standard analysis.

  13. Review of Singular Cooling Inlet and Linear Pressure Drop for ITER Coils Cable in Conduit Conductor

    Science.gov (United States)

    Nicollet, S.; Bessette, D.; Cloez, H.; Decool, P.; Lacroix, B.; Lebailly, C. A.; Serries, J. P.

    2006-04-01

    New tests and measurements performed (Othello Facility, EFDA Task) on TF mock up cooling inlet and different central spirals (characteristics: hydraulic outer diameter and perforation ratio) are presented, as well as the new model of singular and linear friction factor. The ITER Coils CICC hydraulic length pressure drop is determined in operating conditions (m=8 g/s, P=0.6 MPa and T=5 K): the important result is an increase in linear pressure drop for the TF (290 Pa/m) and CS (430 Pa/m), in comparison with prototype model coils TFMC (100 Pa/m) and CSMC (180 Pa/m). The main reason is the reduction of the central spiral diameter and associated increase of friction factor and bundle to total mass flow ratio α (from 1/3 up to 2/3 typically). The ratio of singular cooling inlet to CICC linear pressure drop is estimated: TF mock up ratio (3 m) is lower than previous CS mock up tested (12 m), due to design changes. The cryogenic power necessary to compensate the CICC pressure drop is calculated for the 4 primary loop circuits: typically 2.3 kW at 5 K for TF winding system represents 40% of the whole average TF winding magnet heat loads during operation.

  14. Analysis and design of singular Markovian jump systems

    CERN Document Server

    Wang, Guoliang; Yan, Xinggang

    2014-01-01

    This monograph is an up-to-date presentation of the analysis and design of singular Markovian jump systems (SMJSs) in which the transition rate matrix of the underlying systems is generally uncertain, partially unknown and designed. The problems addressed include stability, stabilization, H∞ control and filtering, observer design, and adaptive control. applications of Markov process are investigated by using Lyapunov theory, linear matrix inequalities (LMIs), S-procedure and the stochastic Barbalat's Lemma, among other techniques.Features of the book include:·???????? study of the stability pr

  15. Load-Flow in Multiphase Distribution Networks: Existence, Uniqueness, Non-Singularity, and Linear Models

    Energy Technology Data Exchange (ETDEWEB)

    Bernstein, Andrey [National Renewable Energy Laboratory (NREL), Golden, CO (United States); Dall-Anese, Emiliano [National Renewable Energy Laboratory (NREL), Golden, CO (United States); Zhao, Changhong [National Renewable Energy Laboratory (NREL), Golden, CO (United States); Wang, Cong [Ecole Polytechnique Federale de Lausanne (EPFL); Le Boudec, Jean-Yves [Ecole Polytechnique Federale de Lausanne (EPFL)

    2018-04-06

    This paper considers unbalanced multiphase distribution systems with generic topology and different load models, and extends the Z-bus iterative load-flow algorithm based on a fixed-point interpretation of the AC load-flow equations. Explicit conditions for existence and uniqueness of load-flow solutions are presented. These conditions also guarantee convergence of the load-flow algorithm to the unique solution. The proposed methodology is applicable to generic systems featuring (i) wye connections; (ii) ungrounded delta connections; (iii) a combination of wye-connected and delta-connected sources/loads; and, (iv) a combination of line-to-line and line-to-grounded-neutral devices at the secondary of distribution transformers. Further, a sufficient condition for the non-singularity of the load-flow Jacobian is proposed. Finally, linear load-flow models are derived, and their approximation accuracy is analyzed. Theoretical results are corroborated through experiments on IEEE test feeders.

  16. Complexity, Analysis and Control of Singular Biological Systems

    CERN Document Server

    Zhang, Qingling; Zhang, Xue

    2012-01-01

    Complexity, Analysis and Control of Singular Biological Systems follows the control of real-world biological systems at both ecological and phyisological levels concentrating on the application of now-extensively-investigated singular system theory. Much effort has recently been dedicated to the modelling and analysis of developing bioeconomic systems and the text establishes singular examples of these, showing how proper control can help to maintain sustainable economic development of biological resources. The book begins from the essentials of singular systems theory and bifurcations before tackling  the use of various forms of control in singular biological systems using examples including predator-prey relationships and viral vaccination and quarantine control. Researchers and graduate students studying the control of complex biological systems are shown how a variety of methods can be brought to bear and practitioners working with the economics of biological systems and their control will also find the ...

  17. Pulses in singularly perturbed reaction-diffusion systems

    NARCIS (Netherlands)

    Veerman, Frederik Willem Johan

    2013-01-01

    In this thesis, the existence and stability of pulse solutions in two-component, singularly perturbed reaction-diffusion systems is analysed using dynamical systems techniques. New phenomena in very general types of systems emerge when geometrical techniques are applied.

  18. An investigation of singular Lagrangians as field systems

    International Nuclear Information System (INIS)

    Rabei, E.M.

    1995-07-01

    The link between the treatment of singular Lagrangians as field systems and the general approach is studied. It is shown that singular Lagrangians as field systems are always in exact agreement with the general approach. Two examples and the singular Lagrangian with zero rank Hessian matrix are studied. The equations of motion in the field systems are equivalent to the equations which contain acceleration, and the constraints are equivalent to the equations which do not contain acceleration in the general approach treatment. (author). 10 refs

  19. INTERVAL STATE ESTIMATION FOR SINGULAR DIFFERENTIAL EQUATION SYSTEMS WITH DELAYS

    Directory of Open Access Journals (Sweden)

    T. A. Kharkovskaia

    2016-07-01

    Full Text Available The paper deals with linear differential equation systems with algebraic restrictions (singular systems and a method of interval observer design for this kind of systems. The systems contain constant time delay, measurement noise and disturbances. Interval observer synthesis is based on monotone and cooperative systems technique, linear matrix inequations, Lyapunov function theory and interval arithmetic. The set of conditions that gives the possibility for interval observer synthesis is proposed. Results of synthesized observer operation are shown on the example of dynamical interindustry balance model. The advantages of proposed method are that it is adapted to observer design for uncertain systems, if the intervals of admissible values for uncertain parameters are given. The designed observer is capable to provide asymptotically definite limits on the estimation accuracy, since the interval of admissible values for the object state is defined at every instant. The obtained result provides an opportunity to develop the interval estimation theory for complex systems that contain parametric uncertainty, varying delay and nonlinear elements. Interval observers increasingly find applications in economics, electrical engineering, mechanical systems with constraints and optimal flow control.

  20. A singular value decomposition linear programming (SVDLP) optimization technique for circular cone based robotic radiotherapy

    Science.gov (United States)

    Liang, Bin; Li, Yongbao; Wei, Ran; Guo, Bin; Xu, Xuang; Liu, Bo; Li, Jiafeng; Wu, Qiuwen; Zhou, Fugen

    2018-01-01

    With robot-controlled linac positioning, robotic radiotherapy systems such as CyberKnife significantly increase freedom of radiation beam placement, but also impose more challenges on treatment plan optimization. The resampling mechanism in the vendor-supplied treatment planning system (MultiPlan) cannot fully explore the increased beam direction search space. Besides, a sparse treatment plan (using fewer beams) is desired to improve treatment efficiency. This study proposes a singular value decomposition linear programming (SVDLP) optimization technique for circular collimator based robotic radiotherapy. The SVDLP approach initializes the input beams by simulating the process of covering the entire target volume with equivalent beam tapers. The requirements on dosimetry distribution are modeled as hard and soft constraints, and the sparsity of the treatment plan is achieved by compressive sensing. The proposed linear programming (LP) model optimizes beam weights by minimizing the deviation of soft constraints subject to hard constraints, with a constraint on the l 1 norm of the beam weight. A singular value decomposition (SVD) based acceleration technique was developed for the LP model. Based on the degeneracy of the influence matrix, the model is first compressed into lower dimension for optimization, and then back-projected to reconstruct the beam weight. After beam weight optimization, the number of beams is reduced by removing the beams with low weight, and optimizing the weights of the remaining beams using the same model. This beam reduction technique is further validated by a mixed integer programming (MIP) model. The SVDLP approach was tested on a lung case. The results demonstrate that the SVD acceleration technique speeds up the optimization by a factor of 4.8. Furthermore, the beam reduction achieves a similar plan quality to the globally optimal plan obtained by the MIP model, but is one to two orders of magnitude faster. Furthermore, the SVDLP

  1. Adaptive Control of the Chaotic System via Singular System Approach

    Directory of Open Access Journals (Sweden)

    Yudong Li

    2014-01-01

    Full Text Available This paper deals with the control problem of the chaotic system subject to disturbance. The sliding mode surface is designed by singular system approach, and sufficient condition for convergence is given. Then, the adaptive sliding mode controller is designed to make the state arrive at the sliding mode surface in finite time. Finally, Lorenz system is considered as an example to show the effectiveness of the proposed method.

  2. Geometric singular perturbation analysis of systems with friction

    DEFF Research Database (Denmark)

    Bossolini, Elena

    This thesis is concerned with the application of geometric singular perturbation theory to mechanical systems with friction. The mathematical background on geometric singular perturbation theory, on the blow-up method, on non-smooth dynamical systems and on regularization is presented. Thereafter...... use a Poincaré compactification to study the system near infinity. At infinity, the critical manifold loses hyperbolicity with an exponential rate. We use an adaptation of the blow-up method to recover the hyperbolicity. This enables the identification of a new attracting manifold, that organises...... singular, in contrast to the regular stiction solutions that are forward unique. In order to further the understanding of the non-unique dynamics, we introduce a regularization of the model. This gives a singularly perturbed problem that captures the main features of the original discontinuous problem. We...

  3. The initial value problem for linearized gravitational perturbations of the Schwarzschild naked singularity

    Energy Technology Data Exchange (ETDEWEB)

    Dotti, Gustavo; Gleiser, Reinaldo J [Facultad de Matematica, AstronomIa y Fisica (FaMAF), Universidad Nacional de Cordoba, Ciudad Universitaria, 5000 Cordoba (Argentina)

    2009-11-07

    The coupled equations for the scalar modes of the linearized Einstein equations around Schwarzschild's spacetime were reduced by Zerilli to a (1+1) wave equation partial deriv{sup 2}PSI{sub z} /partial derivt{sup 2} +HPSI{sub z} =0, where H= -partial deriv{sup 2} /partial derivx{sup 2} + V(x) is the Zerilli 'Hamiltonian' and x is the tortoise radial coordinate. From its definition, for smooth metric perturbations the field PSI{sub z} is singular at r{sub s} = -6M/(l - 1)(l +2), with l being the mode harmonic number. The equation PSI{sub z} obeys is also singular, since V has a second-order pole at r{sub s}. This is irrelevant to the black hole exterior stability problem, where r > 2M > 0, and r{sub s} < 0, but it introduces a non-trivial problem in the naked singular case where M < 0, then r{sub s} > 0, and the singularity appears in the relevant range of r (0 < r < infinity). We solve this problem by developing a new approach to the evolution of the even mode, based on a new gauge invariant function, PSI-circumflex, that is a regular function of the metric perturbation for any value of M. The relation of PSI-circumflex to PSI{sub z} is provided by an intertwiner operator. The spatial pieces of the (1 + 1) wave equations that PSI-circumflex and PSI{sub z} obey are related as a supersymmetric pair of quantum Hamiltonians H and H-circumflex. For M < 0,H-circumflex has a regular potential and a unique self-adjoint extension in a domain D defined by a physically motivated boundary condition at r = 0. This allows us to address the issue of evolution of gravitational perturbations in this non-globally hyperbolic background. This formulation is used to complete the proof of the linear instability of the Schwarzschild naked singularity, by showing that a previously found unstable mode belongs to a complete basis of H-circumflex in D, and thus is excitable by generic initial data. This is further illustrated by numerically solving the linearized equations for

  4. Linear integral equations and soliton systems

    International Nuclear Information System (INIS)

    Quispel, G.R.W.

    1983-01-01

    A study is presented of classical integrable dynamical systems in one temporal and one spatial dimension. The direct linearizations are given of several nonlinear partial differential equations, for example the Korteweg-de Vries equation, the modified Korteweg-de Vries equation, the sine-Gordon equation, the nonlinear Schroedinger equation, and the equation of motion for the isotropic Heisenberg spin chain; the author also discusses several relations between these equations. The Baecklund transformations of these partial differential equations are treated on the basis of a singular transformation of the measure (or equivalently of the plane-wave factor) occurring in the corresponding linear integral equations, and the Baecklund transformations are used to derive the direct linearization of a chain of so-called modified partial differential equations. Finally it is shown that the singular linear integral equations lead in a natural way to the direct linearizations of various nonlinear difference-difference equations. (Auth.)

  5. PWR control system design using advanced linear and non-linear methodologies

    International Nuclear Information System (INIS)

    Rabindran, N.; Whitmarsh-Everiss, M.J.

    2004-01-01

    Consideration is here given to the methodology deployed for non-linear heuristic analysis in the time domain supported by multi-variable linear control system design methods for the purposes of operational dynamics and control system analysis. This methodology is illustrated by the application of structural singular value μ analysis to Pressurised Water Reactor control system design. (author)

  6. A class of singular Ro-matrices and extensions to semidefinite linear complementarity problems

    Directory of Open Access Journals (Sweden)

    Sivakumar K.C.

    2013-01-01

    Full Text Available For ARnxn and qRn, the linear complementarity problem LCP(A, q is to determine if there is xRn such that x ≥ 0; y = Ax + q ≥ 0 and xT y = 0. Such an x is called a solution of LCP(A,q. A is called an Ro-matrix if LCP(A,0 has zero as the only solution. In this article, the class of R0-matrices is extended to include typically singular matrices, by requiring in addition that the solution x above belongs to a subspace of Rn. This idea is then extended to semidefinite linear complementarity problems, where a characterization is presented for the multplicative transformation.

  7. Existence of solutions to singular fractional differential systems with impulses

    Directory of Open Access Journals (Sweden)

    Xingyuan Liu

    2012-11-01

    Full Text Available By constructing a weighted Banach space and a completely continuous operator, we establish the existence of solutions for singular fractional differential systems with impulses. Our results are proved using the Leray-Schauder nonlinear alternative, and are illustrated with examples.

  8. Refined Fuchs inequalities for systems of linear differential equations

    International Nuclear Information System (INIS)

    Gontsov, R R

    2004-01-01

    We refine the Fuchs inequalities obtained by Corel for systems of linear meromorphic differential equations given on the Riemann sphere. Fuchs inequalities enable one to estimate the sum of exponents of the system over all its singular points. We refine these well-known inequalities by considering the Jordan structure of the leading coefficient of the Laurent series for the matrix of the right-hand side of the system in the neighbourhood of a singular point

  9. Relaxation periodic solutions of one singular perturbed system with delay

    Science.gov (United States)

    Kashchenko, A. A.

    2017-12-01

    In this paper, we consider a singularly perturbed system of two differential equations with delay, simulating two coupled oscillators with a nonlinear compactly supported feedback. We reduce studying nonlocal dynamics of initial system to studying dynamics of special finite-dimensional mappings: rough stable (unstable) cycles of these mappings correspond to exponentially orbitally stable (unstable) relaxation solutions of initial problem. We show that dynamics of initial model depends on coupling coefficient crucially. Multistability is proved.

  10. Robust Guaranteed Cost Observer Design for Singular Markovian Jump Time-Delay Systems with Generally Incomplete Transition Probability

    Directory of Open Access Journals (Sweden)

    Yanbo Li

    2014-01-01

    Full Text Available This paper is devoted to the investigation of the design of robust guaranteed cost observer for a class of linear singular Markovian jump time-delay systems with generally incomplete transition probability. In this singular model, each transition rate can be completely unknown or only its estimate value is known. Based on stability theory of stochastic differential equations and linear matrix inequality (LMI technique, we design an observer to ensure that, for all uncertainties, the resulting augmented system is regular, impulse free, and robust stochastically stable with the proposed guaranteed cost performance. Finally, a convex optimization problem with LMI constraints is formulated to design the suboptimal guaranteed cost filters for linear singular Markovian jump time-delay systems with generally incomplete transition probability.

  11. Early light vision isomorphic singular (ELVIS) system

    Science.gov (United States)

    Jannson, Tomasz P.; Ternovskiy, Igor V.; DeBacker, Theodore A.; Caulfield, H. John

    2000-07-01

    In the shallow water military scenarios, UUVs (Unmanned Underwater Vehicles) are required to protect assets against mines, swimmers, and other underwater military objects. It would be desirable if such UUVs could autonomously see in a similar way as humans, at least, at the primary visual cortex-level. In this paper, an attempt to such a UUV system development is proposed.

  12. Singular divergence instability thresholds of kinematically constrained circulatory systems

    Energy Technology Data Exchange (ETDEWEB)

    Kirillov, O.N., E-mail: o.kirillov@hzdr.de [Magnetohydrodynamics Division, Helmholtz-Zentrum Dresden-Rossendorf, P.O. Box 510119, D-01314 Dresden (Germany); Challamel, N. [University of South Brittany, LIMATB, Lorient (France); Darve, F. [Laboratoire Sols Solides Structures, UJF-INPG-CNRS, Grenoble (France); Lerbet, J. [IBISC, Universite d' Evry Val d' Essone, 40 Rue Pelvoux, CE 1455 Courcouronnes, 91020 Evry Cedex (France); Nicot, F. [Cemagref, Unite de Recherche Erosion Torrentielle Neige et Avalanches, Grenoble (France)

    2014-01-10

    Static instability or divergence threshold of both potential and circulatory systems with kinematic constraints depends singularly on the constraints' coefficients. Particularly, the critical buckling load of the kinematically constrained Ziegler's pendulum as a function of two coefficients of the constraint is given by the Plücker conoid of degree n=2. This simple mechanical model exhibits a structural instability similar to that responsible for the Velikhov–Chandrasekhar paradox in the theory of magnetorotational instability.

  13. Canard solutions of two-dimensional singularly perturbed systems

    Energy Technology Data Exchange (ETDEWEB)

    Chen Xianfeng [Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240 (China)]. E-mail: chenxf@sjtu.edu.cn; Yu Pei [Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240 (China); Department of Applied Mathematics, University of Western Ontario London, Ont., N6A 5B7 (Canada); Han Maoan [Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240 (China); Zhang Weijiang [Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240 (China)

    2005-02-01

    In this paper, some new lemmas on asymptotic analysis are established. We apply an asymptotic method to study generalized two-dimensional singularly perturbed systems with one parameter, whose critical manifold has an m-22 th-order degenerate extreme point. Certain sufficient conditions are obtained for the existence of canard solutions, which are the extension and correction of some existing results. Finally, one numerical example is given.

  14. A Direct and Non-Singular UKF Approach Using Euler Angle Kinematics for Integrated Navigation Systems.

    Science.gov (United States)

    Ran, Changyan; Cheng, Xianghong

    2016-09-02

    This paper presents a direct and non-singular approach based on an unscented Kalman filter (UKF) for the integration of strapdown inertial navigation systems (SINSs) with the aid of velocity. The state vector includes velocity and Euler angles, and the system model contains Euler angle kinematics equations. The measured velocity in the body frame is used as the filter measurement. The quaternion nonlinear equality constraint is eliminated, and the cross-noise problem is overcome. The filter model is simple and easy to apply without linearization. Data fusion is performed by an UKF, which directly estimates and outputs the navigation information. There is no need to process navigation computation and error correction separately because the navigation computation is completed synchronously during the filter time updating. In addition, the singularities are avoided with the help of the dual-Euler method. The performance of the proposed approach is verified by road test data from a land vehicle equipped with an odometer aided SINS, and a singularity turntable test is conducted using three-axis turntable test data. The results show that the proposed approach can achieve higher navigation accuracy than the commonly-used indirect approach, and the singularities can be efficiently removed as the result of dual-Euler method.

  15. Fuzzy Stochastic Optimal Guaranteed Cost Control of Bio-Economic Singular Markovian Jump Systems.

    Science.gov (United States)

    Li, Li; Zhang, Qingling; Zhu, Baoyan

    2015-11-01

    This paper establishes a bio-economic singular Markovian jump model by considering the price of the commodity as a Markov chain. The controller is designed for this system such that its biomass achieves the specified range with the least cost in a finite-time. Firstly, this system is described by Takagi-Sugeno fuzzy model. Secondly, a new design method of fuzzy state-feedback controllers is presented to ensure not only the regularity, nonimpulse, and stochastic singular finite-time boundedness of this kind of systems, but also an upper bound achieved for the cost function in the form of strict linear matrix inequalities. Finally, two examples including a practical example of eel seedling breeding are given to illustrate the merit and usability of the approach proposed in this paper.

  16. Robust control of linear descriptor systems

    CERN Document Server

    Feng, Yu

    2017-01-01

    This book develops original results regarding singular dynamic systems following two different paths. The first consists of generalizing results from classical state-space cases to linear descriptor systems, such as dilated linear matrix inequality (LMI) characterizations for descriptor systems and performance control under regulation constraints. The second is a new path, which considers descriptor systems as a powerful tool for conceiving new control laws, understanding and deciphering some controller’s architecture and even homogenizing different—existing—ways of obtaining some new and/or known results for state-space systems. The book also highlights the comprehensive control problem for descriptor systems as an example of using the descriptor framework in order to transform a non-standard control problem into a classic stabilization control problem. In another section, an accurate solution is derived for the sensitivity constrained linear optimal control also using the descriptor framework. The boo...

  17. Generalized Cross-Gramian for Linear Systems

    DEFF Research Database (Denmark)

    Shaker, Hamid Reza

    2012-01-01

    The cross-gramian is a well-known matrix with embedded controllability and observability information. The cross-gramian is related to the Hankel operator and the Hankel singular values of a linear square system and it has several interesting properties. These properties make the cross-gramian pop......The cross-gramian is a well-known matrix with embedded controllability and observability information. The cross-gramian is related to the Hankel operator and the Hankel singular values of a linear square system and it has several interesting properties. These properties make the cross......-gramian popular in several applications including model reduction, control configuration selection and sensitivity analysis. The ordinary cross-gramian which has been defined in the literature is the solution of a Sylvester equation. This Sylvester equation is not always solvable and therefore for some linear...... square symmetric systems, the ordinary cross-gramian does not exist. To cope with this problem, a new generalized cross-gramian is introduced in this paper. In contrast to the ordinary cross-gramian, the generalized cross-gramian can be easily obtained for general linear systems and therefore can be used...

  18. Smoothness and numerical solution of linear integral equations of the second type with weakly singular kernels

    International Nuclear Information System (INIS)

    Bechlars, J.

    1978-12-01

    1) Integrable (L 1 ) singularities, occuring on the boundary or along the diagonal direction, and jumps along the diagonal direction do not disturb the compactness of otherwise continuous integral operator kernels. So the theory of compact operators can be applied for solving the integral equation. 2) Provided the regular parts of the kernel are sufficiently differentiable, the continuous differentiability (Cn) of the right hand side is transposed to the solution, if the kernel has no singularities or no singularities on the boundary and no jump. In the case of singularities in connection with a jump examples show, that this result is not valid in general. Therefore a second definition of smoothness has been introduced (Csup((n,α)) : continuous differentiability in the interior and 'limitation of derivatives') which can be applied in such cases and on the other side shows satisfactory error behaviour during interpolation and includes singularities from logarithms and negative powers. Provided diagonal singularities or singularities on the boundary can be asigned to Csup((n+1,α-1)) (0 2 also Csup((2,α)) (0 -2 ). This is confirmed by numerical examples. (orig./HSI) [de

  19. Analytical study for singular system of transistor circuits

    Directory of Open Access Journals (Sweden)

    Devendra Kumar

    2014-06-01

    Full Text Available In this paper, we propose a user friendly algorithm based on homotopy analysis transform method for solving observer design in generalized state space or singular system of transistor circuits. The homotopy analysis transform method is an innovative adjustment in Laplace transform method and makes the calculation much simpler. The effectiveness of technique is described and illustrated with an example. The obtained results are in a good agreement with the existing ones in open literature and it is shown that the scheme proposed here is robust, efficient, easy to implement and computationally very attractive.

  20. SENR /NRPy + : Numerical relativity in singular curvilinear coordinate systems

    Science.gov (United States)

    Ruchlin, Ian; Etienne, Zachariah B.; Baumgarte, Thomas W.

    2018-03-01

    We report on a new open-source, user-friendly numerical relativity code package called SENR /NRPy + . Our code extends previous implementations of the BSSN reference-metric formulation to a much broader class of curvilinear coordinate systems, making it ideally suited to modeling physical configurations with approximate or exact symmetries. In the context of modeling black hole dynamics, it is orders of magnitude more efficient than other widely used open-source numerical relativity codes. NRPy + provides a Python-based interface in which equations are written in natural tensorial form and output at arbitrary finite difference order as highly efficient C code, putting complex tensorial equations at the scientist's fingertips without the need for an expensive software license. SENR provides the algorithmic framework that combines the C codes generated by NRPy + into a functioning numerical relativity code. We validate against two other established, state-of-the-art codes, and achieve excellent agreement. For the first time—in the context of moving puncture black hole evolutions—we demonstrate nearly exponential convergence of constraint violation and gravitational waveform errors to zero as the order of spatial finite difference derivatives is increased, while fixing the numerical grids at moderate resolution in a singular coordinate system. Such behavior outside the horizons is remarkable, as numerical errors do not converge to zero near punctures, and all points along the polar axis are coordinate singularities. The formulation addresses such coordinate singularities via cell-centered grids and a simple change of basis that analytically regularizes tensor components with respect to the coordinates. Future plans include extending this formulation to allow dynamical coordinate grids and bispherical-like distribution of points to efficiently capture orbiting compact binary dynamics.

  1. Singular Continuous Floquet Operator for Periodic Quantum Systems

    CERN Document Server

    Bourget, O

    2004-01-01

    Consider the Floquet operator of a time independent quantum system, acting on a separable Hilbert space, periodically perturbed by a rank one kick: $e^{-iH_0T}e^{-i\\kappa T |\\phi\\ket\\bra\\phi|}$ where $T$, $\\kappa$ are respectively the period and the coupling constant and $H_0$ is a pure point self-adjoint operator, bounded from below. Under some hypotheses on the vector $\\phi$, cyclic for $H_0$ we prove the following: If the gaps between the eigenvalues $(\\lambda_n)$ are such that: $\\lambda_{n+1}-\\lambda_{n}\\geq C n^{-\\gamma}$ for some $\\gamma \\in ]0,1[$ and $C>0$, then the Floquet operator of the perturbed system is purely singular continuous T-a.e. If $H_0$ is the Hamiltonian of the one-dimensional rotator on $L^2({\\mathbb R}/T_0{\\mathbb Z})$ and the ratio $2\\pi T/T_0^2$ is irrational, then the Floquet operator is purely singular continuous as soon as $\\kappa T \

  2. Singular Continuous Floquet Operator for Systems with Increasing Gaps

    CERN Document Server

    Bourget, O

    2002-01-01

    Consider the Floquet operator of a time independent quantum system, periodically perturbed by a rank one kick, acting on a separable Hilbert space: $e^{-iH_0T}e^{-i\\kappa T |\\phi \\ket \\bra \\phi|}$ where $T$ and $\\kappa$ are the period and the coupling constant respectively. Assume the spectrum of the self adjoint operator $H_0$ is pure point, simple, bounded from below and the gaps between the eigenvalues $(\\lambda_n)$ grow like: $\\lambda_{n+1} - \\lambda_{n} \\sim C n^d$ with $d \\geq 2$. Under some hypotheses on the arithmetical nature of the eigenvalues and on the vector $\\phi$, cyclic for $H_0$, we prove the Floquet operator of the perturbed system has purely singular continuous spectrum.

  3. Well-posedness of the second-order linear singular Dirichlet problem

    Czech Academy of Sciences Publication Activity Database

    Lomtatidze, Alexander; Opluštil, Z.

    2015-01-01

    Roč. 22, č. 3 (2015), s. 409-419 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : singular Dirichlet problem * well-posedness Subject RIV: BA - General Mathematics Impact factor: 0.417, year: 2015 http://www.degruyter.com/view/j/gmj.2015.22.issue-3/gmj-2015-0023/gmj-2015-0023. xml

  4. Non-linear singular problems in p-adic analysis: associative algebras of p-adic distributions

    International Nuclear Information System (INIS)

    Albeverio, S; Khrennikov, A Yu; Shelkovich, V M

    2005-01-01

    We propose an algebraic theory which can be used for solving both linear and non-linear singular problems of p-adic analysis related to p-adic distributions (generalized functions). We construct the p-adic Colombeau-Egorov algebra of generalized functions, in which Vladimirov's pseudo-differential operator plays the role of differentiation. This algebra is closed under Fourier transformation and associative convolution. Pointvalues of generalized functions are defined, and it turns out that any generalized function is uniquely determined by its pointvalues. We also construct an associative algebra of asymptotic distributions, which is generated by the linear span of the set of associated homogeneous p-adic distributions. This algebra is embedded in the Colombeau-Egorov algebra as a subalgebra. In addition, a new technique for constructing weak asymptotics is developed

  5. Linearization of the Lorenz system

    International Nuclear Information System (INIS)

    Li, Chunbiao; Sprott, Julien Clinton; Thio, Wesley

    2015-01-01

    A partial and complete piecewise linearized version of the Lorenz system is proposed. The linearized versions have an independent total amplitude control parameter. Additional further linearization leads naturally to a piecewise linear version of the diffusionless Lorenz system. A chaotic circuit with a single amplitude controller is then implemented using a new switch element, producing a chaotic oscillation that agrees with the numerical calculation for the piecewise linear diffusionless Lorenz system. - Highlights: • A partial and complete piecewise linearized version of the Lorenz system are addressed. • The linearized versions have an independent total amplitude control parameter. • A piecewise linear version of the diffusionless Lorenz system is derived by further linearization. • A corresponding chaotic circuit without any multiplier is implemented for the chaotic oscillation

  6. Full-Order Disturbance-Observer-Based Control for Singular Hybrid System

    Directory of Open Access Journals (Sweden)

    Xiuming Yao

    2013-01-01

    Full Text Available The problem of the disturbance-observer-based control for singular hybrid system with two types of disturbances is addressed in this paper. Under the assumption that the system states are, unavailable, full-order observers (for both system states and the disturbance and a nonlinear control scheme are constructed, such that the composite system can be guaranteed to be stochastically admissible, and the two types of disturbances can be attenuated and rejected, simultaneously. Based on the Lyapunov stability theory, sufficient conditions for the existence of the desired full-order disturbance-observer-based controllers are established in terms of linear matrix inequalities (LMIs. Finally, a numerical example is provided to show the effectiveness of the proposed approaches.

  7. On the C(R) stability of uncertain singularly perturbed systems

    International Nuclear Information System (INIS)

    Sun, Y.-J.

    2009-01-01

    In this paper, a simple criterion for the C(R) stability of uncertain singularly perturbed systems is proposed. Such a criterion can be easily checked by some algebraic inequality. The upper bound of the singular perturbation parameter ε is also given by estimating the unique positive zero of specific function. Finally, a numerical example is provided to illustrate the main result

  8. Chaos synchronization of a unified chaotic system via partial linearization

    International Nuclear Information System (INIS)

    Yu Yongguang; Li Hanxiong; Duan Jian

    2009-01-01

    A partial linearization method is proposed for realizing the chaos synchronization of an unified chaotic system. Through synchronizing partial state of the chaotic systems can result in the synchronization of their entire states, and the resulting controller is singularity free. The results can be easily extended to the synchronization of other similar chaotic systems. Simulation results are conducted to show the effectiveness of the method.

  9. Quantum Linear System Algorithm for Dense Matrices

    Science.gov (United States)

    Wossnig, Leonard; Zhao, Zhikuan; Prakash, Anupam

    2018-02-01

    Solving linear systems of equations is a frequently encountered problem in machine learning and optimization. Given a matrix A and a vector b the task is to find the vector x such that A x =b . We describe a quantum algorithm that achieves a sparsity-independent runtime scaling of O (κ2√{n }polylog(n )/ɛ ) for an n ×n dimensional A with bounded spectral norm, where κ denotes the condition number of A , and ɛ is the desired precision parameter. This amounts to a polynomial improvement over known quantum linear system algorithms when applied to dense matrices, and poses a new state of the art for solving dense linear systems on a quantum computer. Furthermore, an exponential improvement is achievable if the rank of A is polylogarithmic in the matrix dimension. Our algorithm is built upon a singular value estimation subroutine, which makes use of a memory architecture that allows for efficient preparation of quantum states that correspond to the rows of A and the vector of Euclidean norms of the rows of A .

  10. On a class of strongly degenerate and singular linear elliptic equation

    International Nuclear Information System (INIS)

    Duong Minh Duc, D.M.; Le Dung.

    1992-11-01

    We consider a class of strongly degenerate linear elliptic equation. The boundedness and the Holder regularity of the weak solutions in the weighted Sobolev-Hardy spaces will be studied. (author). 9 refs

  11. Introduction to coordinated linear systems

    NARCIS (Netherlands)

    Kempker, P.L.

    2014-01-01

    This chapter serves as an introduction to the concepts of coordinated linear systems, in formal as well as intuitive terms. The concept of a coordinated linear system is introduced and formulated, and some basic properties are derived, providing both a motivaton and a formal basis for the following

  12. Existence of weak solutions to a nonlinear reaction-diffusion system with singular sources

    Directory of Open Access Journals (Sweden)

    Ida de Bonis

    2017-09-01

    Full Text Available We discuss the existence of a class of weak solutions to a nonlinear parabolic system of reaction-diffusion type endowed with singular production terms by reaction. The singularity is due to a potential occurrence of quenching localized to the domain boundary. The kind of quenching we have in mind is due to a twofold contribution: (i the choice of boundary conditions, modeling in our case the contact with an infinite reservoir filled with ready-to-react chemicals and (ii the use of a particular nonlinear, non-Lipschitz structure of the reaction kinetics. Our working techniques use fine energy estimates for approximating non-singular problems and uniform control on the set where singularities are localizing.

  13. Feedback systems for linear colliders

    CERN Document Server

    Hendrickson, L; Himel, Thomas M; Minty, Michiko G; Phinney, N; Raimondi, Pantaleo; Raubenheimer, T O; Shoaee, H; Tenenbaum, P G

    1999-01-01

    Feedback systems are essential for stable operation of a linear collider, providing a cost-effective method for relaxing tight tolerances. In the Stanford Linear Collider (SLC), feedback controls beam parameters such as trajectory, energy, and intensity throughout the accelerator. A novel dithering optimization system which adjusts final focus parameters to maximize luminosity contributed to achieving record performance in the 1997-98 run. Performance limitations of the steering feedback have been investigated, and improvements have been made. For the Next Linear Collider (NLC), extensive feedback systems are planned as an intregal part of the design. Feedback requiremetns for JLC (the Japanese Linear Collider) are essentially identical to NLC; some of the TESLA requirements are similar but there are significant differences. For NLC, algorithms which incorporate improvements upon the SLC implementation are being prototyped. Specialized systems for the damping rings, rf and interaction point will operate at hi...

  14. Window observers for linear systems

    Directory of Open Access Journals (Sweden)

    Utkin Vadim

    2000-01-01

    Full Text Available Given a linear system x ˙ = A x + B u with output y = C x and a window function ω ( t , i.e., ∀ t , ω ( t ∈ {0,1 }, and assuming that the window function is Lebesgue measurable, we refer to the following observer, x ˆ = A x + B u + ω ( t L C ( x − x ˆ as a window observer. The stability issue is treated in this paper. It is proven that for linear time-invariant systems, the window observer can be stabilized by an appropriate design under a very mild condition on the window functions, albeit for linear time-varying system, some regularity of the window functions is required to achieve observer designs with the asymptotic stability. The corresponding design methods are developed. An example is included to illustrate the possible applications

  15. Linear analysis of rotationally invariant, radially variant tomographic imaging systems

    International Nuclear Information System (INIS)

    Huesmann, R.H.

    1990-01-01

    This paper describes a method to analyze the linear imaging characteristics of rotationally invariant, radially variant tomographic imaging systems using singular value decomposition (SVD). When the projection measurements from such a system are assumed to be samples from independent and identically distributed multi-normal random variables, the best estimate of the emission intensity is given by the unweighted least squares estimator. The noise amplification of this estimator is inversely proportional to the singular values of the normal matrix used to model projection and backprojection. After choosing an acceptable noise amplification, the new method can determine the number of parameters and hence the number of pixels that should be estimated from data acquired from an existing system with a fixed number of angles and projection bins. Conversely, for the design of a new system, the number of angles and projection bins necessary for a given number of pixels and noise amplification can be determined. In general, computing the SVD of the projection normal matrix has cubic computational complexity. However, the projection normal matrix for this class of rotationally invariant, radially variant systems has a block circulant form. A fast parallel algorithm to compute the SVD of this block circulant matrix makes the singular value analysis practical by asymptotically reducing the computation complexity of the method by a multiplicative factor equal to the number of angles squared

  16. Linear collider systems and costs

    International Nuclear Information System (INIS)

    Loew, G.A.

    1993-05-01

    The purpose of this paper is to examine some of the systems and sub-systems involved in so-called ''conventional'' e + e - linear colliders and to study how their design affects the overall cost of these machines. There are presently a total of at least six 500 GeV c. of m. linear collider projects under study in the world. Aside from TESLA (superconducting linac at 1.3 GHz) and CLIC (two-beam accelerator with main linac at 30GHz), the other four proposed e + e - linear colliders can be considered ''conventional'' in that their main linacs use the proven technique of driving room temperature accelerator sections with pulsed klystrons and modulators. The centrally distinguishing feature between these projects is their main linac rf frequency: 3 GHz for the DESY machine, 11.424 GHz for the SLAC and JLC machines, and 14 GHz for the VLEPP machine. The other systems, namely the electron and positron sources, preaccelerators, compressors, damping rings and final foci, are fairly similar from project to project. Probably more than 80% of the cost of these linear colliders will be incurred in the two main linacs facing each other and it is therefore in their design and construction that major savings or extra costs may be found

  17. Detecting singular weak-dissipation limit for flutter onset in reversible systems

    Science.gov (United States)

    Bigoni, Davide; Misseroni, Diego; Tommasini, Mirko; Kirillov, Oleg N.; Noselli, Giovanni

    2018-02-01

    A "flutter machine" is introduced for the investigation of a singular interface between the classical and reversible Hopf bifurcations that is theoretically predicted to be generic in nonconservative reversible systems with vanishing dissipation. In particular, such a singular interface exists for the Pflüger viscoelastic column moving in a resistive medium, which is proven by means of the perturbation theory of multiple eigenvalues with the Jordan block. The laboratory setup, consisting of a cantilevered viscoelastic rod loaded by a positional force with nonzero curl produced by dry friction, demonstrates high sensitivity of the classical Hopf bifurcation onset to the ratio between the weak air drag and Kelvin-Voigt damping in the Pflüger column. Thus, the Whitney umbrella singularity is experimentally confirmed, responsible for discontinuities accompanying dissipation-induced instabilities in a broad range of physical contexts.

  18. Multipoint Singular Boundary-Value Problem for Systems of Nonlinear Differential Equations

    Directory of Open Access Journals (Sweden)

    Zdeněk Šmarda

    2009-01-01

    Full Text Available A singular Cauchy-Nicoletti problem for a system of nonlinear ordinary differential equations is considered. With the aid of combination of Ważewski's topological method and Schauder's principle, the theorem concerning the existence of a solution of this problem (having the graph in a prescribed domain is proved.

  19. Stability bound analysis of singularly perturbed systems with time-delay

    Directory of Open Access Journals (Sweden)

    Sun Fengqi

    2013-01-01

    Full Text Available This paper considers the stability bound problem of singularly perturbed systems with time-delay. Some stability criteria are derived by constructing appropriate Lyapunov-Krasovskii functionals. The proposed criteria are less conservative than the existing ones. Two numerical examples are given to illustrate the advantages and effectiveness of the proposed methods.

  20. Monodromy of a two degrees of freedom Liouville integrable system with many focus-focus singular points

    International Nuclear Information System (INIS)

    Cushman, Richard; Zhilinskii, Boris

    2002-01-01

    This letter deals with the global monodromy of singular Lagrangian toral fibrations defined by two degrees of freedom Liouville integrable systems with only focus-focus singular points. We show that any global monodromy matrix in Sl(2,Ζ ) is realizable by such a system. (author). Letter-to-the-editor

  1. Optimal control of dissipative nonlinear dynamical systems with triggers of coupled singularities

    International Nuclear Information System (INIS)

    Hedrih, K

    2008-01-01

    This paper analyses the controllability of motion of nonconservative nonlinear dynamical systems in which triggers of coupled singularities exist or appear. It is shown that the phase plane method is useful for the analysis of nonlinear dynamics of nonconservative systems with one degree of freedom of control strategies and also shows the way it can be used for controlling the relative motion in rheonomic systems having equivalent scleronomic conservative or nonconservative system For the system with one generalized coordinate described by nonlinear differential equation of nonlinear dynamics with trigger of coupled singularities, the functions of system potential energy and conservative force must satisfy some conditions defined by a Theorem on the existence of a trigger of coupled singularities and the separatrix in the form of 'an open a spiral form' of number eight. Task of the defined dynamical nonconservative system optimal control is: by using controlling force acting to the system, transfer initial state of the nonlinear dynamics of the system into the final state of the nonlinear dynamics in the minimal time for that optimal control task

  2. Optimal control of dissipative nonlinear dynamical systems with triggers of coupled singularities

    Energy Technology Data Exchange (ETDEWEB)

    Hedrih, K [Faculty of Mechanical Engineering University of Nis, Mathematical Institute SANU, ul. Vojvode Tankosic 3/V/22, 18000-Nis (Serbia)], E-mail: katica@masfak.ni.ac.yu, E-mail: khedrih@eunet.yu

    2008-02-15

    This paper analyses the controllability of motion of nonconservative nonlinear dynamical systems in which triggers of coupled singularities exist or appear. It is shown that the phase plane method is useful for the analysis of nonlinear dynamics of nonconservative systems with one degree of freedom of control strategies and also shows the way it can be used for controlling the relative motion in rheonomic systems having equivalent scleronomic conservative or nonconservative system For the system with one generalized coordinate described by nonlinear differential equation of nonlinear dynamics with trigger of coupled singularities, the functions of system potential energy and conservative force must satisfy some conditions defined by a Theorem on the existence of a trigger of coupled singularities and the separatrix in the form of 'an open a spiral form' of number eight. Task of the defined dynamical nonconservative system optimal control is: by using controlling force acting to the system, transfer initial state of the nonlinear dynamics of the system into the final state of the nonlinear dynamics in the minimal time for that optimal control task.

  3. A theoretical analysis of the feasibility of a singularity-induced micro-electroporation system.

    Directory of Open Access Journals (Sweden)

    Gregory D Troszak

    Full Text Available Electroporation, the permeabilization of the cell membrane lipid bilayer due to a pulsed electric field, has important implications in the biotechnology, medicine, and food industries. Traditional macro and micro-electroporation devices have facing electrodes, and require significant potential differences to induce electroporation. The goal of this theoretical study is to investigate the feasibility of singularity-induced micro-electroporation; an electroporation configuration aimed at minimizing the potential differences required to induce electroporation by separating adjacent electrodes with a nanometer-scale insulator. In particular, this study aims to understand the effect of (1 insulator thickness and (2 electrode kinetics on electric field distributions in the singularity-induced micro-electroporation configuration. A non-dimensional primary current distribution model of the micro-electroporation channel shows that while increasing insulator thickness results in smaller electric field magnitudes, electroporation can still be performed with insulators thick enough to be made with microfabrication techniques. Furthermore, a secondary current distribution model of the singularity-induced micro-electroporation configuration with inert platinum electrodes and water electrolyte indicates that electrode kinetics do not inhibit charge transfer to the extent that prohibitively large potential differences are required to perform electroporation. These results indicate that singularity-induced micro-electroporation could be used to develop an electroporation system that consumes minimal power, making it suitable for remote applications such as the sterilization of water and other liquids.

  4. On the use of blowup to study regularizations of singularities of piecewise smooth dynamical systems in R^3

    DEFF Research Database (Denmark)

    Kristiansen, Kristian Uldall; Hogan, S. J.

    2015-01-01

    approach by considering the case of a fold line. We quickly extend a main result of Reves and Seara in a simple manner. Then, for the two-fold singularity, we show that the regularized system only fully retains the features of the singular canards in the piecewise smooth system in the cases when...... the sliding region does not include a full sector of singular canards. In particular, we show that every locally unique primary singular canard persists the regularizing perturbation. For the case of a sector of primary singular canards, we show that the regularized system contains a canard, provided...... a certain nonresonance condition holds. Finally, we provide numerical evidence for the existence of secondary canards near resonance....

  5. Reduced-order model based active disturbance rejection control of hydraulic servo system with singular value perturbation theory.

    Science.gov (United States)

    Wang, Chengwen; Quan, Long; Zhang, Shijie; Meng, Hongjun; Lan, Yuan

    2017-03-01

    Hydraulic servomechanism is the typical mechanical/hydraulic double-dynamics coupling system with the high stiffness control and mismatched uncertainties input problems, which hinder direct applications of many advanced control approaches in the hydraulic servo fields. In this paper, by introducing the singular value perturbation theory, the original double-dynamics coupling model of the hydraulic servomechanism was reduced to a integral chain system. So that, the popular ADRC (active disturbance rejection control) technology could be directly applied to the reduced system. In addition, the high stiffness control and mismatched uncertainties input problems are avoided. The validity of the simplified model is analyzed and proven theoretically. The standard linear ADRC algorithm is then developed based on the obtained reduced-order model. Extensive comparative co-simulations and experiments are carried out to illustrate the effectiveness of the proposed method. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

  6. Linear operator inequalities for strongly stable weakly regular linear systems

    NARCIS (Netherlands)

    Curtain, RF

    2001-01-01

    We consider the question of the existence of solutions to certain linear operator inequalities (Lur'e equations) for strongly stable, weakly regular linear systems with generating operators A, B, C, 0. These operator inequalities are related to the spectral factorization of an associated Popov

  7. Homogenization in time of singularly perturbed mechanical systems

    CERN Document Server

    Bornemann, Folkmar

    1998-01-01

    This book is about the explicit elimination of fast oscillatory scales in dynamical systems, which is important for efficient computer-simulations and our understanding of model hierarchies. The author presents his new direct method, homogenization in time, based on energy principles and weak convergence techniques. How to use this method is shown in several general cases taken from classical and quantum mechanics. The results are applied to special problems from plasma physics, molecular dynamics and quantum chemistry. Background material from functional analysis is provided and explained to make this book accessible for a general audience of graduate students and researchers.

  8. Singular Eigenfunctions of Calogero-Sutherland Type Systems and How to Transform Them into Regular Ones

    Directory of Open Access Journals (Sweden)

    Edwin Langmann

    2007-02-01

    Full Text Available There exists a large class of quantum many-body systems of Calogero-Sutherland type where all particles can have different masses and coupling constants and which nevertheless are such that one can construct a complete (in a certain sense set of exact eigenfunctions and corresponding eigenvalues, explicitly. Of course there is a catch to this result: if one insists on these eigenfunctions to be square integrable then the corresponding Hamiltonian is necessarily non-hermitean (and thus provides an example of an exactly solvable PT-symmetric quantum-many body system, and if one insists on the Hamiltonian to be hermitean then the eigenfunctions are singular and thus not acceptable as quantum mechanical eigenfunctions. The standard Calogero-Sutherland Hamiltonian is special due to the existence of an integral operator which allows to transform these singular eigenfunctions into regular ones.

  9. The approximate solution of singular integro-differential equations systems on smooth contours in spaces Lp

    OpenAIRE

    Iu. Caraus

    1997-01-01

    This article generalizes the results which were obtained in the paper [1], written together with my scientific-adviser, doctor-habilitat, professor Zolotarevschi V. Theoretical foundation of the collocation method and of mechanical quadrature method for singular integro-differential equations systems (SIDE) in the case when the equations are given on a closed contour satisfying some conditions of smoothness, without their reduction to the unit circle, is given below. Let $\\Gamma $ be a s...

  10. Geometric Desingularization of a Cusp Singularity in Slow-Fast Systems with Applications to Zeeman's Examples

    NARCIS (Netherlands)

    Broer, Henk W.; Kaper, Tasso J.; Krupa, Martin

    2013-01-01

    The cusp singularity-a point at which two curves of fold points meet-is a prototypical example in Takens' classification of singularities in constrained equations, which also includes folds, folded saddles, folded nodes, among others. In this article, we study cusp singularities in singularly

  11. Singular Nonlinear H∞ Optimal Control Problem

    NARCIS (Netherlands)

    Schaft, A.J. van der

    1996-01-01

    The theory of nonlinear H∞ optimal control for affine nonlinear systems is extended to the more general context of singular H∞ optimal control of nonlinear systems using ideas from the linear H∞ theory. Our approach yields under certain assumptions a necessary and sufficient condition for

  12. Dynamic linearization system for a radiation gauge

    International Nuclear Information System (INIS)

    Panarello, J.A.

    1977-01-01

    The linearization system and process converts a high resolution non-linear analog input signal, representative of the thickness of an object, into a high resolution linear analog output signal suitable for use in driving a variety of output devices. The system requires only a small amount of memory for storing pre-calculated non-linear correction coefficients. The system channels the input signal to separate circuit paths so that it may be used directly to; locate an appropriate correction coefficient; develop a correction term after an appropriate correction coefficient is located; and develop a linearized signal having the same high resolution inherent in the input signal. The system processes the linearized signal to compensate for the possible errors introduced by radiation source noise. The processed linearized signal is the high resolution linear analog output signal which accurately represents the thickness of the object being gauged

  13. Algorithms for large scale singular value analysis of spatially variant tomography systems

    International Nuclear Information System (INIS)

    Cao-Huu, Tuan; Brownell, G.; Lachiver, G.

    1996-01-01

    The problem of determining the eigenvalues of large matrices occurs often in the design and analysis of modem tomography systems. As there is an interest in solving systems containing an ever-increasing number of variables, current research effort is being made to create more robust solvers which do not depend on some special feature of the matrix for convergence (e.g. block circulant), and to improve the speed of already known and understood solvers so that solving even larger systems in a reasonable time becomes viable. Our standard techniques for singular value analysis are based on sparse matrix factorization and are not applicable when the input matrices are large because the algorithms cause too much fill. Fill refers to the increase of non-zero elements in the LU decomposition of the original matrix A (the system matrix). So we have developed iterative solutions that are based on sparse direct methods. Data motion and preconditioning techniques are critical for performance. This conference paper describes our algorithmic approaches for large scale singular value analysis of spatially variant imaging systems, and in particular of PCR2, a cylindrical three-dimensional PET imager 2 built at the Massachusetts General Hospital (MGH) in Boston. We recommend the desirable features and challenges for the next generation of parallel machines for optimal performance of our solver

  14. On pole structure assignment in linear systems

    Czech Academy of Sciences Publication Activity Database

    Loiseau, J.-J.; Zagalak, Petr

    2009-01-01

    Roč. 82, č. 7 (2009), s. 1179-1192 ISSN 0020-7179 R&D Projects: GA ČR(CZ) GA102/07/1596 Institutional research plan: CEZ:AV0Z10750506 Keywords : linear systems * linear state feedback * pole structure assignment Subject RIV: BC - Control Systems Theory Impact factor: 1.124, year: 2009 http://library.utia.cas.cz/separaty/2009/AS/zagalak-on pole structure assignment in linear systems.pdf

  15. Linear systems and operators in Hilbert space

    CERN Document Server

    Fuhrmann, Paul A

    2014-01-01

    A treatment of system theory within the context of finite dimensional spaces, this text is appropriate for students with no previous experience of operator theory. The three-part approach, with notes and references for each section, covers linear algebra and finite dimensional systems, operators in Hilbert space, and linear systems in Hilbert space. 1981 edition.

  16. Dynamic stabilization of regular linear systems

    NARCIS (Netherlands)

    Weiss, G; Curtain, RF

    We consider a general class of infinite-dimensional linear systems, called regular linear systems, for which convenient representations are known to exist both in time and in frequency domain, For this class of systems, we investigate the concepts of stabilizability and detectability, in particular,

  17. Polynomial computation of Hankel singular values

    NARCIS (Netherlands)

    Kwakernaak, H.

    1992-01-01

    A revised and improved version of a polynomial algorithm is presented. It was published by N.J. Young (1990) for the computation of the singular values and vectors of the Hankel operator defined by a linear time-invariant system with a rotational transfer matrix. Tentative numerical experiments

  18. Displacement measurement system for linear array detector

    International Nuclear Information System (INIS)

    Zhang Pengchong; Chen Ziyu; Shen Ji

    2011-01-01

    It presents a set of linear displacement measurement system based on encoder. The system includes displacement encoders, optical lens and read out circuit. Displacement read out unit includes linear CCD and its drive circuit, two amplifier circuits, second order Butterworth low-pass filter and the binarization circuit. The coding way is introduced, and various parts of the experimental signal waveforms are given, and finally a linear experimental test results are given. The experimental results are satisfactory. (authors)

  19. Optimal control of singularly perturbed nonlinear systems with state-variable inequality constraints

    Science.gov (United States)

    Calise, A. J.; Corban, J. E.

    1990-01-01

    The established necessary conditions for optimality in nonlinear control problems that involve state-variable inequality constraints are applied to a class of singularly perturbed systems. The distinguishing feature of this class of two-time-scale systems is a transformation of the state-variable inequality constraint, present in the full order problem, to a constraint involving states and controls in the reduced problem. It is shown that, when a state constraint is active in the reduced problem, the boundary layer problem can be of finite time in the stretched time variable. Thus, the usual requirement for asymptotic stability of the boundary layer system is not applicable, and cannot be used to construct approximate boundary layer solutions. Several alternative solution methods are explored and illustrated with simple examples.

  20. Patterns and singular features of extreme fluctuational paths of a periodically driven system

    Energy Technology Data Exchange (ETDEWEB)

    Chen, Zhen, E-mail: czkillua@icloud.com; Liu, Xianbin, E-mail: xbliu@nuaa.edu.cn

    2016-05-20

    Large fluctuations of an overdamped periodically driven oscillating system are investigated theoretically and numerically in the limit of weak noise. Optimal paths fluctuating to certain point are given by statistical analysis using the concept of prehistory probability distribution. The validity of statistical results is verified by solutions of boundary value problem. Optimal paths are found to change topologically when terminating points lie at opposite side of a switching line. Patterns of extreme paths are plotted through a proper parameterization of Lagrangian manifold having complicated structures. Several extreme paths to the same point are obtained by multiple solutions of boundary value solutions. Actions along various extreme paths are calculated and associated analysis is performed in relation to the singular features of the patterns. - Highlights: • Both extreme and optimal paths are obtained by various methods. • Boundary value problems are solved to ensure the validity of statistical results. • Topological structure of Lagrangian manifold is considered. • Singularities of the pattern of extreme paths are studied.

  1. Homoclinic Solutions for a Class of Second Order Nonautonomous Singular Hamiltonian Systems

    Directory of Open Access Journals (Sweden)

    Ziheng Zhang

    2014-01-01

    Full Text Available We are concerned with the existence of homoclinic solutions for the following second order nonautonomous singular Hamiltonian systems u¨+atWuu=0, (HS where -∞singularity at 0≠ξ∈ℝN, and Wuu is the gradient of W at u. The novelty of this paper is that, for the case that N≥3 and (HS is nonautonomous (neither periodic nor almost periodic, we show that (HS possesses at least one nontrivial homoclinic solution. Our main hypotheses are the strong force condition of Gordon and the uniqueness of a global maximum of W. Different from the cases that (HS is autonomous at≡1 or (HS is periodic or almost periodic, as far as we know, this is the first result concerning the case that (HS is nonautonomous and N≥3. Besides the usual conditions on W, we need the assumption that a′t<0 for all t∈ℝ to guarantee the existence of homoclinic solution. Recent results in the literature are generalized and significantly improved.

  2. Examples of integrable and non-integrable systems on singular symplectic manifolds

    Science.gov (United States)

    Delshams, Amadeu; Kiesenhofer, Anna; Miranda, Eva

    2017-05-01

    We present a collection of examples borrowed from celestial mechanics and projective dynamics. In these examples symplectic structures with singularities arise naturally from regularization transformations, Appell's transformation or classical changes like McGehee coordinates, which end up blowing up the symplectic structure or lowering its rank at certain points. The resulting geometrical structures that model these examples are no longer symplectic but symplectic with singularities which are mainly of two types: bm-symplectic and m-folded symplectic structures. These examples comprise the three body problem as non-integrable exponent and some integrable reincarnations such as the two fixed-center problem. Given that the geometrical and dynamical properties of bm-symplectic manifolds and folded symplectic manifolds are well-understood [10-12,9,15,13,14,24,20,22,25,28], we envisage that this new point of view in this collection of examples can shed some light on classical long-standing problems concerning the study of dynamical properties of these systems seen from the Poisson viewpoint.

  3. On a conjecture on linear systems

    Indian Academy of Sciences (India)

    Green's conjecture; linear systems; hyper-elliptic curves. ... Sonica Anand linear systems. Let C be a smooth curve of genus g ≥ 2 and let L be a globally generated line bundle on C. The evaluation map gives rise to an exact sequence. 0 → E ..... The syzygies of canonically embedded curves were computed by Schreyer [8].

  4. Numerical solution of large sparse linear systems

    International Nuclear Information System (INIS)

    Meurant, Gerard; Golub, Gene.

    1982-02-01

    This note is based on one of the lectures given at the 1980 CEA-EDF-INRIA Numerical Analysis Summer School whose aim is the study of large sparse linear systems. The main topics are solving least squares problems by orthogonal transformation, fast Poisson solvers and solution of sparse linear system by iterative methods with a special emphasis on preconditioned conjuguate gradient method [fr

  5. Hamiltonian and Variational Linear Distributed Systems

    NARCIS (Netherlands)

    Rapisarda, P.; Trentelman, H.L.

    2002-01-01

    We use the formalism of bilinear- and quadratic differential forms in order to study Hamiltonian and variational linear distributed systems. It was shown that a system described by ordinary linear constant-coefficient differential equations is Hamiltonian if and only if it is variational. In this

  6. Balanced truncation for linear switched systems

    DEFF Research Database (Denmark)

    Petreczky, Mihaly; Wisniewski, Rafal; Leth, John-Josef

    2013-01-01

    In this paper, we present a theoretical analysis of the model reduction algorithm for linear switched systems from Shaker and Wisniewski (2011, 2009) and . This algorithm is a reminiscence of the balanced truncation method for linear parameter varying systems (Wood et al., 1996) [3]. Specifically...

  7. Linear systems on balancing chemical reaction problem

    Science.gov (United States)

    Kafi, R. A.; Abdillah, B.

    2018-01-01

    The concept of linear systems appears in a variety of applications. This paper presents a small sample of the wide variety of real-world problems regarding our study of linear systems. We show that the problem in balancing chemical reaction can be described by homogeneous linear systems. The solution of the systems is obtained by performing elementary row operations. The obtained solution represents the finding coefficients of chemical reaction. In addition, we present a computational calculation to show that mathematical software such as Matlab can be used to simplify completion of the systems, instead of manually using row operations.

  8. The mathematics of networks of linear systems

    CERN Document Server

    Fuhrmann, Paul A

    2015-01-01

    This book provides the mathematical foundations of networks of linear control systems, developed from an algebraic systems theory perspective. This includes a thorough treatment of questions of controllability, observability, realization theory, as well as feedback control and observer theory. The potential of networks for linear systems in controlling large-scale networks of interconnected dynamical systems could provide insight into a diversity of scientific and technological disciplines. The scope of the book is quite extensive, ranging from introductory material to advanced topics of current research, making it a suitable reference for graduate students and researchers in the field of networks of linear systems. Part I can be used as the basis for a first course in algebraic system theory, while Part II serves for a second, advanced, course on linear systems. Finally, Part III, which is largely independent of the previous parts, is ideally suited for advanced research seminars aimed at preparing graduate ...

  9. Linear and Branching System Metrics

    NARCIS (Netherlands)

    J., Hilston; de Alfaro, Luca; Faella, Marco; M.Z., Kwiatkowska; Telek, M.; Stoelinga, Mariëlle Ida Antoinette

    We extend the classical system relations of trace inclusion, trace equivalence, simulation, and bisimulation to a quantitative setting in which propositions are interpreted not as boolean values, but as elements of arbitrary metric spaces. Trace inclusion and equivalence give rise to asymmetrical

  10. Non-isothermal Smoluchowski-Poisson equation as a singular limit of the Navier-Stokes-Fourier-Poisson system

    Czech Academy of Sciences Publication Activity Database

    Feireisl, Eduard; Laurençot, P.

    2007-01-01

    Roč. 88, - (2007), s. 325-349 ISSN 0021-7824 R&D Projects: GA ČR GA201/05/0164 Institutional research plan: CEZ:AV0Z10190503 Keywords : Navier-Stokes-Fourier- Poisson system * Smoluchowski- Poisson system * singular limit Subject RIV: BA - General Mathematics Impact factor: 1.118, year: 2007

  11. The approximate solution of singular integro-differential equations systems on smooth contours in spaces Lp

    Directory of Open Access Journals (Sweden)

    Iu. Caraus

    1997-08-01

    Full Text Available This article generalizes the results which were obtained in the paper [1], written together with my scientific-adviser, doctor-habilitat, professor Zolotarevschi V. Theoretical foundation of the collocation method and of mechanical quadrature method for singular integro-differential equations systems (SIDE in the case when the equations are given on a closed contour satisfying some conditions of smoothness, without their reduction to the unit circle, is given below. Let $\\Gamma $ be a smooth Jordan border limiting the one-spanned area $F^{+}$, containing a point $ t=0$, $ F^{-}= C \\setminus \\{ F^{+}\\cup \\Gamma \\}$, $C $ is a full complex plane. Let $z= \\psi (w-$ be a function, mapping comformally and single-valuedly the surface $\\Gamma_{0}=\\{|w| >1 \\} $ on $F^{-} $ so that $ \\psi (\\infty = \\infty ,\\psi^{ (\\prime }(\\infty >0$. We shall assume that the function $ z= \\psi (w$ has its second derivative, satisfying on $\\Gamma_{0} $ the H\\"older condition with some parameter $ \

  12. Linear heating system for measurement of thermoluminescence ...

    Indian Academy of Sciences (India)

    Unknown

    scence intensity is monitored. The theory of TL usually assumes that the sample temperature varies linearly with time, although more general theories have been formu- lated and calculations made for non-linear heating system. Previous descriptions of apparatus for the measurement of TL have been published elsewhere ...

  13. Isolators Including Main Spring Linear Guide Systems

    Science.gov (United States)

    Goold, Ryan (Inventor); Buchele, Paul (Inventor); Hindle, Timothy (Inventor); Ruebsamen, Dale Thomas (Inventor)

    2017-01-01

    Embodiments of isolators, such as three parameter isolators, including a main spring linear guide system are provided. In one embodiment, the isolator includes first and second opposing end portions, a main spring mechanically coupled between the first and second end portions, and a linear guide system extending from the first end portion, across the main spring, and toward the second end portion. The linear guide system expands and contracts in conjunction with deflection of the main spring along the working axis, while restricting displacement and rotation of the main spring along first and second axes orthogonal to the working axis.

  14. Stochastic stability properties of jump linear systems

    Science.gov (United States)

    Feng, Xiangbo; Loparo, Kenneth A.; Ji, Yuandong; Chizeck, Howard J.

    1992-01-01

    Jump linear systems are defined as a family of linear systems with randomly jumping parameters (usually governed by a Markov jump process) and are used to model systems subject to failures or changes in structure. The authors study stochastic stability properties in jump linear systems and the relationship among various moment and sample path stability properties. It is shown that all second moment stability properties are equivalent and are sufficient for almost sure sample path stability, and a testable necessary and sufficient condition for second moment stability is derived. The Lyapunov exponent method for the study of almost sure sample stability is discussed, and a theorem which characterizes the Lyapunov exponents of jump linear systems is presented.

  15. Linear systems a measurement based approach

    CERN Document Server

    Bhattacharyya, S P; Mohsenizadeh, D N

    2014-01-01

    This brief presents recent results obtained on the analysis, synthesis and design of systems described by linear equations. It is well known that linear equations arise in most branches of science and engineering as well as social, biological and economic systems. The novelty of this approach is that no models of the system are assumed to be available, nor are they required. Instead, a few measurements made on the system can be processed strategically to directly extract design values that meet specifications without constructing a model of the system, implicitly or explicitly. These new concepts are illustrated by applying them to linear DC and AC circuits, mechanical, civil and hydraulic systems, signal flow block diagrams and control systems. These applications are preliminary and suggest many open problems. The results presented in this brief are the latest effort in this direction and the authors hope these will lead to attractive alternatives to model-based design of engineering and other systems.

  16. Synchronization of linear systems via relative actuation

    OpenAIRE

    Tuna, S. Emre

    2016-01-01

    Synchronization in networks of discrete-time linear time-invariant systems is considered under relative actuation. Neither input nor output matrices are assumed to be commensurable. A distributed algorithm that ensures synchronization via dynamic relative output feedback is presented.

  17. Singular value decomposition for photon-processing nuclear imaging systems and applications for reconstruction and computing null functions.

    Science.gov (United States)

    Jha, Abhinav K; Barrett, Harrison H; Frey, Eric C; Clarkson, Eric; Caucci, Luca; Kupinski, Matthew A

    2015-09-21

    Recent advances in technology are enabling a new class of nuclear imaging systems consisting of detectors that use real-time maximum-likelihood (ML) methods to estimate the interaction position, deposited energy, and other attributes of each photon-interaction event and store these attributes in a list format. This class of systems, which we refer to as photon-processing (PP) nuclear imaging systems, can be described by a fundamentally different mathematical imaging operator that allows processing of the continuous-valued photon attributes on a per-photon basis. Unlike conventional photon-counting (PC) systems that bin the data into images, PP systems do not have any binning-related information loss. Mathematically, while PC systems have an infinite-dimensional null space due to dimensionality considerations, PP systems do not necessarily suffer from this issue. Therefore, PP systems have the potential to provide improved performance in comparison to PC systems. To study these advantages, we propose a framework to perform the singular-value decomposition (SVD) of the PP imaging operator. We use this framework to perform the SVD of operators that describe a general two-dimensional (2D) planar linear shift-invariant (LSIV) PP system and a hypothetical continuously rotating 2D single-photon emission computed tomography (SPECT) PP system. We then discuss two applications of the SVD framework. The first application is to decompose the object being imaged by the PP imaging system into measurement and null components. We compare these components to the measurement and null components obtained with PC systems. In the process, we also present a procedure to compute the null functions for a PC system. The second application is designing analytical reconstruction algorithms for PP systems. The proposed analytical approach exploits the fact that PP systems acquire data in a continuous domain to estimate a continuous object function. The approach is parallelizable and

  18. Robust Stability Analysis of the Space Launch System Control Design: A Singular Value Approach

    Science.gov (United States)

    Pei, Jing; Newsome, Jerry R.

    2015-01-01

    Classical stability analysis consists of breaking the feedback loops one at a time and determining separately how much gain or phase variations would destabilize the stable nominal feedback system. For typical launch vehicle control design, classical control techniques are generally employed. In addition to stability margins, frequency domain Monte Carlo methods are used to evaluate the robustness of the design. However, such techniques were developed for Single-Input-Single-Output (SISO) systems and do not take into consideration the off-diagonal terms in the transfer function matrix of Multi-Input-Multi-Output (MIMO) systems. Robust stability analysis techniques such as H(sub infinity) and mu are applicable to MIMO systems but have not been adopted as standard practices within the launch vehicle controls community. This paper took advantage of a simple singular-value-based MIMO stability margin evaluation method based on work done by Mukhopadhyay and Newsom and applied it to the SLS high-fidelity dynamics model. The method computes a simultaneous multi-loop gain and phase margin that could be related back to classical margins. The results presented in this paper suggest that for the SLS system, traditional SISO stability margins are similar to the MIMO margins. This additional level of verification provides confidence in the robustness of the control design.

  19. Dynamical systems generated by linear maps

    CERN Document Server

    Dolićanin, Ćemal B

    2014-01-01

    The book deals with dynamical systems, generated by linear mappings of finite dimensional spaces and their applications. These systems have a relatively simple structure from the point of view of the modern dynamical systems theory. However, for the dynamical systems of this sort, it is possible to obtain explicit answers to specific questions being useful in applications. The considered problems are natural and look rather simple, but in reality in the course of investigation, they confront users with plenty of subtle questions, and their detailed analysis needs a substantial effort. The problems arising are related to linear algebra and dynamical systems theory, and therefore, the book can be considered as a natural amplification, refinement and supplement to linear algebra and dynamical systems theory textbooks.

  20. Algorithms in Singular

    Directory of Open Access Journals (Sweden)

    Hans Schonemann

    1996-12-01

    Full Text Available Some algorithms for singularity theory and algebraic geometry The use of Grobner basis computations for treating systems of polynomial equations has become an important tool in many areas. This paper introduces of the concept of standard bases (a generalization of Grobner bases and the application to some problems from algebraic geometry. The examples are presented as SINGULAR commands. A general introduction to Grobner bases can be found in the textbook [CLO], an introduction to syzygies in [E] and [St1]. SINGULAR is a computer algebra system for computing information about singularities, for use in algebraic geometry. The basic algorithms in SINGULAR are several variants of a general standard basis algorithm for general monomial orderings (see [GG]. This includes wellorderings (Buchberger algorithm ([B1], [B2] and tangent cone orderings (Mora algorithm ([M1], [MPT] as special cases: It is able to work with non-homogeneous and homogeneous input and also to compute in the localization of the polynomial ring in 0. Recent versions include algorithms to factorize polynomials and a factorizing Grobner basis algorithm. For a complete description of SINGULAR see [Si].

  1. Application of linear prediction and singular value decomposition for the analysis of periodic oscillations in coherent excitation spectra of condensed media and solid interfaces.

    Science.gov (United States)

    Hoogestraat, D; Al-Shamery, K

    2010-03-03

    The observation of periodic responses after absorption of ultrashort laser pulses in condensed media and at solid interfaces is a common phenomena in various time-resolved spectroscopic methods using laser pulses shorter than the period of the coherently excited vibrations. Normally these signals have to be separated from strong slowly decaying backgrounds related to the creation of nonequilibrium carriers. The recording normally requires either a small period of time or lacks temporal resolution to obtain the good signal-to-noise ratio necessary for the observation of the vibrations. The standard method used for the analysis of the data is a curve-fitting routine to the time-domain data. However, the disadvantage is the necessity to estimate the number of spectral components before fitting. This paper will introduce under which conditions linear prediction and singular value decomposition in combination with an iterative nonlinear fitting in the time and spectral domain may extract an unknown number of spectral components including amplitude, lifetime, frequency and phase. Such information is essential to unambiguously evaluate the dominant optical excitation process, the phase of the initial displacement, the symmetry of the excited vibrational mode and the specific vibration generation process.

  2. Correlated Levy Noise in Linear Dynamical Systems

    International Nuclear Information System (INIS)

    Srokowski, T.

    2011-01-01

    Linear dynamical systems, driven by a non-white noise which has the Levy distribution, are analysed. Noise is modelled by a specific stochastic process which is defined by the Langevin equation with a linear force and the Levy distributed symmetric white noise. Correlation properties of the process are discussed. The Fokker-Planck equation driven by that noise is solved. Distributions have the Levy shape and their width, for a given time, is smaller than for processes in the white noise limit. Applicability of the adiabatic approximation in the case of the linear force is discussed. (author)

  3. Robust Fault Estimation for a Class of T-S Fuzzy Singular Systems with Time-Varying Delay via Improved Delay Partitioning Approach

    Directory of Open Access Journals (Sweden)

    Chao Sun

    2016-01-01

    Full Text Available The problem of delay-dependent robust fault estimation for a class of Takagi-Sugeno (T-S fuzzy singular systems is investigated. By decomposing the delay interval into two unequal subintervals and with a new and tighter integral inequality transformation, an improved delay-dependent stability criterion is given in terms of linear matrix inequalities (LMIs to guarantee that the fuzzy singular system with time-varying delay is regular, impulse-free, and stable firstly. Then, based on this criterion, by considering the system fault as an auxiliary disturbance vector and constructing an appropriate fuzzy augmented system, a fault estimation observer is designed to ensure that the error dynamic system is regular, impulse-free, and robustly stable with a prescribed H∞ performance satisfied for all actuator and sensor faults simultaneously, and the obtained fault estimates can practically better depict the size and shape of the faults. Finally, numerical examples are given to show the effectiveness of the proposed approach.

  4. Study of microarray time series data based on Forward-Backward Linear Prediction and Singular Value Decomposition.

    Science.gov (United States)

    Choong, Miew Keen; Levy, David; Yan, Hong

    2009-01-01

    We propose a method to analyse the periodicities of gene expression profiles based on the spectral domain approach. Our spectral reconstruction method outperforms three other recently proposed methods, which do not require any prior knowledge. It is proven that an alternative method for studying cell-cycle regulation is possible even where very little prior knowledge is available. We also investigate the potential of combining signals with similar frequency components to form an overdetermined system of equations, and use least squares solution to estimate the spectral frequency. Results show that this new method is able to estimate the peak frequency more accurately.

  5. Received Signal Strength Recovery in Green WLAN Indoor Positioning System Using Singular Value Thresholding

    Directory of Open Access Journals (Sweden)

    Lin Ma

    2015-01-01

    Full Text Available Green WLAN is a promising technique for accessing future indoor Internet services. It is designed not only for high-speed data communication purposes but also for energy efficiency. The basic strategy of green WLAN is that all the access points are not always powered on, but rather work on-demand. Though powering off idle access points does not affect data communication, a serious asymmetric matching problem will arise in a WLAN indoor positioning system due to the fact the received signal strength (RSS readings from the available access points are different in their offline and online phases. This asymmetry problem will no doubt invalidate the fingerprint algorithm used to estimate the mobile device location. Therefore, in this paper we propose a green WLAN indoor positioning system, which can recover RSS readings and achieve good localization performance based on singular value thresholding (SVT theory. By solving the nuclear norm minimization problem, SVT recovers not only the radio map, but also online RSS readings from a sparse matrix by sensing only a fraction of the RSS readings. We have implemented the method in our lab and evaluated its performances. The experimental results indicate the proposed system could recover the RSS readings and achieve good localization performance.

  6. Geometric Control of Patterned Linear Systems

    CERN Document Server

    Hamilton, Sarah C

    2012-01-01

    This monograph is aiming at researchers of systems control, especially those interested in multiagent systems, distributed and decentralized control, and structured systems. The book assumes no prior background in geometric control theory; however, a first year graduate course in linear control systems is desirable.  Since not all control researchers today are exposed to geometric control theory, the book also adopts a tutorial style by way of examples that illustrate the geometric and abstract algebra concepts used in linear geometric control. In addition, the matrix calculations required for the studied control synthesis problems of linear multivariable control are illustrated via a set of running design examples. As such, some of the design examples are of higher dimension than one may typically see in a text; this is so that all the geometric features of the design problem are illuminated.

  7. Fault tolerant control for switched linear systems

    CERN Document Server

    Du, Dongsheng; Shi, Peng

    2015-01-01

    This book presents up-to-date research and novel methodologies on fault diagnosis and fault tolerant control for switched linear systems. It provides a unified yet neat framework of filtering, fault detection, fault diagnosis and fault tolerant control of switched systems. It can therefore serve as a useful textbook for senior and/or graduate students who are interested in knowing the state-of-the-art of filtering, fault detection, fault diagnosis and fault tolerant control areas, as well as recent advances in switched linear systems.  

  8. Linear response theory for quantum open systems

    OpenAIRE

    Wei, J. H.; Yan, YiJing

    2011-01-01

    Basing on the theory of Feynman's influence functional and its hierarchical equations of motion, we develop a linear response theory for quantum open systems. Our theory provides an effective way to calculate dynamical observables of a quantum open system at its steady-state, which can be applied to various fields of non-equilibrium condensed matter physics.

  9. Controller Reconfiguration for non-linear systems

    NARCIS (Netherlands)

    Kanev, S.K.; Verhaegen, M.H.G.

    2000-01-01

    This paper outlines an algorithm for controller reconfiguration for non-linear systems, based on a combination of a multiple model estimator and a generalized predictive controller. A set of models is constructed, each corresponding to a different operating condition of the system. The interacting

  10. When to call a linear system nonnegative

    NARCIS (Netherlands)

    Nieuwenhuis, J.W.

    1998-01-01

    In this paper we will consider discrete time invariant linear systems that allow for an input-state-output representation with a finite dimensional state space, and that have a finite number of inputs and outputs. The basic issue in this paper is when to call these systems nonnegative. An important

  11. Iris identification system based on Fourier coefficients and singular value decomposition

    Science.gov (United States)

    Somnugpong, Sawet; Phimoltares, Suphakant; Maneeroj, Saranya

    2011-12-01

    Nowadays, both personal identification and classification are very important. In order to identify the person for some security applications, physical or behavior-based characteristics of individuals with high uniqueness might be analyzed. Biometric becomes the mostly used in personal identification purpose. There are many types of biometric information currently used. In this work, iris, one kind of personal characteristics is considered because of its uniqueness and collectable. Recently, the problem of various iris recognition systems is the limitation of space to store the data in a variety of environments. This work proposes the iris recognition system with small-size of feature vector causing a reduction in space complexity term. For this experiment, each iris is presented in terms of frequency domain, and based on neural network classification model. First, Fast Fourier Transform (FFT) is used to compute the Discrete Fourier Coefficients of iris data in frequency domain. Once the iris data was transformed into frequency-domain matrix, Singular Value Decomposition (SVD) is used to reduce a size of the complex matrix to single vector. All of these vectors would be input for neural networks for the classification step. With this approach, the merit of our technique is that size of feature vector is smaller than that of other techniques with the acceptable level of accuracy when compared with other existing techniques.

  12. Conduction cooling systems for linear accelerator cavities

    Science.gov (United States)

    Kephart, Robert

    2017-05-02

    A conduction cooling system for linear accelerator cavities. The system conducts heat from the cavities to a refrigeration unit using at least one cavity cooler interconnected with a cooling connector. The cavity cooler and cooling connector are both made from solid material having a very high thermal conductivity of approximately 1.times.10.sup.4 W m.sup.-1 K.sup.-1 at temperatures of approximately 4 degrees K. This allows for very simple and effective conduction of waste heat from the linear accelerator cavities to the cavity cooler, along the cooling connector, and thence to the refrigeration unit.

  13. Chaos as an intermittently forced linear system.

    Science.gov (United States)

    Brunton, Steven L; Brunton, Bingni W; Proctor, Joshua L; Kaiser, Eurika; Kutz, J Nathan

    2017-05-30

    Understanding the interplay of order and disorder in chaos is a central challenge in modern quantitative science. Approximate linear representations of nonlinear dynamics have long been sought, driving considerable interest in Koopman theory. We present a universal, data-driven decomposition of chaos as an intermittently forced linear system. This work combines delay embedding and Koopman theory to decompose chaotic dynamics into a linear model in the leading delay coordinates with forcing by low-energy delay coordinates; this is called the Hankel alternative view of Koopman (HAVOK) analysis. This analysis is applied to the Lorenz system and real-world examples including Earth's magnetic field reversal and measles outbreaks. In each case, forcing statistics are non-Gaussian, with long tails corresponding to rare intermittent forcing that precedes switching and bursting phenomena. The forcing activity demarcates coherent phase space regions where the dynamics are approximately linear from those that are strongly nonlinear.The huge amount of data generated in fields like neuroscience or finance calls for effective strategies that mine data to reveal underlying dynamics. Here Brunton et al.develop a data-driven technique to analyze chaotic systems and predict their dynamics in terms of a forced linear model.

  14. Dual-range linearized transimpedance amplifier system

    Science.gov (United States)

    Wessendorf, Kurt O.

    2010-11-02

    A transimpedance amplifier system is disclosed which simultaneously generates a low-gain output signal and a high-gain output signal from an input current signal using a single transimpedance amplifier having two different feedback loops with different amplification factors to generate two different output voltage signals. One of the feedback loops includes a resistor, and the other feedback loop includes another resistor in series with one or more diodes. The transimpedance amplifier system includes a signal linearizer to linearize one or both of the low- and high-gain output signals by scaling and adding the two output voltage signals from the transimpedance amplifier. The signal linearizer can be formed either as an analog device using one or two summing amplifiers, or alternately can be formed as a digital device using two analog-to-digital converters and a digital signal processor (e.g. a microprocessor or a computer).

  15. Final focus systems for linear colliders

    International Nuclear Information System (INIS)

    Helm, R.; Irwing, J.

    1992-01-01

    Final focus systems for linear colliders present many exacting challenges in beam optics, component design, and beam quality. Efforts to resolve these problems as they relate to a new generation of linear colliders are under way at several laboratories around the world. We outline criteria for final focus systems and discuss the current state of understanding and resolution of the outstanding problems. We discuss tolerances on alignment, field quality and stability for optical elements, and the implications for beam parameters such as emittance, energy spread , bunch length, and stability in position and energy. Beam-based correction procedures, which in principle can alleviate many of the tolerances, are described. Preliminary results from the Final Focus Test Beam (FFTB) under construction at SLAC are given. Finally, we mention conclusions from operating experience at the Stanford Linear Collider (SLC). (Author) 16 refs., 4 tabs., 6 figs

  16. Final focus systems for linear colliders

    International Nuclear Information System (INIS)

    Helm, R.; Irwin, J.

    1992-08-01

    Final focus systems for linear colliders present many exacting challenges in beam optics, component design, and beam quality. Efforts to resolve these problems as they relate to a new generation of linear colliders are under way at several laboratories around the world. We will outline criteria for final focus systems and discuss the current state of understanding and resolution of the outstanding problems. We will discuss tolerances on alignment, field quality and stability for optical elements, and the implications for beam parameters such as emittance, energy spread, bunch length, and stability in position and energy. Beam-based correction procedures, which in principle can alleviate many of the tolerances, will be described. Preliminary results from the Final Focus Test Beam (FFTB) under construction at SLAC will be given. Finally, we mention conclusions from operating experience at the Stanford Linear Collider (SLC)

  17. On exponential stabilizability of linear neutral systems

    Directory of Open Access Journals (Sweden)

    Dusser Xavier

    2001-01-01

    Full Text Available In this paper, we deal with linear neutral functional differential systems. Using an extended state space and an extended control operator, we transform the initial neutral system in an infinite dimensional linear system. We give a sufficient condition for admissibility of the control operator B , conditions under which operator B can be acceptable in order to work with controllability and stabilizability. Necessary and sufficient conditions for exact controllability are provided; in terms of a gramian of controllability N ( μ . Assuming admissibility and exact controllability, a feedback control law is defined from the inverse of the operator N ( μ in order to stabilize exponentially the closed loop system. In this case, the semigroup generated by the closed loop system has an arbitrary decay rate.

  18. Singular vectors, predictability and ensemble forecasting for weather and climate

    International Nuclear Information System (INIS)

    Palmer, T N; Zanna, Laure

    2013-01-01

    The local instabilities of a nonlinear dynamical system can be characterized by the leading singular vectors of its linearized operator. The leading singular vectors are perturbations with the greatest linear growth and are therefore key in assessing the system’s predictability. In this paper, the analysis of singular vectors for the predictability of weather and climate and ensemble forecasting is discussed. An overview of the role of singular vectors in informing about the error growth rate in numerical models of the atmosphere is given. This is followed by their use in the initialization of ensemble weather forecasts. Singular vectors for the ocean and coupled ocean–atmosphere system in order to understand the predictability of climate phenomena such as ENSO and meridional overturning circulation are reviewed and their potential use to initialize seasonal and decadal forecasts is considered. As stochastic parameterizations are being implemented, some speculations are made about the future of singular vectors for the predictability of weather and climate for theoretical applications and at the operational level. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Lyapunov analysis: from dynamical systems theory to applications’. (review)

  19. Application of matrix singular value properties for evaluating gain and phase margins of multiloop systems. [stability margins for wing flutter suppression and drone lateral attitude control

    Science.gov (United States)

    Mukhopadhyay, V.; Newsom, J. R.

    1982-01-01

    A stability margin evaluation method in terms of simultaneous gain and phase changes in all loops of a multiloop system is presented. A universal gain-phase margin evaluation diagram is constructed by generalizing an existing method using matrix singular value properties. Using this diagram and computing the minimum singular value of the system return difference matrix over the operating frequency range, regions of guaranteed stability margins can be obtained. Singular values are computed for a wing flutter suppression and a drone lateral attitude control problem. The numerical results indicate that this method predicts quite conservative stability margins. In the second example if the eigenvalue magnitude is used instead of the singular value, as a measure of nearness to singularity, more realistic stability margins are obtained. However, this relaxed measure generally cannot guarantee global stability.

  20. Bisimulation theory for switching linear systems

    NARCIS (Netherlands)

    Pola, G.; van der Schaft, Arjan; Di Benedetto, Maria D.

    2004-01-01

    A general notion of hybrid bisimulation is proposed and related to the notions of algebraic, state-space and input-output equivalences for the class of switching linear systems. An algebraic characterization of hybrid bisimulations and a procedure converging in a finite number of steps to the

  1. Disturbance Decoupling of Switched Linear Systems

    NARCIS (Netherlands)

    Yurtseven, E.; Heemels, W.P.M.H.; Camlibel, M.K.

    2010-01-01

    In this paper we consider disturbance decoupling problems for switched linear systems. We will provide necessary and sufficient conditions for three different versions of disturbance decoupling, which differ based on which signals are considered to be the disturbance. In the first version the

  2. Consys Linear Control System Design Software Package

    International Nuclear Information System (INIS)

    Diamantidis, Z.

    1987-01-01

    This package is created in order to help engineers, researchers, students and all who work on linear control systems. The software includes all time and frequency domain analysises, spectral analysises and networks, active filters and regulators design aids. The programmes are written on Hewlett Packard computer in Basic 4.0

  3. Microwave Feeding System Devices Of Linear Collider

    CERN Document Server

    Bogdanovich, B Yu; Kaminsky, V I; Lalayan, M V; Sobenin, N P; Zavadtsev, D A

    2004-01-01

    The simulations, manufacturing and experimental results for two devices of linear collider RF power distribution system are presented. One of these devices is magic tee with movable choke plungers in E- and H-arms for the tuning the coupling-factor and RF phase of highpower accelerating cavities. The QEXT

  4. Linear covariance analysis for gimbaled pointing systems

    Science.gov (United States)

    Christensen, Randall S.

    Linear covariance analysis has been utilized in a wide variety of applications. Historically, the theory has made significant contributions to navigation system design and analysis. More recently, the theory has been extended to capture the combined effect of navigation errors and closed-loop control on the performance of the system. These advancements have made possible rapid analysis and comprehensive trade studies of complicated systems ranging from autonomous rendezvous to vehicle ascent trajectory analysis. Comprehensive trade studies are also needed in the area of gimbaled pointing systems where the information needs are different from previous applications. It is therefore the objective of this research to extend the capabilities of linear covariance theory to analyze the closed-loop navigation and control of a gimbaled pointing system. The extensions developed in this research include modifying the linear covariance equations to accommodate a wider variety of controllers. This enables the analysis of controllers common to gimbaled pointing systems, with internal states and associated dynamics as well as actuator command filtering and auxiliary controller measurements. The second extension is the extraction of power spectral density estimates from information available in linear covariance analysis. This information is especially important to gimbaled pointing systems where not just the variance but also the spectrum of the pointing error impacts the performance. The extended theory is applied to a model of a gimbaled pointing system which includes both flexible and rigid body elements as well as input disturbances, sensor errors, and actuator errors. The results of the analysis are validated by direct comparison to a Monte Carlo-based analysis approach. Once the developed linear covariance theory is validated, analysis techniques that are often prohibitory with Monte Carlo analysis are used to gain further insight into the system. These include the creation

  5. Collimation systems in the next linear collider

    International Nuclear Information System (INIS)

    Merminga, N.; Irwin, J.; Helm, R.; Ruth, R.D.

    1991-02-01

    Experience indicates that beam collimation will be an essential element of the next generation e + E - linear colliders. A proposal for using nonlinear lenses to drive beam tails to large amplitudes was presented in a previous paper. Here we study the optimization of such systems including effects of wakefields and optical aberrations. Protection and design of the scrapers in these systems are discussed. 9 refs., 7 figs

  6. H∞ Filtering for Discrete Markov Jump Singular Systems with Mode-Dependent Time Delay Based on T-S Fuzzy Model

    Directory of Open Access Journals (Sweden)

    Cheng Gong

    2014-01-01

    Full Text Available This paper investigates the H∞ filtering problem of discrete singular Markov jump systems (SMJSs with mode-dependent time delay based on T-S fuzzy model. First, by Lyapunov-Krasovskii functional approach, a delay-dependent sufficient condition on H∞-disturbance attenuation is presented, in which both stability and prescribed H∞ performance are required to be achieved for the filtering-error systems. Then, based on the condition, the delay-dependent H∞ filter design scheme for SMJSs with mode-dependent time delay based on T-S fuzzy model is developed in term of linear matrix inequality (LMI. Finally, an example is given to illustrate the effectiveness of the result.

  7. An Explicit Formulation of Singularity-Free Dynamic Equations of Mechanical Systems in Lagrangian Form---Part Two: Multibody Systems

    Directory of Open Access Journals (Sweden)

    Pål Johan From

    2012-04-01

    Full Text Available This paper presents the explicit dynamic equations of multibody mechanical systems. This is the second paper on this topic. In the first paper the dynamics of a single rigid body from the Boltzmann--Hamel equations were derived. In this paper these results are extended to also include multibody systems. We show that when quasi-velocities are used, the part of the dynamic equations that appear from the partial derivatives of the system kinematics are identical to the single rigid body case, but in addition we get terms that come from the partial derivatives of the inertia matrix, which are not present in the single rigid body case. We present for the first time the complete and correct derivation of multibody systems based on the Boltzmann--Hamel formulation of the dynamics in Lagrangian form where local position and velocity variables are used in the derivation to obtain the singularity-free dynamic equations. The final equations are written in global variables for both position and velocity. The main motivation of these papers is to allow practitioners not familiar with differential geometry to implement the dynamic equations of rigid bodies without the presence of singularities. Presenting the explicit dynamic equations also allows for more insight into the dynamic structure of the system. Another motivation is to correct some errors commonly found in the literature. Unfortunately, the formulation of the Boltzmann-Hamel equations used here are presented incorrectly. This has been corrected by the authors, but we present here, for the first time, the detailed mathematical details on how to arrive at the correct equations. We also show through examples that using the equations presented here, the dynamics of a single rigid body is reduced to the standard equations on a Lagrangian form, for example Euler's equations for rotational motion and Euler--Lagrange equations for free motion.

  8. Stability problems for linear hyperbolic systems

    International Nuclear Information System (INIS)

    Eckhoff, K.S.

    1975-05-01

    The stability properties for the trivial solution of a general linear hyperbolic system of partial differential equations of the first order are studied. It is shown that results may be obtained by studying the stability properties of certain systems of ordinary differential equations which can be constructed from the hyperbolic system (the so-called transport equations). In some cases the associated stability problem for the transport equations can in fact be shown to be equivalent to the stability problem for the hyperbolic system, but in general the transport equations will only give the necessary conditions for stability. (Auth.)

  9. Sampling strategies based on singular vectors for assimilated models in ocean forecasting systems

    Science.gov (United States)

    Fattorini, Maria; Brandini, Carlo; Ortolani, Alberto

    2016-04-01

    Meteorological and oceanographic models do need observations, not only as a ground truth element to verify the quality of the models, but also to keep model forecast error acceptable: through data assimilation techniques which merge measured and modelled data, natural divergence of numerical solutions from reality can be reduced / controlled and a more reliable solution - called analysis - is computed. Although this concept is valid in general, its application, especially in oceanography, raises many problems due to three main reasons: the difficulties that have ocean models in reaching an acceptable state of equilibrium, the high measurements cost and the difficulties in realizing them. The performances of the data assimilation procedures depend on the particular observation networks in use, well beyond the background quality and the used assimilation method. In this study we will present some results concerning the great impact of the dataset configuration, in particular measurements position, on the evaluation of the overall forecasting reliability of an ocean model. The aim consists in identifying operational criteria to support the design of marine observation networks at regional scale. In order to identify the observation network able to minimize the forecast error, a methodology based on Singular Vectors Decomposition of the tangent linear model is proposed. Such a method can give strong indications on the local error dynamics. In addition, for the purpose of avoiding redundancy of information contained in the data, a minimal distance among data positions has been chosen on the base of a spatial correlation analysis of the hydrodynamic fields under investigation. This methodology has been applied for the choice of data positions starting from simplified models, like an ideal double-gyre model and a quasi-geostrophic one. Model configurations and data assimilation are based on available ROMS routines, where a variational assimilation algorithm (4D-var) is

  10. Identification of general linear mechanical systems

    Science.gov (United States)

    Sirlin, S. W.; Longman, R. W.; Juang, J. N.

    1983-01-01

    Previous work in identification theory has been concerned with the general first order time derivative form. Linear mechanical systems, a large and important class, naturally have a second order form. This paper utilizes this additional structural information for the purpose of identification. A realization is obtained from input-output data, and then knowledge of the system input, output, and inertia matrices is used to determine a set of linear equations whereby we identify the remaining unknown system matrices. Necessary and sufficient conditions on the number, type and placement of sensors and actuators are given which guarantee identificability, and less stringent conditions are given which guarantee generic identifiability. Both a priori identifiability and a posteriori identifiability are considered, i.e., identifiability being insured prior to obtaining data, and identifiability being assured with a given data set.

  11. Linear systems optimal and robust control

    CERN Document Server

    Sinha, Alok

    2007-01-01

    Introduction Overview Contents of the Book State Space Description of a Linear System Transfer Function of a Single Input/Single Output (SISO) System State Space Realizations of a SISO System SISO Transfer Function from a State Space Realization Solution of State Space Equations Observability and Controllability of a SISO System Some Important Similarity Transformations Simultaneous Controllability and Observability Multiinput/Multioutput (MIMO) Systems State Space Realizations of a Transfer Function Matrix Controllability and Observability of a MIMO System Matrix-Fraction Description (MFD) MFD of a Transfer Function Matrix for the Minimal Order of a State Space Realization Controller Form Realization from a Right MFD Poles and Zeros of a MIMO Transfer Function Matrix Stability Analysis State Feedback Control and Optimization State Variable Feedback for a Single Input System Computation of State Feedback Gain Matrix for a Multiinput System State Feedback Gain Matrix for a Multi...

  12. Asymptotic diagonalization of the discrete Lax pair around singularities and conservation laws for dynamical systems

    Science.gov (United States)

    Habibullin, I. T.; Poptsova, M. N.

    2015-03-01

    A method of the formal diagonalization of the discrete linear operator with a parameter is studied. In the case when the operator provides a Lax operator for a nonlinear quad system the formal diagonalization method allows one to describe effectively conservation laws and generalized symmetries for this system. Asymptotic representation of the Lax operators eigenfunctions are constructed and infinite series of conservation laws are described for the quad system connected with A3(1) affine Lie algebra, for the modified discrete Boussinesq system and for the discrete Tzitzeica equation. For a newly found multiquadratic discrete model conservation laws and several generalized symmetries are presented.

  13. Singular nonlinear H-infinity optimal control problem

    NARCIS (Netherlands)

    Maas, W.C.A.; Maas, W.C.A.; van der Schaft, Arjan

    1996-01-01

    The theory of nonlinear H∞ of optimal control for affine nonlinear systems is extended to the more general context of singular H∞ optimal control of nonlinear systems using ideas from the linear H∞ theory. Our approach yields under certain assumptions a necessary and sufficient condition for

  14. The theory of singular perturbations

    CERN Document Server

    De Jager, E M

    1996-01-01

    The subject of this textbook is the mathematical theory of singular perturbations, which despite its respectable history is still in a state of vigorous development. Singular perturbations of cumulative and of boundary layer type are presented. Attention has been given to composite expansions of solutions of initial and boundary value problems for ordinary and partial differential equations, linear as well as quasilinear; also turning points are discussed. The main emphasis lies on several methods of approximation for solutions of singularly perturbed differential equations and on the mathemat

  15. Singular Initial Value Problem for Certain Classes of Systems of Ordinary Differential Equations

    Directory of Open Access Journals (Sweden)

    Josef Diblík

    2013-01-01

    dimension of the set of initial data generating such solutions is estimated. An asymptotic behavior of solutions is determined as well and relevant asymptotic formulas are derived. The method of functions defined implicitly and the topological method (Ważewski's method are used in the proofs. The results generalize some previous ones on singular initial value problems for differential equations.

  16. Spectral Analysis of a Quantum System with a Double Line Singular Interaction

    Czech Academy of Sciences Publication Activity Database

    Kondej, S.; Krejčiřík, David

    2013-01-01

    Roč. 49, č. 4 (2013), s. 831-859 ISSN 0034-5318 R&D Projects: GA ČR GAP203/11/0701 Institutional support: RVO:61389005 Keywords : Schrödinger operator * singular perturbation * spectral analysis * Hardy inequality * resonance Subject RIV: BE - Theoretical Physics Impact factor: 0.614, year: 2013

  17. Root System of Singular Perturbations of the Harmonic Oscillator Type Operators

    Czech Academy of Sciences Publication Activity Database

    Mityagin, B.; Siegl, Petr

    2016-01-01

    Roč. 106, č. 2 (2016), s. 147-167 ISSN 0377-9017 Institutional support: RVO:61389005 Keywords : non-self-adjoint operators * harmonic oscillator * Riesz basis * quadratic forms * singular petentials Subject RIV: BE - Theoretical Physics Impact factor: 1.671, year: 2016

  18. Statistical analysis of effective singular values in matrix rank determination

    Science.gov (United States)

    Konstantinides, Konstantinos; Yao, Kung

    1988-01-01

    A major problem in using SVD (singular-value decomposition) as a tool in determining the effective rank of a perturbed matrix is that of distinguishing between significantly small and significantly large singular values to the end, conference regions are derived for the perturbed singular values of matrices with noisy observation data. The analysis is based on the theories of perturbations of singular values and statistical significance test. Threshold bounds for perturbation due to finite-precision and i.i.d. random models are evaluated. In random models, the threshold bounds depend on the dimension of the matrix, the noisy variance, and predefined statistical level of significance. Results applied to the problem of determining the effective order of a linear autoregressive system from the approximate rank of a sample autocorrelation matrix are considered. Various numerical examples illustrating the usefulness of these bounds and comparisons to other previously known approaches are given.

  19. Nested observer for linear hybrid dynamical systems

    International Nuclear Information System (INIS)

    Abdi, M.; Bensalah, H.; Cherki, B.

    2009-01-01

    The synthesis of observers for linear hybrid dynamical systems ''HDS,'' is significant from the point of view of the applications (control, diagnoses...); it is still, largely open. We proposed a new approach inspired from a new method of identification, where we could obtain better results with respect to discrimination between the discrete states in conflicts and time necessary to this latter. The results of the suggested technique proved to be satisfactory.

  20. Lectures on algebraic system theory: Linear systems over rings

    Science.gov (United States)

    Kamen, E. W.

    1978-01-01

    The presentation centers on four classes of systems that can be treated as linear systems over a ring. These are: (1) discrete-time systems over a ring of scalars such as the integers; (2) continuous-time systems containing time delays; (3) large-scale discrete-time systems; and (4) time-varying discrete-time systems.

  1. Remarks on gauge variables and singular Lagrangians

    International Nuclear Information System (INIS)

    Chela-Flores, J.; Janica-de-la-Torre, R.; Kalnay, A.J.; Rodriguez-Gomez, J.; Rodriguez-Nunez, J.; Tascon, R.

    1977-01-01

    The relevance is discussed of gauge theory, based on a singular Lagrangian density, to the foundations of field theory. The idea that gauge transformations could change the physics of systems where the Lagrangian is singular is examined. (author)

  2. On the approximation of the canard explosion point in singularly perturbed systems without an explicit small parameter

    DEFF Research Database (Denmark)

    Brøns, Morten; Kristiansen, Kristian Uldall

    2017-01-01

    A canard explosion is the dramatic change of period and amplitude of a limit cycle of a system of nonlinear ODEs in a very narrow interval of the bifurcation parameter. It occurs in slow–fast systems and is well understood in singular perturbation problems where a small parameter epsilon defines...... the time-scale separation. We present an iterative algorithm for the determination of the canard explosion point which can be applied for a general slow–fast system without an explicit small parameter. We also present assumptions under which the algorithm gives accurate estimates of the canard explosion...

  3. Singularities in a Teacup

    Indian Academy of Sciences (India)

    IAS Admin

    Standard presentations of optics concentrate on ideal systems made for imaging which bring all rays from a point ... One of the standard topics we study in school is the action of a spherical mirror. Figure 1 shows a set of ..... singularities of smooth maps, and the beauty of the mathematics needed to understand them, Arnold ...

  4. Linear systems and multiplicity of ideals

    International Nuclear Information System (INIS)

    Le Dung Trang

    2008-06-01

    Using a geometric interpretation of the multiplicity, we give a geometric way to calculate the multiplicity. We consider the particular case of a non-singular complex surface and give an example with a geometric proof of a result. Most of this note is written in the language of complex analytic spaces, but the results can be stated and proved in the case of schemes of finite type over an infinite field with equi-characteristic local rings

  5. Analytical Solutions for Systems of Singular Partial Differential-Algebraic Equations

    Directory of Open Access Journals (Sweden)

    U. Filobello-Nino

    2015-01-01

    Full Text Available This paper proposes power series method (PSM in order to find solutions for singular partial differential-algebraic equations (SPDAEs. We will solve three examples to show that PSM method can be used to search for analytical solutions of SPDAEs. What is more, we will see that, in some cases, Padé posttreatment, besides enlarging the domain of convergence, may be employed in order to get the exact solution from the truncated series solutions of PSM.

  6. Linear unsaturating magnetoresistance in disordered systems

    Science.gov (United States)

    Lai, Ying Tong; Lara, Silvia; Love, Cameron; Ramakrishnan, Navneeth; Adam, Shaffique

    Theoretical works have shown that disordered systems exhibit classical magnetoresistance (MR). In this talk, we examine a variety of experimental systems that observe linear MR at high magnetic fields, including silver chalcogenides, graphene, graphite and Weyl semimetals. We show that a careful analysis of the magnitude of the MR, as well as the field strength at which the MR changes from quadratic to linear, reveal important properties of the system, such as the ratio of the root-mean-square fluctuations in the carrier density and the average carrier density. By looking at other properties such as the zero-field mobility, we show that this carrier density inhomogeneity is consistent with what is known about the microscopic impurities in these experiments. The application of this disorder-induced MR to a variety of different experimental scenarios underline the universality of these theoretical models. This work is supported by the Singapore National Research Foundation (NRF-NRFF2012-01) and the Singapore Ministry of Education and Yale-NUS College through Grant Number R-607-265-01312.

  7. a Continuous-Time Positive Linear System

    Directory of Open Access Journals (Sweden)

    Kyungsup Kim

    2013-01-01

    Full Text Available This paper discusses a computational method to construct positive realizations with sparse matrices for continuous-time positive linear systems with multiple complex poles. To construct a positive realization of a continuous-time system, we use a Markov sequence similar to the impulse response sequence that is used in the discrete-time case. The existence of the proposed positive realization can be analyzed with the concept of a polyhedral convex cone. We provide a constructive algorithm to compute positive realizations with sparse matrices of some positive systems under certain conditions. A sufficient condition for the existence of a positive realization, under which the proposed constructive algorithm works well, is analyzed.

  8. Optimal Control of Switching Linear Systems

    Directory of Open Access Journals (Sweden)

    Ali Benmerzouga

    2004-06-01

    Full Text Available A solution to the control of switching linear systems with input constraints was given in Benmerzouga (1997 for both the conventional enumeration approach and the new approach. The solution given there turned out to be not unique. The main objective in this work is to determine the optimal control sequences {Ui(k ,  i = 1,..., M ;  k = 0, 1, ...,  N -1} which transfer the system from a given initial state  X0  to a specific target state  XT  (or to be as close as possible by using the same discrete time solution obtained in Benmerzouga (1997 and minimizing a running cost-to-go function. By using the dynamic programming technique, the optimal solution is found for both approaches given in Benmerzouga (1997. The computational complexity of the modified algorithm is also given.

  9. Linear concentration system; Sistema de concentracion lineal

    Energy Technology Data Exchange (ETDEWEB)

    Gonzalez Lugo, J.I; Leon Rovira, N; Aguayo Tellez, H [Instituto Tecnologico y de Estudios Superiores de Monterrey, Monterrey, Nuevo Leon (Mexico)]. E-mails: a00812662@itesm.mx; noel.leon@itesm.mx; haguayo@itesm.mx

    2013-03-15

    Solar linear concentration technologies to generate high temperatures are limited to the ranges of 200 to 500 degrees Celsius. While its performance has been tested through prototypes and pilot plants around the world, there are still areas of opportunity that can be exploited to obtain a linear concentration that achieves temperatures above this range in order to have a better use of the available solar energy. Because of this: It is possible to develop a linear concentration system that can track the sun with minimal movement of the absorber-receiver while maintaining temperatures above 850 degrees Celsius sufficient for industrial processes that require that temperature. The methodology consists of a series of stages (conceptual design, simulation, evaluation, development concept, results and validation) through which concepts are generated that allow design and evaluation of solar concentrator configurations with the help of simulation software. We have designed a linear parabolic concentrating system which comprises a set of mirrors segments with different focal lengths that works within the range of 600 degrees Celsius; however, it is advancing in the development of a double concentration to reach 850 degrees Celsius. [Spanish] Las tecnologias de concentracion lineal solar para generar altas temperaturas se ven limitadas a los rangos de 200 a 500 grados centigrados. Si bien su funcionamiento ha sido probado a traves de prototipos y plantas piloto alrededor del mundo, aun existen areas de oportunidad que pueden ser aprovechadas para obtener un sistema de concentracion lineal que permita alcanzar temperaturas mayores a este rango para asi tener un mejor aprovechamiento de la energia solar disponible. Debido a esto: Es posible desarrollar un sistema de concentracion lineal capaz de seguir la trayectoria del Sol con minimo movimiento del absorbedor-recibidor al mismo tiempo que mantiene temperaturas superiores a los 850 grados centigrados suficientes para

  10. Relative null controllability of linear systems with multiple delays in ...

    African Journals Online (AJOL)

    varying multiple delays in state and control are developed. If the uncontrolled system is uniformly asymptotically stable, and if the linear system is controllable, then the linear system is null controllable. Journal of the Nigerian Association of ...

  11. Point force singularities outside a drop covered with an incompressible surfactant: Image systems and their applications

    Science.gov (United States)

    Shaik, Vaseem A.; Ardekani, Arezoo M.

    2017-11-01

    In this work we derive the image flow fields for point force singularities placed outside a stationary drop covered with an insoluble, nondiffusing, and incompressible surfactant. We assume the interface to be Newtonian and use the Boussinesq-Scriven constitutive law for the interfacial stress tensor. We use this analytical solution to investigate two different problems. First, we derive the mobility matrix for two drops of arbitrary sizes covered with an incompressible surfactant. In the second example, we calculate the velocity of a swimming microorganism (modeled as a Stokes dipole) outside a drop covered with an incompressible surfactant.

  12. Linear-array systems for aerospace NDE

    International Nuclear Information System (INIS)

    Smith, Robert A.; Willsher, Stephen J.; Bending, Jamie M.

    1999-01-01

    Rapid large-area inspection of composite structures for impact damage and multi-layered aluminum skins for corrosion has been a recognized priority for several years in both military and civil aerospace applications. Approaches to this requirement have followed two clearly different routes: the development of novel large-area inspection systems, and the enhancement of current ultrasonic or eddy-current methods to reduce inspection times. Ultrasonic inspection is possible with standard flaw detection equipment but the addition of a linear ultrasonic array could reduce inspection times considerably. In order to investigate their potential, 9-element and 17-element linear ultrasonic arrays for composites, and 64-element arrays for aluminum skins, have been developed to DERA specifications for use with the ANDSCAN area scanning system. A 5 m 2 composite wing surface has been scanned with a scan resolution of approximately 3 mm in 6 hours. With subsequent software and hardware improvements all four composite wing surfaces (top/bottom, left/right) of a military fighter aircraft can potentially be inspected in less than a day. Array technology has been very widely used in the medical ultrasound field although rarely above 10 MHz, whereas lap-joint inspection requires a pulse center-frequency of 12 to 20 MHz in order to resolve the separate interfaces in the lap joint. A 128 mm-long multi-element array of 5 mmx2 mm ultrasonic elements for use with the ANDSCAN scanning software was produced to a DERA specification by an NDT manufacturer with experience in the medical imaging field. This paper analyses the performance of the transducers that have been produced and evaluates their use in scanning systems of different configurations

  13. Investigation of relation between singular points and number of limit cycles for a rotor-AMBs system

    International Nuclear Information System (INIS)

    Li, J.; Tian, Y.; Zhang, W.

    2009-01-01

    The relation between singular points and the number of limit cycles is investigated for a rotor-active magnetic bearings system with time-varying stiffness and single-degree-of-freedom. The averaged equation of the system is a perturbed polynomial Hamiltonian system of degree 5. The dynamic characteristics of the unperturbed system are first analyzed for a certain parameter group. The number of limit cycles and their configurations of the perturbed system under eight different parametric groups are obtained and the influence of eight control conditions on the number of limit cycles is studied. The results obtained here will play an important leading role in the study of the properties of nonlinear dynamics and control of the rotor-active magnetic bearings system with time-varying stiffness.

  14. Asymptotic Solutions of Singular Perturbed Problems with an Instable Spectrum of the Limiting Operator

    Directory of Open Access Journals (Sweden)

    Burkhan T. Kalimbetov

    2012-01-01

    Full Text Available The regularization method is applied for the construction of algorithm for an asymptotical solution for linear singular perturbed systems with the irreversible limit operator. The main idea of this method is based on the analysis of dual singular points of investigated equations and passage in the space of the larger dimension, what reduces to study of systems of first-order partial differential equations with incomplete initial data.

  15. A Kalman decomposition to detect temporal linear system srtucture

    NARCIS (Netherlands)

    Willigenburg, Van L.G.; Koning, De W.L.

    2015-01-01

    Feedback controllers for non-linear systems are often based on a linearized dynamic model. Such a linearized model may be temporarily uncontrollable and/or unreconstructable. This paper introduces the so-called differential Kalman decomposition of time-varying linear systems. It is based on

  16. Integrated Urban System and Energy Consumption Model: Public and Singular Buildings

    Directory of Open Access Journals (Sweden)

    Rocco Papa

    2014-05-01

    Full Text Available The present paper illustrates the results of the first steps of a study on one aspect investigated as the preliminary step of the definition of the analysis - comprehension model of the relation between: city, buildings, and user behavior, for the reduction of energy consumption within the research project “Smart Energy Master” for the energetic governance of the territory (PON_MIUR n. pos. 04a2_00120 CUP Ricerca: E61H12000130005, at the Department of Civil, Building and Environmental Engineering - University of Naples Federico II, principal investigator prof. Carmela Gargiulo.Specifically the literary review aimed at determining if, and in what measure, the presence of public and singular buildings is present in the energy consumption estimate models,  proposed by the scientific community, for the city or neighborhood scale.The difficulties in defining the weight of these singular buildings on the total energy consumption and the impossibility to define mean values that are significant for all subsets and different types as well as for each one, have forced model makers to either ignore them completely or chose a portion of this specific stock to include.

  17. Identification problems in linear transformation system

    International Nuclear Information System (INIS)

    Delforge, Jacques.

    1975-01-01

    An attempt was made to solve the theoretical and numerical difficulties involved in the identification problem relative to the linear part of P. Delattre's theory of transformation systems. The theoretical difficulties are due to the very important problem of the uniqueness of the solution, which must be demonstrated in order to justify the value of the solution found. Simple criteria have been found when measurements are possible on all the equivalence classes, but the problem remains imperfectly solved when certain evolution curves are unknown. The numerical difficulties are of two kinds: a slow convergence of iterative methods and a strong repercussion of numerical and experimental errors on the solution. In the former case a fast convergence was obtained by transformation of the parametric space, while in the latter it was possible, from sensitivity functions, to estimate the errors, to define and measure the conditioning of the identification problem then to minimize this conditioning as a function of the experimental conditions [fr

  18. Dynamics of delayed piecewise linear systems

    Directory of Open Access Journals (Sweden)

    Laszlo E. Kollar

    2003-02-01

    Full Text Available In this paper the dynamics of the controlled pendulum is investigated assuming backlash and time delays. The upper equilibrium of the pendulum is stabilized by a piecewise constant control force which is the linear combination of the sampled values of the angle and the angular velocity of the pendulum. The control force is provided by a motor which drives one of the wheels of the cart through an elastic teeth belt. The contact between the teeth of the gear (rigid and the belt (elastic introduces a nonlinearity known as ``backlash" and causes the oscillation of the controlled pendulum around its upper equilibrium. The processing and sampling delays in the determination of the control force tend to destabilize the controlled system as well. We obtain conditions guaranteeing that the pendulum remains in the neighborhood of the upper equilibrium. Experimental findings obtained on a computer controlled inverted pendulum cart structure are also presented showing good agreement with the simulation results.

  19. Singular perturbation analysis of the steady-state Poisson-Nernst-Planck system: Applications to ion channels.

    Science.gov (United States)

    Singer, A; Gillespie, D; Norbury, J; Eisenberg, R S

    2008-01-01

    Ion channels are proteins with a narrow hole down their middle that control a wide range of biological function by controlling the flow of spherical ions from one macroscopic region to another. Ion channels do not change their conformation on the biological time scale once they are open, so they can be described by a combination of Poisson and drift-diffusion (Nernst-Planck) equations called PNP in biophysics. We use singular perturbation techniques to analyse the steady-state PNP system for a channel with a general geometry and a piecewise constant permanent charge profile. We construct an outer solution for the case of a constant permanent charge density in three dimensions that is also a valid solution of the one-dimensional system. The asymptotical current-voltage (I-V ) characteristic curve of the device (obtained by the singular perturbation analysis) is shown to be a very good approximation of the numerical I-V curve (obtained by solving the system numerically). The physical constraint of non-negative concentrations implies a unique solution, i.e., for each given applied potential there corresponds a unique electric current (relaxing this constraint yields non-physical multiple solutions for sufficiently large voltages).

  20. Linear Quantum Systems: Non-Classical States and Robust Stability

    Science.gov (United States)

    2016-06-29

    paper is to extend linear systems and signals theory to include single photon quantum signals . We provide detailed results describing how quantum...v) physical realizability results for finite level quantum systems. 15. SUBJECT TERMS Control Theory , Quantum Feedback, Quantum Algorithms 16...nominal linear models, and (v) physical realizability results for finite level quantum systems. Introduction: Classical linear systems theory

  1. Superconducting linear accelerator system for NSC

    Indian Academy of Sciences (India)

    This paper reports the construction of a superconducting linear accelerator as a booster to the 15 UD Pelletron accelerator at Nuclear Science Centre, New Delhi. The LINAC will use superconducting niobium quarter wave resonators as the accelerating element. Construction of the linear accelerator has progressed ...

  2. LQG/LTR [linear quadratic Gaussian with loop transfer recovery] robust control system design for a low-pressure feedwater heater train

    International Nuclear Information System (INIS)

    Murphy, G.V.; Bailey, J.M.

    1990-01-01

    This paper uses the linear quadratic Gaussian with loop transfer recovery (LQG/LTR) control system design method to obtain a level control system for a low-pressure feedwater heater train. The control system performance and stability robustness are evaluated for a given set of system design specifications. The tools for analysis are the return ratio, return difference, and inverse return difference singular-valve plots for a loop break at the plant output. 3 refs., 7 figs., 2 tabs

  3. Method of mechanical quadratures for solving singular integral equations of various types

    Science.gov (United States)

    Sahakyan, A. V.; Amirjanyan, H. A.

    2018-04-01

    The method of mechanical quadratures is proposed as a common approach intended for solving the integral equations defined on finite intervals and containing Cauchy-type singular integrals. This method can be used to solve singular integral equations of the first and second kind, equations with generalized kernel, weakly singular equations, and integro-differential equations. The quadrature rules for several different integrals represented through the same coefficients are presented. This allows one to reduce the integral equations containing integrals of different types to a system of linear algebraic equations.

  4. Symmetric linear systems - An application of algebraic systems theory

    Science.gov (United States)

    Hazewinkel, M.; Martin, C.

    1983-01-01

    Dynamical systems which contain several identical subsystems occur in a variety of applications ranging from command and control systems and discretization of partial differential equations, to the stability augmentation of pairs of helicopters lifting a large mass. Linear models for such systems display certain obvious symmetries. In this paper, we discuss how these symmetries can be incorporated into a mathematical model that utilizes the modern theory of algebraic systems. Such systems are inherently related to the representation theory of algebras over fields. We will show that any control scheme which respects the dynamical structure either implicitly or explicitly uses the underlying algebra.

  5. A Linear System of Differential Equations Related to Vector-Valued Jack Polynomials on the Torus

    Science.gov (United States)

    Dunkl, Charles F.

    2017-06-01

    For each irreducible module of the symmetric group S_{N} there is a set of parametrized nonsymmetric Jack polynomials in N variables taking values in the module. These polynomials are simultaneous eigenfunctions of a commutative set of operators, self-adjoint with respect to two Hermitian forms, one called the contravariant form and the other is with respect to a matrix-valued measure on the N-torus. The latter is valid for the parameter lying in an interval about zero which depends on the module. The author in a previous paper [SIGMA 12 (2016), 033, 27 pages] proved the existence of the measure and that its absolutely continuous part satisfies a system of linear differential equations. In this paper the system is analyzed in detail. The N-torus is divided into (N-1)! connected components by the hyperplanes x_{i}=x_{j}, isingularities of the system. The main result is that the orthogonality ! measure has no singular part with respect to Haar measure, and thus is given by a matrix function times Haar measure. This function is analytic on each of the connected components.

  6. Reduction of Linear Functional Systems using Fuhrmann's Equivalence

    Directory of Open Access Journals (Sweden)

    Mohamed S. Boudellioua

    2016-11-01

    Full Text Available Functional systems arise in the treatment of systems of partial differential equations, delay-differential equations, multidimensional equations, etc. The problem of reducing a linear functional system to a system containing fewer equations and unknowns was first studied by Serre. Finding an equivalent presentation of a linear functional system containing fewer equations and fewer unknowns can generally simplify both the study of the structural properties of the linear functional system and of different numerical analysis issues, and it can sometimes help in solving the linear functional system. In this paper, Fuhrmann's equivalence is used to present a constructive result on the reduction of under-determined linear functional systems to a single equation involving a single unknown. This equivalence transformation has been studied by a number of authors and has been shown to play an important role in the theory of linear functional systems.

  7. High density linear systems for fusion power

    International Nuclear Information System (INIS)

    Ellis, W.R.; Krakowski, R.A.

    1975-01-01

    The physics and technological limitations and uncertainties associated with the linear theta pinch are discussed in terms of a generalized energy balance, which has as its basis the ratio (Q/sub E/) of total electrical energy generated to net electrical energy consumed. Included in this total is the virtual energy of bred fissile fuel, if a hybrid blanket is used, as well as the actual of real energy deposited in the blanket by the fusion neutron. The advantages and disadvantages of the pulsed operation demanded by the linear theta pinch are also discussed

  8. Analysis of Linear Hybrid Systems in CLP

    DEFF Research Database (Denmark)

    Banda, Gourinath; Gallagher, John Patrick

    2009-01-01

    In this paper we present a procedure for representing the semantics of linear hybrid automata (LHAs) as constraint logic programs (CLP); flexible and accurate analysis and verification of LHAs can then be performed using generic CLP analysis and transformation tools. LHAs provide an expressive...... and argue that we contribute to the general field of using static analysis tools for verification...

  9. Evaluation of Linear and Non-Linear Control Schemes Applied to a Hydraulic Servo System

    DEFF Research Database (Denmark)

    Andersen, Torben Ole; Hansen, Michael Rygaard; Pedersen, Henrik Clemmensen

    2005-01-01

    is used as test facility acting as load for the hydraulic servo system. An experimentally verified non-linear model of the complete system has been developed and used to design a series of both linear and non-linear control schemes. The controllers from each category are compared with respect to design......Due to the innovation of low-cost electronics such as sensors, microcontrollers etc., the focus on highperformance motion control is increasing. This work focuses on position control of single-input single-output hydraulic servo-systems in general. A hydraulically actuated robotic manipulator...

  10. Evaluation of Linear and Non-Linear Control Schemes Applied to a Hydraulic Servo System

    DEFF Research Database (Denmark)

    Andersen, Torben Ole; Hansen, Michael Rygaard; Pedersen, Henrik Clemmensen

    2005-01-01

    Due to the innovation of low-cost electronics such as sensors, microcontrollers etc., the focus on highperformance motion control is increasing. This work focuses on position control of single-input single-output hydraulic servo-systems in general. A hydraulically actuated robotic manipulator...... is used as test facility acting as load for the hydraulic servo system. An experimentally verified non-linear model of the complete system has been developed and used to design a series of both linear and non-linear control schemes. The controllers from each category are compared with respect to design...

  11. A SYSTEMIC VISION OF BIOLOGY: OVERCOMING LINEARITY

    Directory of Open Access Journals (Sweden)

    M. Mayer

    2005-07-01

    were used to build  a hipermedia  material.  This  technology  permit  overcomes a linear  communication, improving the  comprehension  of the network perspective.   The teachers  speeches revealed  their  conceptual  con- structions along the  course,  showed the development of the  competences  in identify  interconnection points  in the flow and chemical cycling of energy, compatible  with a systemic view of life.

  12. Classification of subsurface objects using singular values derived from signal frames

    Science.gov (United States)

    Chambers, David H; Paglieroni, David W

    2014-05-06

    The classification system represents a detected object with a feature vector derived from the return signals acquired by an array of N transceivers operating in multistatic mode. The classification system generates the feature vector by transforming the real-valued return signals into complex-valued spectra, using, for example, a Fast Fourier Transform. The classification system then generates a feature vector of singular values for each user-designated spectral sub-band by applying a singular value decomposition (SVD) to the N.times.N square complex-valued matrix formed from sub-band samples associated with all possible transmitter-receiver pairs. The resulting feature vector of singular values may be transformed into a feature vector of singular value likelihoods and then subjected to a multi-category linear or neural network classifier for object classification.

  13. Analysis of latent structures in linear systems

    DEFF Research Database (Denmark)

    Høskuldsson, Agnar

    2004-01-01

    In chemometrics the emphasis is on latent structure models. The latent structure is the part of the data that the modeling task is based upon. This paper is addressing some fundamental issues, when latent structures are used. The paper consists of three parts. The first part is concerned defining...... the latent structure of a linear model. Here the ‘atomic’ parts of the algorithms that generate the latent structure for linear models are analyzed. It is shown how the PLS algorithm fits within this way of presenting the numerical procedures. The second part is concerning graphic illustrations...... to use for deciding if single or multiple latent structures should be used. The last part is about choosing the variables that should be used in the analysis. The traditional procedures to select variables to include in the model are presented and the insufficiencies of such approaches are demonstrated...

  14. Dynamics of unsymmetric piecewise-linear/non-linear systems using finite elements in time

    Science.gov (United States)

    Wang, Yu

    1995-08-01

    The dynamic response and stability of a single-degree-of-freedom system with unsymmetric piecewise-linear/non-linear stiffness are analyzed using the finite element method in the time domain. Based on a Hamilton's weak principle, this method provides a simple and efficient approach for predicting all possible fundamental and sub-periodic responses. The stability of the steady state response is determined by using Floquet's theory without any special effort for calculating transition matrices. This method is applied to a number of examples, demonstrating its effectiveness even for a strongly non-linear problem involving both clearance and continuous stiffness non-linearities. Close agreement is found between available published findings and the predictions of the finite element in time approach, which appears to be an efficient and reliable alternative technique for non-linear dynamic response and stability analysis of periodic systems.

  15. Cotton-Type and Joint Invariants for Linear Elliptic Systems

    Directory of Open Access Journals (Sweden)

    A. Aslam

    2013-01-01

    that Cotton-type invariants derived from these two approaches are identical. Furthermore, Cotton-type and joint invariants for a general system of two linear elliptic equations are also obtained from the Laplace-type and joint invariants for a system of two linear hyperbolic equations equivalent to the system of linear elliptic equations by complex changes of the independent variables. Examples are presented to illustrate the results.

  16. Incremental Closed-loop Identification of Linear Parameter Varying Systems

    DEFF Research Database (Denmark)

    Bendtsen, Jan Dimon; Trangbæk, Klaus

    2011-01-01

    , closed-loop system identification is more difficult than open-loop identification. In this paper we prove that the so-called Hansen Scheme, a technique known from linear time-invariant systems theory for transforming closed-loop system identification problems into open-loop-like problems, can be extended......This paper deals with system identification for control of linear parameter varying systems. In practical applications, it is often important to be able to identify small plant changes in an incremental manner without shutting down the system and/or disconnecting the controller; unfortunately...... to accommodate linear parameter varying systems as well....

  17. Solving block linear systems with low-rank off-diagonal blocks is easily parallelizable

    Energy Technology Data Exchange (ETDEWEB)

    Menkov, V. [Indiana Univ., Bloomington, IN (United States)

    1996-12-31

    An easily and efficiently parallelizable direct method is given for solving a block linear system Bx = y, where B = D + Q is the sum of a non-singular block diagonal matrix D and a matrix Q with low-rank blocks. This implicitly defines a new preconditioning method with an operation count close to the cost of calculating a matrix-vector product Qw for some w, plus at most twice the cost of calculating Qw for some w. When implemented on a parallel machine the processor utilization can be as good as that of those operations. Order estimates are given for the general case, and an implementation is compared to block SSOR preconditioning.

  18. Biclustering via Sparse Singular Value Decomposition

    KAUST Repository

    Lee, Mihee

    2010-02-16

    Sparse singular value decomposition (SSVD) is proposed as a new exploratory analysis tool for biclustering or identifying interpretable row-column associations within high-dimensional data matrices. SSVD seeks a low-rank, checkerboard structured matrix approximation to data matrices. The desired checkerboard structure is achieved by forcing both the left- and right-singular vectors to be sparse, that is, having many zero entries. By interpreting singular vectors as regression coefficient vectors for certain linear regressions, sparsity-inducing regularization penalties are imposed to the least squares regression to produce sparse singular vectors. An efficient iterative algorithm is proposed for computing the sparse singular vectors, along with some discussion of penalty parameter selection. A lung cancer microarray dataset and a food nutrition dataset are used to illustrate SSVD as a biclustering method. SSVD is also compared with some existing biclustering methods using simulated datasets. © 2010, The International Biometric Society.

  19. Energy balance in a system with quasispherical linear compression

    International Nuclear Information System (INIS)

    Es'kov, A.G.; Kozlov, N.P.; Kurtmullaev, R.K.; Semenov, V.N.; Khvesyuk, V.I.; Yaminskii, A.V.

    1983-01-01

    This letter reports the resists of some experimental studies and a numerical simulation of the Tor-linear fusion system, 1 in which a heavy plasma shell with a closed magnetic structure is compressed in a quasispherical manner. The parameters of the Tor-Linear, at the Kurchatov Institute of Atomic Energy in Moscow are as follows: The energy stored in the system which accelerates the linear is E = 0.5 MJ; the linear mass is m = 0.2 kg; the working volume of the linear module is 1.5 x 10 -3 m 3 ; the linear velocity is approx.10 3 m/s; the guiding field in the toriod in the linear is 1--10 x 10 21 m -3 ; and the intial volume of the plasma in the linear chamber is 2.5 x 10 -4 m 3 . In this series of experiments, new solutions were developed for all the systems of the plasma--linear complex of the Tor-Linear: to produce a plasma toroid, to transport it, and to trap it in the linear cavity

  20. Superconducting linear accelerator system for NSC

    Indian Academy of Sciences (India)

    2.4 Control system. A distributed control system has been developed for the Pelletron-LINAC accelerator sys- tem (figure 7). It runs on a network of Pentium computers under the LINUX operating system. The devices of the accelerator are connected to several computers using CAMAC interface. The design is based on a ...

  1. Decentralized linear quadratic power system stabilizers for multi ...

    Indian Academy of Sciences (India)

    Power system stabilizer; linear quadratic regulator; small-signal stability; transient stability. Abstract. Linear quadratic stabilizers are well-known for their superior control capabilities when compared to the conventional lead–lag power system stabilizers. However, they have not seen much of practical importance as the state ...

  2. New approach to solve symmetric fully fuzzy linear systems

    Indian Academy of Sciences (India)

    it is important to develop mathematical models and numerical procedures that would appropri- ately treat ... A general model for solving a fuzzy linear system whose coefficient matrix is crisp and the right hand side .... To represent the above problem as fully fuzzy linear system, we represent x as a quantity of the product 1 ...

  3. Minimal solution of general dual fuzzy linear systems

    International Nuclear Information System (INIS)

    Abbasbandy, S.; Otadi, M.; Mosleh, M.

    2008-01-01

    Fuzzy linear systems of equations, play a major role in several applications in various area such as engineering, physics and economics. In this paper, we investigate the existence of a minimal solution of general dual fuzzy linear equation systems. Two necessary and sufficient conditions for the minimal solution existence are given. Also, some examples in engineering and economic are considered

  4. Model Reduction by Moment Matching for Linear Switched Systems

    DEFF Research Database (Denmark)

    Bastug, Mert; Petreczky, Mihaly; Wisniewski, Rafal

    2014-01-01

    A moment-matching method for the model reduction of linear switched systems (LSSs) is developed. The method is based based upon a partial realization theory of LSSs and it is similar to the Krylov subspace methods used for moment matching for linear systems. The results are illustrated by numerical...

  5. Singularity Theory and its Applications

    CERN Document Server

    Stewart, Ian; Mond, David; Montaldi, James

    1991-01-01

    A workshop on Singularities, Bifuraction and Dynamics was held at Warwick in July 1989, as part of a year-long symposium on Singularity Theory and its applications. The proceedings fall into two halves: Volume I mainly on connections with algebraic geometry and volume II on connections with dynamical systems theory, bifurcation theory and applications in the sciences. The papers are original research, stimulated by the symposium and workshop: All have been refereed and none will appear elsewhere. The main topic of volume II is new methods for the study of bifurcations in nonlinear dynamical systems, and applications of these.

  6. LINPACK, Subroutine Library for Linear Equation System Solution and Matrix Calculation

    International Nuclear Information System (INIS)

    Dongarra, J.J.

    1979-01-01

    1 - Description of problem or function: LINPACK is a collection of FORTRAN subroutines which analyze and solve various classes of systems of simultaneous linear algebraic equations. The collection deals with general, banded, symmetric indefinite, symmetric positive definite, triangular, and tridiagonal square matrices, as well as with least squares problems and the QR and singular value decompositions of rectangular matrices. A subroutine-naming convention is employed in which each subroutine name consists of five letters which represent a coded specification (TXXYY) of the computation done by that subroutine. The first letter, T, indicates the matrix data type. Standard FORTRAN allows the use of three such types: S REAL, D DOUBLE PRECISION, and C COMPLEX. In addition, some FORTRAN systems allow a double-precision complex type: Z COMPLEX*16. The second and third letters of the subroutine name, XX, indicate the form of the matrix or its decomposition: GE: General, GB: General band, PO: Positive definite, PP: Positive definite packed, PB: Positive definite band, SI: Symmetric indefinite, SP: Symmetric indefinite packed, HI: Hermitian indefinite, HP: Hermitian indefinite packed, TR: Triangular, GT: General tridiagonal, PT: Positive definite tridiagonal, CH: Cholesky decomposition, QR: Orthogonal-triangular decomposition, SV: Singular value decomposition. The final two letters, YY, indicate the computation done by the particular subroutine: FA: Factor, CO: Factor and estimate condition, SL: Solve, DI: Determinant and/or inverse and/or inertia, DC: Decompose, UD: Update, DD: Down-date, EX Exchange. The following chart shows all the LINPACK subroutines. The initial 'S' in the names may be replaced by D, C or Z and the initial 'C' in the complex-only names may be replaced by a Z. SGE: FA, CO, SL, DI; SGB: FA, CO, SL, DI; SPO: FA, CO, SL, DI; SPP: FA, CO, SL, DI; SPB: FA, CO, SL, DI; SSI: FA, CO, SL, DI; SSP: FA, CO, SL, DI; CHI: FA, CO, SL, DI; CHP: FA, CO, SL, DI; STR

  7. Useful tools for non-linear systems: Several non-linear integral inequalities

    Czech Academy of Sciences Publication Activity Database

    Agahi, H.; Mohammadpour, A.; Mesiar, Radko; Vaezpour, M. S.

    2013-01-01

    Roč. 49, č. 1 (2013), s. 73-80 ISSN 0950-7051 R&D Projects: GA ČR GAP402/11/0378 Institutional support: RVO:67985556 Keywords : Monotone measure * Comonotone functions * Integral inequalities * Universal integral Subject RIV: BA - General Mathematics Impact factor: 3.058, year: 2013 http://library.utia.cas.cz/separaty/2013/E/mesiar-useful tools for non-linear systems several non-linear integral inequalities.pdf

  8. Enhancement of the thermoelectric efficiency in a T-shaped quantum dot system in the linear and nonlinear regimes

    Science.gov (United States)

    Gómez-Silva, G.; Orellana, P. A.; Anda, E. V.

    2018-02-01

    In the present work, we investigate the thermoelectric properties of a T-shaped double quantum dot system coupled to two metallic leads incorporating the intra-dot Coulomb interaction. We explore the role of the interference effects and Coulomb blockade on the thermoelectric efficiency of the system in the linear and nonlinear regimes. We studied as well the effect of a Van-Hove singularity of the leads density of states (DOS) at the neighborhood of the Fermi energy, a situation that can be obtained using a carbon nanotube, a graphene nano-ribbon or other contacts with one-dimensional properties. The system is studied above the Kondo temperature. The Coulomb blockade of the electronic charges is studied using the Hubbard III approximation, which properly describes the transport properties of this regime. In the linear response, our results show an enhancement of the thermopower and the figure of merit of the system. For a nonlinear situation, we calculate the thermoelectric efficiency and power output, concluding that the T-shaped double quantum dot is an efficient thermoelectric device. Moreover, we demonstrate the great importance of the DOS Van-Hove singularity at the neighborhood of the Fermi energy to obtain a very significant increase in the thermoelectric efficiency of the system.

  9. Robust control for fractional variable-order chaotic systems with non-singular kernel

    Science.gov (United States)

    Zuñiga-Aguilar, C. J.; Gómez-Aguilar, J. F.; Escobar-Jiménez, R. F.; Romero-Ugalde, H. M.

    2018-01-01

    This paper investigates the chaos control for a class of variable-order fractional chaotic systems using robust control strategy. The variable-order fractional models of the non-autonomous biological system, the King Cobra chaotic system, the Halvorsen's attractor and the Burke-Shaw system, have been derived using the fractional-order derivative with Mittag-Leffler in the Liouville-Caputo sense. The fractional differential equations and the control law were solved using the Adams-Bashforth-Moulton algorithm. To test the control stability efficiency, different statistical indicators were introduced. Finally, simulation results demonstrate the effectiveness of the proposed robust control.

  10. A Methodology for Multiple Rule System Integration and Resolution Within a Singular Knowledge Base

    Science.gov (United States)

    Kautzmann, Frank N., III

    1988-01-01

    Expert Systems which support knowledge representation by qualitative modeling techniques experience problems, when called upon to support integrated views embodying description and explanation, especially when other factors such as multiple causality, competing rule model resolution, and multiple uses of knowledge representation are included. A series of prototypes are being developed to demonstrate the feasibility of automating the process of systems engineering, design and configuration, and diagnosis and fault management. A study involves not only a generic knowledge representation; it must also support multiple views at varying levels of description and interaction between physical elements, systems, and subsystems. Moreover, it will involve models of description and explanation for each level. This multiple model feature requires the development of control methods between rule systems and heuristics on a meta-level for each expert system involved in an integrated and larger class of expert system. The broadest possible category of interacting expert systems is described along with a general methodology for the knowledge representation and control of mutually exclusive rule systems.

  11. A new active absorption system and its performance to linear and non-linear waves

    DEFF Research Database (Denmark)

    Andersen, Thomas Lykke; Clavero, M.; Frigaard, Peter Bak

    2016-01-01

    Highlights •An active absorption system for wavemakers has been developed. •The theory for flush mounted gauges has been extended to cover also small gaps. •The new system has been validated in a wave flume with wavemakers in both ends. •A generation and absorption procedure for highly non-linear...

  12. On Dynamic Systems with Piecewise Linear Feature

    Directory of Open Access Journals (Sweden)

    Amalia Ţîrdea

    2010-10-01

    Full Text Available Impact dynamics is considered to be one of the most important problems which arise in vibrating systems. Such impact oscillator occurs in the motion with amplitude constraining stop. In the past years, this simple model has been found rich phenomena and given benefit for understanding of impact systems. Different types of impacting response, such as periodic and non-periodic oscillations, can be predicted by using bifurcation diagrams. Many mechanical systems in engineering applications represent systems which are driven in some way and which undergo intermittent or a continuous sequence of contacts with limiting motion by constraints. For example, the principles of the operation of vibration hammers, impact dampers, inertial shakers, milling and forming machines etc, are based on the impact action for moving bodies. With other equipment, machines with clearances, heat exchangers, steam generator tubes, fuel rods in nuclear power plants, rolling railway wheel sets, piping systems, gear transmissions and so on, impacts also occur, but they are undesirable as they bring about failures, strains, and increased noise levels.

  13. Geometric Singularities of the Stokes Problem

    Directory of Open Access Journals (Sweden)

    Nejmeddine Chorfi

    2014-01-01

    Full Text Available When the domain is a polygon of ℝ2, the solution of a partial differential equation is written as a sum of a regular part and a linear combination of singular functions. The purpose of this paper is to present explicitly the singular functions of Stokes problem. We prove the Kondratiev method in the case of the crack. We finish by giving some regularity results.

  14. Lyapunov, singular and bred vectors in a multi-scale system: an empirical exploration of vectors related to instabilities

    International Nuclear Information System (INIS)

    Norwood, Adrienne; Kalnay, Eugenia; Ide, Kayo; Yang, Shu-Chih; Wolfe, Christopher

    2013-01-01

    We compute and compare the three types of vectors frequently used to explore the instability properties of dynamical models, namely Lyapunov vectors (LVs), singular vectors (SVs) and bred vectors (BVs) in two systems, using the Wolfe–Samelson (2007 Tellus A 59 355–66) algorithm to compute all of the Lyapunov vectors. The first system is the Lorenz (1963 J. Atmos. Sci. 20 130–41) three-variable model. Although the leading Lyapunov vector, LV1, grows fastest globally, the second Lyapunov vector, LV2, which has zero growth globally, often grows faster than LV1 locally. Whenever this happens, BVs grow closer to LV2, suggesting that in larger atmospheric or oceanic models where several instabilities can grow in different areas of the world, BVs will grow toward the fastest growing local unstable mode. A comparison of their growth rates at different times shows that all three types of dynamical vectors have the ability to predict regime changes and the duration of the new regime based on their growth rates in the last orbit of the old regime, as shown for BVs by Evans et al (2004 Bull. Am. Meteorol. Soc. 520–4). LV1 and BVs have similar predictive skill, LV2 has a tendency to produce false alarms, and even LV3 shows that maximum decay is also associated with regime change. Initial and final SVs grow much faster and are the most accurate predictors of regime change, although the characteristics of the initial SVs are strongly dependent on the length of the optimization window. The second system is the toy ‘ocean-atmosphere’ model developed by Peña and Kalnay (2004 Nonlinear Process. Geophys. 11 319–27) coupling three Lorenz (1963 J. Atmos. Sci. 20 130–41) systems with different time scales, in order to test the effects of fast and slow modes of growth on the dynamical vectors. A fast ‘extratropical atmosphere’ is weakly coupled to a fast ‘tropical atmosphere’ which is, in turn, strongly coupled to a slow ‘ocean’ system, the latter coupling

  15. Lyapunov, singular and bred vectors in a multi-scale system: an empirical exploration of vectors related to instabilities

    Science.gov (United States)

    Norwood, Adrienne; Kalnay, Eugenia; Ide, Kayo; Yang, Shu-Chih; Wolfe, Christopher

    2013-06-01

    We compute and compare the three types of vectors frequently used to explore the instability properties of dynamical models, namely Lyapunov vectors (LVs), singular vectors (SVs) and bred vectors (BVs) in two systems, using the Wolfe-Samelson (2007 Tellus A 59 355-66) algorithm to compute all of the Lyapunov vectors. The first system is the Lorenz (1963 J. Atmos. Sci. 20 130-41) three-variable model. Although the leading Lyapunov vector, LV1, grows fastest globally, the second Lyapunov vector, LV2, which has zero growth globally, often grows faster than LV1 locally. Whenever this happens, BVs grow closer to LV2, suggesting that in larger atmospheric or oceanic models where several instabilities can grow in different areas of the world, BVs will grow toward the fastest growing local unstable mode. A comparison of their growth rates at different times shows that all three types of dynamical vectors have the ability to predict regime changes and the duration of the new regime based on their growth rates in the last orbit of the old regime, as shown for BVs by Evans et al (2004 Bull. Am. Meteorol. Soc. 520-4). LV1 and BVs have similar predictive skill, LV2 has a tendency to produce false alarms, and even LV3 shows that maximum decay is also associated with regime change. Initial and final SVs grow much faster and are the most accurate predictors of regime change, although the characteristics of the initial SVs are strongly dependent on the length of the optimization window. The second system is the toy ‘ocean-atmosphere’ model developed by Peña and Kalnay (2004 Nonlinear Process. Geophys. 11 319-27) coupling three Lorenz (1963 J. Atmos. Sci. 20 130-41) systems with different time scales, in order to test the effects of fast and slow modes of growth on the dynamical vectors. A fast ‘extratropical atmosphere’ is weakly coupled to a fast ‘tropical atmosphere’ which is, in turn, strongly coupled to a slow ‘ocean’ system, the latter coupling imitating the

  16. Gradient remediability in linear distributed parabolic systems ...

    African Journals Online (AJOL)

    The aim of this paper is the introduction of a new concept that concerned the analysis of a large class of distributed parabolic systems. It is the general concept of gradient remediability. More precisely, we study with respect to the gradient observation, the existence of an input operator (gradient efficient actuators) ensuring ...

  17. Timelike Constant Mean Curvature Surfaces with Singularities

    DEFF Research Database (Denmark)

    Brander, David; Svensson, Martin

    2014-01-01

    We use integrable systems techniques to study the singularities of timelike non-minimal constant mean curvature (CMC) surfaces in the Lorentz–Minkowski 3-space. The singularities arise at the boundary of the Birkhoff big cell of the loop group involved. We examine the behavior of the surfaces...

  18. Singularity is the Future of ICT Research

    African Journals Online (AJOL)

    PROF. OLIVER OSUAGWA

    2014-06-01

    Jun 1, 2014 ... tech systems, and how in the near future. Artificial Intelligence may impact our lives, AI, Robotics, nanotechnology, mechatronics are collaborative agents of technological singularity. The singularity is already here! Think of modern houses now remotely controlled from far distances, think of e-commerce and.

  19. H2 guaranteed cost control of discrete linear systems

    Directory of Open Access Journals (Sweden)

    W. Colmenares

    2000-01-01

    guaranteed cost performance on a discrete linear uncertain system where the uncertainty is of the norm bounded type. The conditions are presented as a collection of linear matrix inequalities.The solution, however requires a search over a scalar parameter space.

  20. Automatic frequency control system for driving a linear accelerator

    International Nuclear Information System (INIS)

    Helgesson, A.L.

    1976-01-01

    An automatic frequency control system is described for maintaining the drive frequency applied to a linear accelerator to produce maximum particle output from the accelerator. The particle output amplitude is measured and the frequency of the radio frequency source powering the linear accelerator is adjusted to maximize particle output amplitude

  1. Canonical symmetry in a system with singular Lagrangian and ward identities

    International Nuclear Information System (INIS)

    Li Ziping

    1994-01-01

    An algorithm to construct the generator of gauge transformation for a constrained Hamiltonian system is given. The relationships among the coefficients connecting with first-class constraints in the generator is cleared. Based on the phase space generating function, the corresponding Ward identities in canonical formalism is deduced. The preliminary applications of above results to a model in field theory which is functionally equivalent to the mixed Chern-Simons Lagrangian is discussed in detail

  2. Geodesic fields with singularities

    International Nuclear Information System (INIS)

    Kafker, A.H.

    1979-01-01

    The question considered is whether or not a Riemannian metric can be found to make a given curve field on a closed surface into geodesics. Allowing singularities removes the restriction to Euler characteristic zero. The main results are the following: only two types of isolated singularities can occur in a geodesic field on a surface. No geodsic fields exist on a surface with Euler characteristic less than zero. If the Euler characteristic is zero, such a geodesic field can have only removable singularities. Only a limited number of geodesic fields exist on S 2 and RP 2 . A closed geodesic (perhaps made from several curves and singularities) always appears in such a field

  3. Constructing Current Singularity in a 3D Line-tied Plasma

    Science.gov (United States)

    Zhou, Yao; Huang, Yi-Min; Qin, Hong; Bhattacharjee, A.

    2018-01-01

    We revisit Parker’s conjecture of current singularity formation in 3D line-tied plasmas using a recently developed numerical method, variational integration for ideal magnetohydrodynamics in Lagrangian labeling. With the frozen-in equation built-in, the method is free of artificial reconnection, and hence it is arguably an optimal tool for studying current singularity formation. Using this method, the formation of current singularity has previously been confirmed in the Hahm–Kulsrud–Taylor problem in 2D. In this paper, we extend this problem to 3D line-tied geometry. The linear solution, which is singular in 2D, is found to be smooth for arbitrary system length. However, with finite amplitude, the linear solution can become pathological when the system is sufficiently long. The nonlinear solutions turn out to be smooth for short systems. Nonetheless, the scaling of peak current density versus system length suggests that the nonlinear solution may become singular at finite length. With the results in hand, we can neither confirm nor rule out this possibility conclusively, since we cannot obtain solutions with system length near the extrapolated critical value.

  4. State control of discrete-time linear systems to be bound in state variables by equality constraints

    International Nuclear Information System (INIS)

    Filasová, Anna; Krokavec, Dušan; Serbák, Vladimír

    2014-01-01

    The paper is concerned with the problem of designing the discrete-time equivalent PI controller to control the discrete-time linear systems in such a way that the closed-loop state variables satisfy the prescribed equality constraints. Since the problem is generally singular, using standard form of the Lyapunov function and a symmetric positive definite slack matrix, the design conditions are proposed in the form of the enhanced Lyapunov inequality. The results, offering the conditions of the control existence and the optimal performance with respect to the prescribed equality constraints for square discrete-time linear systems, are illustrated with the numerical example to note effectiveness and applicability of the considered approach

  5. Analysis of Nonlinear Missile Guidance Systems Through Linear Adjoint Method

    Directory of Open Access Journals (Sweden)

    Khaled Gamal Eltohamy

    2015-12-01

    Full Text Available In this paper, a linear simulation algorithm, the adjoint method, is modified and employed as an efficient tool for analyzing the contributions of system parameters to the miss - distance of a nonlinear time-varying missile guidance system model. As an example for the application of the linear adjoint method, the effect of missile flight time on the miss - distance is studied. Since the missile model is highly nonlinear and a time-varying linearized model is required to apply the adjoint method, a new technique that utilizes the time-reversed linearized coefficients of the missile as a replacement for the time-varying describing functions is applied and proven to be successful. It is found that, when compared with Monte Carlo generated results, simulation results of this linear adjoint technique provide acceptable accuracy and can be produced with much less effort.

  6. Linear quadratic Gaussian balancing for discrete-time infinite-dimensional linear systems

    NARCIS (Netherlands)

    Opmeer, MR; Curtain, RF

    2004-01-01

    In this paper, we study the existence of linear quadratic Gaussian (LQG)-balanced realizations for discrete-time infinite-dimensional systems. LQG-balanced realizations are those for which the smallest nonnegative self-adjoint solutions of the control and filter Riccati equations are equal. We show

  7. Iterative Solvers within Sequences of Large Linear Systems in Non-linear Structural Mechanics

    Czech Academy of Sciences Publication Activity Database

    Hartmann, S.; Duintjer Tebbens, Jurjen; Quint, K.J.; Meister, A.

    2009-01-01

    Roč. 89, č. 9 (2009), s. 711-728 ISSN 0044-2267 R&D Projects: GA AV ČR KJB100300703 Institutional research plan: CEZ:AV0Z10300504 Keywords : iterative solver * non-symmetric matrices * sequences of linear systems * finite strains * finite elements Subject RIV: BA - General Mathematics Impact factor: 0.866, year: 2009

  8. VT Linear Referencing System - Town-Based 2013

    Data.gov (United States)

    Vermont Center for Geographic Information — LRS2013 is a Linear Referencing System layer that includes Interstate, U.S., State (VT), and other transportation routes logged by the Vermont Agency of...

  9. Optical Tomography System: Charge-coupled Device Linear Image Sensors

    Directory of Open Access Journals (Sweden)

    M. Idroas

    2010-09-01

    Full Text Available This paper discussed an optical tomography system based on charge-coupled device (CCD linear image sensors. The developed system consists of a lighting system, a measurement section and a data acquisition system. Four CCD linear image sensors are configured around a flow pipe with an octagonal-shaped measurement section, for a four projections system. The four CCD linear image sensors consisting of 2048 pixels with a pixel size of 14 micron by 14 micron are used to produce a high-resolution system. A simple optical model is mapped into the system’s sensitivity matrix to relate the optical attenuation due to variations of optical density within the measurement section. A reconstructed tomographic image is produced based on the model using MATLAB software. The designed instrumentation system is calibrated and tested through different particle size measurements from different projections.

  10. Singular and interactive effects of blowdown, salvage logging, and wildfire in sub-boreal pine systems

    Science.gov (United States)

    D'Amato, A.W.; Fraver, S.; Palik, B.J.; Bradford, J.B.; Patty, L.

    2011-01-01

    The role of disturbance in structuring vegetation is widely recognized; however, we are only beginning to understand the effects of multiple interacting disturbances on ecosystem recovery and development. Of particular interest is the impact of post-disturbance management interventions, particularly in light of the global controversy surrounding the effects of salvage logging on forest ecosystem recovery. Studies of salvage logging impacts have focused on the effects of post-disturbance salvage logging within the context of a single natural disturbance event. There have been no formal evaluations of how these effects may differ when followed in short sequence by a second, high severity natural disturbance. To evaluate the impact of this management practice within the context of multiple disturbances, we examined the structural and woody plant community responses of sub-boreal Pinus banksiana systems to a rapid sequence of disturbances. Specifically, we compared responses to Blowdown (B), Fire (F), Blowdown-Fire, and Blowdown-Salvage-Fire (BSF) and compared these to undisturbed control (C) stands. Comparisons between BF and BSF indicated that the primary effect of salvage logging was a decrease in the abundance of structural legacies, such as downed woody debris and snags. Both of these compound disturbance sequences (BF and BSF), resulted in similar woody plant communities, largely dominated by Populus tremuloides; however, there was greater homogeneity in community composition in salvage logged areas. Areas experiencing solely fire (F stands) were dominated by P. banksiana regeneration, and blowdown areas (B stands) were largely characterized by regeneration from shade tolerant conifer species. Our results suggest that salvage logging impacts on woody plant communities are diminished when followed by a second high severity disturbance; however, impacts on structural legacies persist. Provisions for the retention of snags, downed logs, and surviving trees as part

  11. A conceptual design of Final Focus Systems for linear colliders

    International Nuclear Information System (INIS)

    Brown, K.L.

    1987-06-01

    Linear colliders are a relatively recent development in the evolution of particle accelerators. This report discusses some of the approaches that have been considered for the design of Final Focus Systems to demagnify the beam exiting from a linac to the small size suitable for collisions at the interaction point. The system receiving the most attention is the one adopted for the SLAC Linear Collider. However, the theory and optical techniques discussed should be applicable to the design efforts for future machines

  12. Non-Linear Systems Identification Using Neural Networks

    OpenAIRE

    Chen, S.; Billings, S.A.; Grant, P.M.

    1989-01-01

    Multi-layered neural networks offer an exciting alternative for modelling complex non-linear systems. This paper investigates the identification of discrete-time non-linear systems using neural networks with a single hidden layer. New parameter estimation algorithms are derived for the neural network model based on a prediction error formulation and the application to both simulated and real data is included to demonstrate the effectiveness of the neural network approach.

  13. Iterative algorithms for large sparse linear systems on parallel computers

    Science.gov (United States)

    Adams, L. M.

    1982-01-01

    Algorithms for assembling in parallel the sparse system of linear equations that result from finite difference or finite element discretizations of elliptic partial differential equations, such as those that arise in structural engineering are developed. Parallel linear stationary iterative algorithms and parallel preconditioned conjugate gradient algorithms are developed for solving these systems. In addition, a model for comparing parallel algorithms on array architectures is developed and results of this model for the algorithms are given.

  14. Supersparse Linear Integer Models for Optimized Medical Scoring Systems

    OpenAIRE

    Ustun, Berk; Rudin, Cynthia

    2015-01-01

    Scoring systems are linear classification models that only require users to add, subtract and multiply a few small numbers in order to make a prediction. These models are in widespread use by the medical community, but are difficult to learn from data because they need to be accurate and sparse, have coprime integer coefficients, and satisfy multiple operational constraints. We present a new method for creating data-driven scoring systems called a Supersparse Linear Integer Model (SLIM). SLIM...

  15. Synchronization of linearly coupled unified chaotic systems based on linear balanced feedback scheme with constraints

    International Nuclear Information System (INIS)

    Chen, H.-H.; Chen, C.-S.; Lee, C.-I

    2009-01-01

    This paper investigates the synchronization of unidirectional and bidirectional coupled unified chaotic systems. A balanced coupling coefficient control method is presented for global asymptotic synchronization using the Lyapunov stability theorem and a minimum scheme with no constraints/constraints. By using the result of the above analysis, the balanced coupling coefficients are then designed to achieve the chaos synchronization of linearly coupled unified chaotic systems. The feasibility and effectiveness of the proposed chaos synchronization scheme are verified via numerical simulations.

  16. Fundamental solutions of singular SPDEs

    Energy Technology Data Exchange (ETDEWEB)

    Selesi, Dora, E-mail: dora@dmi.uns.ac.rs [Department of Mathematics and Informatics, University of Novi Sad (Serbia)

    2011-07-15

    Highlights: > Fundamental solutions of linear SPDEs are constructed. > Wick-convolution product is introduced for the first time. > Fourier transformation maps Wick-convolution into Wick product. > Solutions of linear SPDEs are expressed via Wick-convolution with fundamental solutions. > Stochastic Helmholtz equation is solved. - Abstract: This paper deals with some models of mathematical physics, where random fluctuations are modeled by white noise or other singular Gaussian generalized processes. White noise, as the distributional derivative od Brownian motion, which is the most important case of a Levy process, is defined in the framework of Hida distribution spaces. The Fourier transformation in the framework of singular generalized stochastic processes is introduced and its applications to solving stochastic differential equations involving Wick products and singularities such as the Dirac delta distribution are presented. Explicit solutions are obtained in form of a chaos expansion in the Kondratiev white noise space, while the coefficients of the expansion are tempered distributions. Stochastic differential equations of the form P({omega}, D) Lozenge u(x, {omega}) = A(x, {omega}) are considered, where A is a singular generalized stochastic process and P({omega}, D) is a partial differential operator with random coefficients. We introduce the Wick-convolution operator * which enables us to express the solution as u = s*A Lozenge I{sup Lozenge (-1)}, where s denotes the fundamental solution and I is the unit random variable. In particular, the stochastic Helmholtz equation is solved, which in physical interpretation describes waves propagating with a random speed from randomly appearing point sources.

  17. Fundamental solutions of singular SPDEs

    International Nuclear Information System (INIS)

    Selesi, Dora

    2011-01-01

    Highlights: → Fundamental solutions of linear SPDEs are constructed. → Wick-convolution product is introduced for the first time. → Fourier transformation maps Wick-convolution into Wick product. → Solutions of linear SPDEs are expressed via Wick-convolution with fundamental solutions. → Stochastic Helmholtz equation is solved. - Abstract: This paper deals with some models of mathematical physics, where random fluctuations are modeled by white noise or other singular Gaussian generalized processes. White noise, as the distributional derivative od Brownian motion, which is the most important case of a Levy process, is defined in the framework of Hida distribution spaces. The Fourier transformation in the framework of singular generalized stochastic processes is introduced and its applications to solving stochastic differential equations involving Wick products and singularities such as the Dirac delta distribution are presented. Explicit solutions are obtained in form of a chaos expansion in the Kondratiev white noise space, while the coefficients of the expansion are tempered distributions. Stochastic differential equations of the form P(ω, D) ◊ u(x, ω) = A(x, ω) are considered, where A is a singular generalized stochastic process and P(ω, D) is a partial differential operator with random coefficients. We introduce the Wick-convolution operator * which enables us to express the solution as u = s*A ◊ I ◊(-1) , where s denotes the fundamental solution and I is the unit random variable. In particular, the stochastic Helmholtz equation is solved, which in physical interpretation describes waves propagating with a random speed from randomly appearing point sources.

  18. Relative Error Model Reduction via Time-Weighted Balanced Stochastic Singular Perturbation

    DEFF Research Database (Denmark)

    Tahavori, Maryamsadat; Shaker, Hamid Reza

    2012-01-01

    A new mixed method for relative error model reduction of linear time invariant (LTI) systems is proposed in this paper. This order reduction technique is mainly based upon time-weighted balanced stochastic model reduction method and singular perturbation model reduction technique. Compared...

  19. B-spline solution of a singularly perturbed boundary value problem arising in biology

    International Nuclear Information System (INIS)

    Lin Bin; Li Kaitai; Cheng Zhengxing

    2009-01-01

    We use B-spline functions to develop a numerical method for solving a singularly perturbed boundary value problem associated with biology science. We use B-spline collocation method, which leads to a tridiagonal linear system. The accuracy of the proposed method is demonstrated by test problems. The numerical result is found in good agreement with exact solution.

  20. Isotopy of Morin singularities

    OpenAIRE

    Saji, Kentaro

    2015-01-01

    We define an equivalence relation called A-isotopy between finitely determined map-germs, which is a strengthened version of A-equivalence. We consider the number of A-isotopy classes of equidimensional Morin singularities, and some other well-known low-dimensional singularities. We also give an application to stable perturbations of simple equi-dimensional map-germs.

  1. Economic MPC for a linear stochastic system of energy units

    DEFF Research Database (Denmark)

    Jørgensen, John Bagterp; Sokoler, Leo Emil; Standardi, Laura

    2016-01-01

    in addition to stochastic power producers such as wind turbines and solar power plants. Control of such large scale systems requires new control algorithms. In this paper, we formulate the control of such a system as an Economic Model Predictive Control (MPC) problem. When the power producers and controllable...... power consumers have linear dynamics, the Economic MPC may be expressed as a linear program. We provide linear models for a number of energy units in an energy system, formulate an Economic MPC for coordination of such a system. We indicate how advances in computational MPC makes the solutions...... of such large-scale models feasible in real-time. The system presented may serve as a benchmark for simulation and control of smart energy systems and we indicate how advances in computational MPC....

  2. Parametric linear hybrid automata for complex environmental systems modeling

    NARCIS (Netherlands)

    Tareen, Samar Hayat Khan; Ahmad, Jamil; Roux, Olivier

    2015-01-01

    Environmental systems, whether they be weather patterns or predator–prey relationships, are dependent on a number different variables, each directly or indirectly affecting the system at large. Since not all of these factors are known, these systems take on non-linear dynamics, making it difficult

  3. Stability and response bounds of non-conservative linear systems

    DEFF Research Database (Denmark)

    Pommer, Christian

    2003-01-01

    For a linear system of second order differential equations the stability is studied by Lyapunov's direct method. The Lyapunov matrix equation is solved and a sufficient condition for stability is expressed by the system matrices. For a system which satisfies the condition for stability the Lyapunov...

  4. Euclidean null controllability of linear systems with delays in state ...

    African Journals Online (AJOL)

    Sufficient conditions are developed for the Euclidean controllability of linear systems with delay in state and in control. Namely, if the uncontrolled system is uniformly asymptotically stable and the control equation proper, then the control system is Euclidean null controllable. Journal of the Nigerian Association of ...

  5. Model Reduction of Linear Switched Systems by Restricting Discrete Dynamics

    DEFF Research Database (Denmark)

    Bastug, Mert; Petreczky, Mihaly; Wisniewski, Rafal

    2014-01-01

    We present a procedure for reducing the number of continuous states of discrete-time linear switched systems, such that the reduced system has the same behavior as the original system for a subset of switching sequences. The proposed method is expected to be useful for abstraction based control...

  6. Introduction to singularities

    CERN Document Server

    Ishii, Shihoko

    2014-01-01

    This book is an introduction to singularities for graduate students and researchers. It is said that algebraic geometry originated in the seventeenth century with the famous work Discours de la méthode pour bien conduire sa raison, et chercher la vérité dans les sciences by Descartes. In that book he introduced coordinates to the study of geometry. After its publication, research on algebraic varieties developed steadily. Many beautiful results emerged in mathematicians’ works. Most of them were about non-singular varieties. Singularities were considered “bad” objects that interfered with knowledge of the structure of an algebraic variety. In the past three decades, however, it has become clear that singularities are necessary for us to have a good description of the framework of varieties. For example, it is impossible to formulate minimal model theory for higher-dimensional cases without singularities. Another example is that the moduli spaces of varieties have natural compactification, the boundar...

  7. The H-N method for solving linear transport equation: theory and application

    International Nuclear Information System (INIS)

    Kaskas, A.; Gulecyuz, M.C.; Tezcan, C.

    2002-01-01

    The system of singular integral equation which is obtained from the integro-differential form of the linear transport equation as a result of Placzec lemma is solved. Application are given using the exit distributions and the infinite medium Green's function. The same theoretical results are also obtained with the use of the singular eigenfunction of the method of elementary solutions

  8. Singularity: Scientific containers for mobility of compute.

    Directory of Open Access Journals (Sweden)

    Gregory M Kurtzer

    Full Text Available Here we present Singularity, software developed to bring containers and reproducibility to scientific computing. Using Singularity containers, developers can work in reproducible environments of their choosing and design, and these complete environments can easily be copied and executed on other platforms. Singularity is an open source initiative that harnesses the expertise of system and software engineers and researchers alike, and integrates seamlessly into common workflows for both of these groups. As its primary use case, Singularity brings mobility of computing to both users and HPC centers, providing a secure means to capture and distribute software and compute environments. This ability to create and deploy reproducible environments across these centers, a previously unmet need, makes Singularity a game changing development for computational science.

  9. The Geometry of Black Hole Singularities

    Directory of Open Access Journals (Sweden)

    Ovidiu Cristinel Stoica

    2014-01-01

    Full Text Available Recent results show that important singularities in General Relativity can be naturally described in terms of finite and invariant canonical geometric objects. Consequently, one can write field equations which are equivalent to Einstein's at nonsingular points but, in addition remain well-defined and smooth at singularities. The black hole singularities appear to be less undesirable than it was thought, especially after we remove the part of the singularity due to the coordinate system. Black hole singularities are then compatible with global hyperbolicity and do not make the evolution equations break down, when these are expressed in terms of the appropriate variables. The charged black holes turn out to have smooth potential and electromagnetic fields in the new atlas. Classical charged particles can be modeled, in General Relativity, as charged black hole solutions. Since black hole singularities are accompanied by dimensional reduction, this should affect Feynman's path integrals. Therefore, it is expected that singularities induce dimensional reduction effects in Quantum Gravity. These dimensional reduction effects are very similar to those postulated in some approaches to make Quantum Gravity perturbatively renormalizable. This may provide a way to test indirectly the effects of singularities, otherwise inaccessible.

  10. The effect of a curvature-dependent surface tension on the singularities at the tips of a straight interface crack

    KAUST Repository

    Zemlyanova, A. Y.

    2013-03-08

    A problem of an interface crack between two semi-planes made out of different materials under an action of an in-plane loading of general tensile-shear type is treated in a semi-analytical manner with the help of Dirichlet-to-Neumann mappings. The boundaries of the crack and the interface between semi-planes are subjected to a curvature-dependent surface tension. The resulting system of six singular integro-differential equations is reduced to the system of three Fredholm equations. It is shown that the introduction of the curvature-dependent surface tension eliminates both classical integrable power singularity of the order 1/2 and an oscillating singularity present in a classical linear elasticity solutions. The numerical results are obtained by solving the original system of singular integro-differential equations by approximating unknown functions with Taylor polynomials. © 2013 The Author.

  11. Modeling and analysis of linear hyperbolic systems of balance laws

    CERN Document Server

    Bartecki, Krzysztof

    2016-01-01

    This monograph focuses on the mathematical modeling of distributed parameter systems in which mass/energy transport or wave propagation phenomena occur and which are described by partial differential equations of hyperbolic type. The case of linear (or linearized) 2 x 2 hyperbolic systems of balance laws is considered, i.e., systems described by two coupled linear partial differential equations with two variables representing physical quantities, depending on both time and one-dimensional spatial variable. Based on practical examples of a double-pipe heat exchanger and a transportation pipeline, two typical configurations of boundary input signals are analyzed: collocated, wherein both signals affect the system at the same spatial point, and anti-collocated, in which the input signals are applied to the two different end points of the system. The results of this book emerge from the practical experience of the author gained during his studies conducted in the experimental installation of a heat exchange cente...

  12. String theory and cosmological singularities

    Indian Academy of Sciences (India)

    time' can have a beginning or end. Well-known examples are singularities inside black holes and initial or final singularities in expanding or contracting universes. In recent times, string theory is providing new perspectives of such singularities ...

  13. A comparison between linear and toroidal Extrap systems

    International Nuclear Information System (INIS)

    Lehnert, B.

    1988-09-01

    The Extrap scheme consists of a Z-pinch immersed in an octupole field generated by currents in a set of external conductors. A comparison between linear and toroidal Extrap geometry is made in this paper. As compared to toroidal systems, linear geometry has the advantages of relative simplicity and of a current drive by means of electrodes. Linear devices are convenient for basic studies of Extrap, at moderately high pinch currents and plasma temperatures. Within the parameter ranges of experiments at high pinch currents and plasma temperatures, linear systems have on the other hand some substantial disadvantages, on account of the plasma interaction with the end regions. This results in a limitation of the energy confinement time, and leads in the case of an ohmically heated plasma to excessively high plasma densities and small pinch radii which also complicate the introduction of the external conductors. (author)

  14. Linear local stability of electrostatic drift modes in helical systems

    International Nuclear Information System (INIS)

    Yamagishi, O.; Nakajima, N.; Sugama, H.; Nakamura, Y.

    2003-01-01

    We investigate the stability of the drift wave in helical systems. For this purpose, we solve the linear local gyrokinetic-Poisson equation, in the electrostatic regime. As a model of helical plasmas, Large helical Device (LHD) is considered. The equation we apply is rather exact in the framework of linear gyrokinetic theory, where only the approximation is the ballooning representation. In this paper, we consider only collisionless cases. All the frequency regime can be naturally reated without any assumptions, and in such cases, ion temperature gradient modes (ITG), trapped electron modes (TEM), and electron temperature gradient modes (ETG) are expected to become unstable linearly independently. (orig.)

  15. Singular formalism and admissible control of spacecraft with rotating flexible solar array

    Directory of Open Access Journals (Sweden)

    Lu Dongning

    2014-02-01

    Full Text Available This paper is concerned with the attitude control of a three-axis-stabilized spacecraft which consists of a central rigid body and a flexible sun-tracking solar array driven by a solar array drive assembly. Based on the linearization of the dynamics of the spacecraft and the modal identities about the flexible and rigid coupling matrices, the spacecraft attitude dynamics is reduced to a formally singular system with periodically varying parameters, which is quite different from a spacecraft with fixed appendages. In the framework of the singular control theory, the regularity and impulse-freeness of the singular system is analyzed and then admissible attitude controllers are designed by Lyapunov’s method. To improve the robustness against system uncertainties, an H∞ optimal control is designed by optimizing the H∞ norm of the system transfer function matrix. Comparative numerical experiments are performed to verify the theoretical results.

  16. H 2 guaranteed cost control of discrete linear systems

    Directory of Open Access Journals (Sweden)

    Colmenares W.

    2000-01-01

    Full Text Available This paper presents necessary and sufficient conditions for the existence of a quadratically stabilizing output feedback controller which also assures H 2 guaranteed cost performance on a discrete linear uncertain system where the uncertainty is of the norm bounded type. The conditions are presented as a collection of linear matrix inequalities.The solution, however requires a search over a scalar parameter space.

  17. Structured Control of Affine Linear Parameter Varying Systems

    DEFF Research Database (Denmark)

    Adegas, Fabiano Daher; Stoustrup, Jakob

    2011-01-01

    This paper presents a new procedure to design structured controllers for discrete-time affine linear parametervarying systems (A LPV). The class of control structures includes decentralized of any order, fixed order output feedback, simultaneous plant-control design, among others. A parametervaryin...... non-convex condition for an upper bound on the induced L2-norm performance is solved by an iterative linear matrix inequalities (LMI) optimization algorithm. Numerical examples demostrate the effectiveness of the proposed approach....

  18. Tape measuring system using linear encoder and digital camera

    Science.gov (United States)

    Eom, Tae Bong; Jeong, Don Young; Kim, Myung Soon; Kim, Jae Wan; Kim, Jong Ahn

    2013-04-01

    We have designed and constructed the calibration system of line standards such as tape and rule for the secondary calibration laboratories. The system consists of the main body with linear stage and linear encoder, the optical microscope with digital camera, and the computer. The base of the system is a aluminum profile with 2.9 m length, 0.09 m height and 0.18 m width. The linear stage and the linear encoder are fixed on the aluminum profile. The micro-stage driven by micrometer is fixed on the carriage of the long linear stage, and the optical microscope with digital camera and the tablet PC are on the this stage. The linear encoder counts the moving distance of the linear stage with resolution of 1 μm and its counting value is transferred to the tablet PC. The image of the scale mark of the tape is captured by the CCD camera of optical microscope and transferred to the PC through USB interface. The computer automatically determines the center of the scale mark by image processing technique and at the same time reads the moving distance of the linear stage. As a result, the computer can calculate the interval between the scale marks of the tape. In order to achieve the high accuracy, the linear encoder should be calibrated using the laser interferometer or the rigid steel rule. This calibration data of the linear encoder is stored at the computer and the computer corrects the reading value of the linear encoder. In order to determine the center of the scale mark, we use three different algorithms. First, the image profile over specified threshold level is fitted in even order polynomial and the axis of the polynomial is used as the center of the line. Second, the left side and right side areas at the center of the image profile are calculated so that two areas are same. Third, the left and right edges of the image profile are determined at every intensity level of the image and the center of the graduation is calculated as an average of the centers of the left

  19. Quantum propagation across cosmological singularities

    Science.gov (United States)

    Gielen, Steffen; Turok, Neil

    2017-05-01

    The initial singularity is the most troubling feature of the standard cosmology, which quantum effects are hoped to resolve. In this paper, we study quantum cosmology with conformal (Weyl) invariant matter. We show that it is natural to extend the scale factor to negative values, allowing a large, collapsing universe to evolve across a quantum "bounce" into an expanding universe like ours. We compute the Feynman propagator for Friedmann-Robertson-Walker backgrounds exactly, identifying curious pathologies in the case of curved (open or closed) universes. We then include anisotropies, fixing the operator ordering of the quantum Hamiltonian by imposing covariance under field redefinitions and again finding exact solutions. We show how complex classical solutions allow one to circumvent the singularity while maintaining the validity of the semiclassical approximation. The simplest isotropic universes sit on a critical boundary, beyond which there is qualitatively different behavior, with potential for instability. Additional scalars improve the theory's stability. Finally, we study the semiclassical propagation of inhomogeneous perturbations about the flat, isotropic case, at linear and nonlinear order, showing that, at least at this level, there is no particle production across the bounce. These results form the basis for a promising new approach to quantum cosmology and the resolution of the big bang singularity.

  20. Dissipativity Analysis of Linear State/Input Delay Systems

    Directory of Open Access Journals (Sweden)

    Guifang Cheng

    2012-01-01

    Full Text Available This paper discusses dissipativity problem for system of linear state/input delay equations. Motivated by dissipativity theory of control systems, we choose a new quadratic supply rate. Using the concept of dissipativity, necessary and sufficient conditions for the linear state/input delay systems to be dissipative and exponentially dissipative are derived. The connection of dissipativity with stability is also considered. Finally, passivity and finite gain are explored, correspondingly. The positive-real and bounded-real lemmas are derived.

  1. State space and input-output linear systems

    CERN Document Server

    Delchamps, David F

    1988-01-01

    It is difficult for me to forget the mild sense of betrayal I felt some ten years ago when I discovered, with considerable dismay, that my two favorite books on linear system theory - Desoer's Notes for a Second Course on Linear Systems and Brockett's Finite Dimensional Linear Systems - were both out of print. Since that time, of course, linear system theory has undergone a transformation of the sort which always attends the maturation of a theory whose range of applicability is expanding in a fashion governed by technological developments and by the rate at which such advances become a part of engineering practice. The growth of the field has inspired the publication of some excellent books; the encyclopedic treatises by Kailath and Chen, in particular, come immediately to mind. Nonetheless, I was inspired to write this book primarily by my practical needs as a teacher and researcher in the field. For the past five years, I have taught a one semester first year gradu­ ate level linear system theory course i...

  2. Lag synchronization of chaotic systems with time-delayed linear ...

    Indian Academy of Sciences (India)

    In this paper, the lag synchronization of chaotic systems with time-delayed linear terms via impulsive control is investigated. Based on the stability theory of impulsive delayed differential equations, some sufficient conditions are obtained guaranteeing the synchronized behaviours between two delayed chaotic systems.

  3. Punctuated equilibrium in a non-linear system of action

    NARCIS (Netherlands)

    J.S. Timmermans (Jos)

    2008-01-01

    textabstractColeman's equilibrium model of social development, the Linear System of Action, is extended to cover the dynamics of societal transitions. The model implemented has the characteristics of a dissipative system. A variation and selection algorithm favoring the retention of relatively

  4. Lag synchronization of chaotic systems with time-delayed linear

    Indian Academy of Sciences (India)

    In this paper, the lag synchronization of chaotic systems with time-delayed linear terms via impulsive control is investigated. Based on the stability theory of impulsive delayed differential equations, some sufficient conditions are obtained guaranteeing the synchronized behaviours between two delayed chaotic systems.

  5. A study on switched linear system identification using game ...

    African Journals Online (AJOL)

    This study deals with application of game-theoretic strategies and neural computing to switched linear system identification, wherein some of the subsystems may be in failed, standby, or working states. The controller is to detect failed subsystems, and switch standby and working subsystems to maintain stable system ...

  6. New approach to solve symmetric fully fuzzy linear systems

    Indian Academy of Sciences (India)

    In this paper, we present a method to solve fully fuzzy linear systems with symmetric coefficient matrix. The symmetric coefficient matrix is decomposed into two systems of equations by using Cholesky method and then a solution can be obtained. Numerical examples are given to illustrate our method.

  7. Criteria for stability of linear dynamical systems with multiple delays ...

    African Journals Online (AJOL)

    In this study we considered a linear Dynamical system with multiple delays and find suitable conditions on the systems parameters such that for a given initial function, we can define a mapping in a carefully chosen complete metric space on which the mapping has a unique fixed point. An asymptotic stability theory for the ...

  8. Lag synchronization of chaotic systems with time-delayed linear ...

    Indian Academy of Sciences (India)

    sive control scheme can reduce the control cost significantly, and so it is of great use in practical applications. Now, in this paper, lag synchronization of chaotic systems with time-delayed linear terms will be investigated. The scheme is showed effective through numerical simulations on chaotic systems. The rest of the paper ...

  9. Theoretical analysis of balanced truncation for linear switched systems

    DEFF Research Database (Denmark)

    Petreczky, Mihaly; Wisniewski, Rafal; Leth, John-Josef

    2012-01-01

    In this paper we present theoretical analysis of model reduction of linear switched systems based on balanced truncation, presented in [1,2]. More precisely, (1) we provide a bound on the estimation error using L2 gain, (2) we provide a system theoretic interpretation of grammians and their singu...

  10. Dynamic Response of Linear Mechanical Systems Modeling, Analysis and Simulation

    CERN Document Server

    Angeles, Jorge

    2012-01-01

    Dynamic Response of Linear Mechanical Systems: Modeling, Analysis and Simulation can be utilized for a variety of courses, including junior and senior-level vibration and linear mechanical analysis courses. The author connects, by means of a rigorous, yet intuitive approach, the theory of vibration with the more general theory of systems. The book features: A seven-step modeling technique that helps structure the rather unstructured process of mechanical-system modeling A system-theoretic approach to deriving the time response of the linear mathematical models of mechanical systems The modal analysis and the time response of two-degree-of-freedom systems—the first step on the long way to the more elaborate study of multi-degree-of-freedom systems—using the Mohr circle Simple, yet powerful simulation algorithms that exploit the linearity of the system for both single- and multi-degree-of-freedom systems Examples and exercises that rely on modern computational toolboxes for both numerical and symbolic compu...

  11. Ultra-high Frequency Linear Fiber Optic Systems

    CERN Document Server

    Lau, Kam

    2011-01-01

    This book provides an in-depth treatment of both linear fiber-optic systems and their key enabling devices. It presents a concise but rigorous treatment of the theory and practice of analog (linear) fiber-optics links and systems that constitute the foundation of Hybrid Fiber Coax infrastructure in present-day CATV distribution and cable modem Internet access. Emerging applications in remote fiber-optic feed for free-space millimeter wave enterprise campus networks are also described. Issues such as dispersion and interferometric noise are treated quantitatively, and means for mitigating them are explained. This broad but concise text will thus be invaluable not only to students of fiber-optics communication but also to practicing engineers. To the second edition of this book important new aspects of linear fiber-optic transmission technologies are added, such as high level system architectural issues, algorithms for deriving the optimal frequency assignment, directly modulated or externally modulated laser t...

  12. Damped oscillations of linear systems a mathematical introduction

    CERN Document Server

    Veselić, Krešimir

    2011-01-01

    The theory of linear damped oscillations was originally developed more than hundred years ago and is still of vital research interest to engineers, mathematicians and physicists alike. This theory plays a central role in explaining the stability of mechanical structures in civil engineering, but it also has applications in other fields such as electrical network systems and quantum mechanics. This volume gives an introduction to linear finite dimensional damped systems as they are viewed by an applied mathematician. After a short overview of the physical principles leading to the linear system model, a largely self-contained mathematical theory for this model is presented. This includes the geometry of the underlying indefinite metric space, spectral theory of J-symmetric matrices and the associated quadratic eigenvalue problem. Particular attention is paid to the sensitivity issues which influence numerical computations. Finally, several recent research developments are included, e.g. Lyapunov stability and ...

  13. Robust computer-aided synthesis and optimization of linear multivariable control systems with varying plant dynamics via AUTOCON

    Science.gov (United States)

    Lefkowitz, C. P.; Tekawy, J. A.; Pujara, P. K.; Safonov, M. G.

    1989-01-01

    AUTOCON is an automated computer-aided design tool for the synthesis and optimization of linear multivariable control systems based upon user-defined control parameter optimization. Violations in stability and performance requirements are computed from constraints on Single Input/Single Output (SISO) open- and closed-loop transfer function frequency responses, and from constraints on the singular-value frequency responses of Multiple Input/Multiple Output (MIMO) transfer functions, for all critical plant variations. Optimum nonlinear programming algorithms are used in the search for local constrained solutions in which violations in stability and performance are caused either to vanish or be minimized for a proper selection of the control parameters. Classical control system stability and performance design can, in this way, be combined with modern multivariable robustness methods to offer general frequency response loop-shaping via a computer-aided design tool. Complete Nichols, Nyquist, Bode, singular-value Bode magnitude and transient response plots are produced, including user-defined boundary responses. AUTOCON is used to synthesize and optimize the lateral/directional flight control system for a typical high-performance aircraft.

  14. Linear dynamical quantum systems analysis, synthesis, and control

    CERN Document Server

    Nurdin, Hendra I

    2017-01-01

    This monograph provides an in-depth treatment of the class of linear-dynamical quantum systems. The monograph presents a detailed account of the mathematical modeling of these systems using linear algebra and quantum stochastic calculus as the main tools for a treatment that emphasizes a system-theoretic point of view and the control-theoretic formulations of quantum versions of familiar problems from the classical (non-quantum) setting, including estimation and filtering, realization theory, and feedback control. Both measurement-based feedback control (i.e., feedback control by a classical system involving a continuous-time measurement process) and coherent feedback control (i.e., feedback control by another quantum system without the intervention of any measurements in the feedback loop) are treated. Researchers and graduates studying systems and control theory, quantum probability and stochastics or stochastic control whether from backgrounds in mechanical or electrical engineering or applied mathematics ...

  15. System identication of a linearized hysteretic system using covariance driven stochastic subspace identication

    DEFF Research Database (Denmark)

    Bajric, Anela

    A single mass Bouc-Wen oscillator with linear static restoring force contribution is approximated by an equivalent linear system. The aim of the linearized model is to emulate the correct force-displacement response of the Bouc-Wenmodel with characteristic hysteretic behaviour. The linearized model...

  16. The Big Bang Singularity

    Science.gov (United States)

    Ling, Eric

    The big bang theory is a model of the universe which makes the striking prediction that the universe began a finite amount of time in the past at the so called "Big Bang singularity." We explore the physical and mathematical justification of this surprising result. After laying down the framework of the universe as a spacetime manifold, we combine physical observations with global symmetrical assumptions to deduce the FRW cosmological models which predict a big bang singularity. Next we prove a couple theorems due to Stephen Hawking which show that the big bang singularity exists even if one removes the global symmetrical assumptions. Lastly, we investigate the conditions one needs to impose on a spacetime if one wishes to avoid a singularity. The ideas and concepts used here to study spacetimes are similar to those used to study Riemannian manifolds, therefore we compare and contrast the two geometries throughout.

  17. Surface Plasmon Singularities

    Directory of Open Access Journals (Sweden)

    Gabriel Martínez-Niconoff

    2012-01-01

    Full Text Available With the purpose to compare the physical features of the electromagnetic field, we describe the synthesis of optical singularities propagating in the free space and on a metal surface. In both cases the electromagnetic field has a slit-shaped curve as a boundary condition, and the singularities correspond to a shock wave that is a consequence of the curvature of the slit curve. As prototypes, we generate singularities that correspond to fold and cusped regions. We show that singularities in free space may generate bifurcation effects while plasmon fields do not generate these kinds of effects. Experimental results for free-space propagation are presented and for surface plasmon fields, computer simulations are shown.

  18. Parametric linear hybrid automata for complex environmental systems modeling

    OpenAIRE

    Tareen, Samar H. K.; Ahmad, Jamil; Roux, Olivier

    2015-01-01

    Environmental systems, whether they be weather patterns or predator–prey relationships, are dependent on a number different variables, each directly or indirectly affecting the system at large. Since not all of these factors are known, these systems take on non-linear dynamics, making it difficult to accurately predict meaningful behavioral trends far into the future. However, such dynamics do not warrant complete ignorance of different efforts to understand and model close approximations of ...

  19. Stability analysis of linear switching systems with time delays

    International Nuclear Information System (INIS)

    Li Ping; Zhong Shouming; Cui Jinzhong

    2009-01-01

    The issue of stability analysis of linear switching system with discrete and distributed time delays is studied in this paper. An appropriate switching rule is applied to guarantee the stability of the whole switching system. Our results use a Riccati-type Lyapunov functional under a condition on the time delay. So, switching systems with mixed delays are developed. A numerical example is given to illustrate the effectiveness of our results.

  20. Control of Non-linear Marine Cooling System

    DEFF Research Database (Denmark)

    Hansen, Michael; Stoustrup, Jakob; Bendtsen, Jan Dimon

    2011-01-01

    We consider the problem of designing control laws for a marine cooling system used for cooling the main engine and auxiliary components aboard several classes of container vessels. We focus on achieving simple set point control for the system and do not consider compensation of the non......-linearities, closed circuit flow dynamics or transport delays that are present in the system. Control laws are therefore designed using classical control theory and the performance of the design is illustrated through two simulation examples....

  1. The graphics software of the Saclay linear accelerator control system

    International Nuclear Information System (INIS)

    Gournay, J.F.

    1987-06-01

    The Control system of the Saclay Linear Accelerator is based upon modern technology hardware. In the graphic software, pictures are created in exactly the same manner for all the graphic devices supported by the system. The informations used to draw a picture are stored in an array called a graphic segment. Three output primitives are used to add graphic material in a segment. Three coordinate systems are defined

  2. On reliability of singular-value decomposition in attractor reconstruction

    International Nuclear Information System (INIS)

    Palus, M.; Dvorak, I.

    1990-12-01

    Applicability of singular-value decomposition for reconstructing the strange attractor from one-dimensional chaotic time series, proposed by Broomhead and King, is extensively tested and discussed. Previously published doubts about its reliability are confirmed: singular-value decomposition, by nature a linear method, is only of a limited power when nonlinear structures are studied. (author). 29 refs, 9 figs

  3. A numerical method for solving singular De`s

    Energy Technology Data Exchange (ETDEWEB)

    Mahaver, W.T.

    1996-12-31

    A numerical method is developed for solving singular differential equations using steepest descent based on weighted Sobolev gradients. The method is demonstrated on a variety of first and second order problems, including linear constrained, unconstrained, and partially constrained first order problems, a nonlinear first order problem with irregular singularity, and two second order variational problems.

  4. Reliable finite element methods for self-adjoint singular perturbation ...

    African Journals Online (AJOL)

    It is well known that the standard finite element method based on the space Vh of continuous piecewise linear functions is not reliable in solving singular perturbation problems. It is also known that the solution of a two-point boundaryvalue singular perturbation problem admits a decomposition into a regular part and a finite ...

  5. Experimental quantum computing to solve systems of linear equations.

    Science.gov (United States)

    Cai, X-D; Weedbrook, C; Su, Z-E; Chen, M-C; Gu, Mile; Zhu, M-J; Li, Li; Liu, Nai-Le; Lu, Chao-Yang; Pan, Jian-Wei

    2013-06-07

    Solving linear systems of equations is ubiquitous in all areas of science and engineering. With rapidly growing data sets, such a task can be intractable for classical computers, as the best known classical algorithms require a time proportional to the number of variables N. A recently proposed quantum algorithm shows that quantum computers could solve linear systems in a time scale of order log(N), giving an exponential speedup over classical computers. Here we realize the simplest instance of this algorithm, solving 2×2 linear equations for various input vectors on a quantum computer. We use four quantum bits and four controlled logic gates to implement every subroutine required, demonstrating the working principle of this algorithm.

  6. SNR Estimation in Linear Systems with Gaussian Matrices

    KAUST Repository

    Suliman, Mohamed Abdalla Elhag

    2017-09-27

    This letter proposes a highly accurate algorithm to estimate the signal-to-noise ratio (SNR) for a linear system from a single realization of the received signal. We assume that the linear system has a Gaussian matrix with one sided left correlation. The unknown entries of the signal and the noise are assumed to be independent and identically distributed with zero mean and can be drawn from any distribution. We use the ridge regression function of this linear model in company with tools and techniques adapted from random matrix theory to achieve, in closed form, accurate estimation of the SNR without prior statistical knowledge on the signal or the noise. Simulation results show that the proposed method is very accurate.

  7. A Proof System for the Linear Time μ-Calculus

    DEFF Research Database (Denmark)

    Dax, Christian; Hofmann, Martin; Lange, Martin

    2006-01-01

    The linear time μ-calculus extends LTL with arbitrary least and greatest fixpoint operators. This gives it the power to express all ω-regular languages, i.e. strictly more than LTL. The validity problem is PSPACE-complete for both LTL and the linear time μ-calculus. In practice it is more difficult...... for the latter because of nestings of fixpoint operators and variables with several occurrences. We present a simple sound and complete infinitary proof system for the linear time μ-calculus and then present two decision procedures for provability in the system, hence validity of formulas. One uses...... nondeterministic Büchi automata, the other one a generalisation of size-change termination analysis (SCT) known from functional programming. The main novelties of this paper are the connection with SCT and the fact that both decision procedures have a better asymptotic complexity than earlier ones and have been...

  8. Input design for linear dynamic systems using maxmin criteria

    DEFF Research Database (Denmark)

    Sadegh, Payman; Hansen, Lars H.; Madsen, Henrik

    1998-01-01

    This paper considers the problem of input design for maximizing the smallest eigenvalue of the information matrix for linear dynamic systems. The optimization of the smallest eigenvalue is of interest in parameter estimation and parameter change detection problems. We describe a simple cutting pl...... plane algorithm to determine the optimal frequency power weights of the input, using successive solutions to linear programs. We present a case study related to estimation of thermal parameters of a building.......This paper considers the problem of input design for maximizing the smallest eigenvalue of the information matrix for linear dynamic systems. The optimization of the smallest eigenvalue is of interest in parameter estimation and parameter change detection problems. We describe a simple cutting...

  9. Design of a dependable Interlock System for linear colliders

    CERN Document Server

    Nouvel, Patrice

    For high energy accelerators, the interlock system is a key part of the machine protection. The interlock principle is to inhibit the beam either on failure of critical equipment and/or on low beam quality evaluation. The dependability of such a system is the most critical parameter. This thesis presents the design of an dependable interlock system for linear collider with an application to the CLIC (Compact Linear Collider) project. This design process is based on the IEEE 1220 standard and is is divided in four steps. First, the specifications are established, with a focus on the dependability, more precisely the reliability and the availability of the system. The second step is the design proposal based on a functional analysis, the CLIC and interfaced systems architecture. Third, the feasibility study is performed, applying the concepts in an accelerator facility. Finally, the last step is the hardware verification. Its aim is to prove that the proposed design is able to reach the requirements.

  10. Numerical Approaches to Spacetime Singularities

    Directory of Open Access Journals (Sweden)

    Beverly K. Berger

    1998-05-01

    Full Text Available This review updates a previous review article. Numerical explorationof the properties of singularities could, in principle, yield detailed understanding of their nature in physically realistic cases. Examples of numerical investigations into the formation of naked singularities, critical behavior in collapse, passage through the Cauchy horizon, chaos of the Mixmaster singularity, and singularities in spatially inhomogeneous cosmologies are discussed.

  11. Seismic analysis of equipment system with non-linearities such as gap and friction using equivalent linearization method

    International Nuclear Information System (INIS)

    Murakami, H.; Hirai, T.; Nakata, M.; Kobori, T.; Mizukoshi, K.; Takenaka, Y.; Miyagawa, N.

    1989-01-01

    Many of the equipment systems of nuclear power plants contain a number of non-linearities, such as gap and friction, due to their mechanical functions. It is desirable to take such non-linearities into account appropriately for the evaluation of the aseismic soundness. However, in usual design works, linear analysis method with rough assumptions is applied from engineering point of view. An equivalent linearization method is considered to be one of the effective analytical techniques to evaluate non-linear responses, provided that errors to a certain extent are tolerated, because it has greater simplicity in analysis and economization in computing time than non-linear analysis. The objective of this paper is to investigate the applicability of the equivalent linearization method to evaluate the maximum earthquake response of equipment systems such as the CANDU Fuelling Machine which has multiple non- linearities

  12. Design techniques for large scale linear measurement systems

    International Nuclear Information System (INIS)

    Candy, J.V.

    1979-03-01

    Techniques to design measurement schemes for systems modeled by large scale linear time invariant systems, i.e., physical systems modeled by a large number (> 5) of ordinary differential equations, are described. The techniques are based on transforming the physical system model to a coordinate system facilitating the design and then transforming back to the original coordinates. An example of a three-stage, four-species, extraction column used in the reprocessing of spent nuclear fuel elements is presented. The basic ideas are briefly discussed in the case of noisy measurements. An example using a plutonium nitrate storage vessel (reprocessing) with measurement uncertainty is also presented

  13. Time-optimal feedback control for linear systems

    International Nuclear Information System (INIS)

    Mirica, S.

    1976-01-01

    The paper deals with the results of qualitative investigations of the time-optimal feedback control for linear systems with constant coefficients. In the first section, after some definitions and notations, two examples are given and it is shown that even the time-optimal control problem for linear systems with constant coefficients which looked like ''completely solved'' requires a further qualitative investigation of the stability to ''permanent perturbations'' of optimal feedback control. In the second section some basic results of the linear time-optimal control problem are reviewed. The third section deals with the definition of Boltyanskii's ''regular synthesis'' and its connection to Filippov's theory of right-hand side discontinuous differential equations. In the fourth section a theorem is proved concerning the stability to perturbations of time-optimal feedback control for linear systems with scalar control. In the last two sections it is proved that, if the matrix which defines the system has only real eigenvalues or is three-dimensional, the time-optimal feedback control defines a regular synthesis and therefore is stable to perturbations. (author)

  14. An optimum linear receiver for multiple channel digital transmission systems

    NARCIS (Netherlands)

    van Etten, Wim

    2007-01-01

    An optimum linear receiver for multiple channel digital transmission systems is developed for the minimum P. and for the zero-forcing criterion. A multidimensional Nyquist criterion is defined together with a theorem on the optimality of a finite length multiple tapped delay line. Furthermore an

  15. Stability Analysis for Multi-Parameter Linear Periodic Systems

    DEFF Research Database (Denmark)

    Seyranian, A.P.; Solem, Frederik; Pedersen, Pauli

    1999-01-01

    This paper is devoted to stability analysis of general linear periodic systems depending on real parameters. The Floquet method and perturbation technique are the basis of the development. We start out with the first and higher-order derivatives of the Floquet matrix with respect to problem...

  16. Relative controllability and null controllability of linear delay systems ...

    African Journals Online (AJOL)

    Necessary and sufficient conditions are established for the relative, absolute controllability and null controllability of the generalized linear delay system and its discrete prototype. The paper presents illuminating examples on previous controllability results by Manitius and Olbrot [7] and carries over the results of Onwuatu [8] ...

  17. Generating Nice Linear Systems for Matrix Gaussian Elimination

    Science.gov (United States)

    Homewood, L. James

    2004-01-01

    In this article an augmented matrix that represents a system of linear equations is called nice if a sequence of elementary row operations that reduces the matrix to row-echelon form, through matrix Gaussian elimination, does so by restricting all entries to integers in every step. Many instructors wish to use the example of matrix Gaussian…

  18. Decentralized linear quadratic power system stabilizers for multi ...

    Indian Academy of Sciences (India)

    Linear quadratic stabilizers are well-known for their superior control capabilities when compared to the conventional lead–lag power system stabilizers. However, they have not seen much of practical importance as the state variables are generally not measurable; especially the generator rotor angle measurement is not ...

  19. Linearization of systems of four second-order ordinary differential ...

    Indian Academy of Sciences (India)

    In this paper we provide invariant linearizability criteria for a class of systems of four second-order ordinary differential equations in terms of a set of 30 constraint equations on the coefficients of all derivative terms. The linearization criteria are derived by the analytic continuation of the geometric approach of projection of ...

  20. Decentralized linear quadratic power system stabilizers for multi ...

    Indian Academy of Sciences (India)

    Abstract. Linear quadratic stabilizers are well-known for their superior control capabilities when compared to the conventional lead–lag power system stabilizers. However, they have not seen much of practical importance as the state variables are generally not measurable; especially the generator rotor angle measurement ...

  1. Monitoring and control system of the Saclay electron linear accelerator

    International Nuclear Information System (INIS)

    Lafontaine, Antoine

    1974-01-01

    A description is given of the automatic monitoring and control system of the 60MeV electron linear accelerator of the Centre d'Etudes Nucleaires de Saclay. The paper is mostly concerned with the programmation of the system. However, in a real time device, there is a very close association between computer and electronics, the latter are therefore described in details and make up most of the paper. [fr

  2. Design and performance of the Stanford Linear Collider Control System

    International Nuclear Information System (INIS)

    Melen, R.E.

    1984-10-01

    The success of the Stanford Linear Collider (SLC) will be dependent upon the implementation of a very large advanced computer-based instrumentation and control system. This paper describes the architectural design of this system as well as a critique of its performance. This critique is based on experience obtained from its use in the control and monitoring of 1/3 of the SLAC linac and in support of an expensive experimental machine physics experimental program. 11 references, 3 figures

  3. Hyperchaotic encryption based on multi-scroll piecewise linear Systems

    Czech Academy of Sciences Publication Activity Database

    García-Martínez, M.; Ontanon-García, L.J.; Campos-Cantón, E.; Čelikovský, Sergej

    2015-01-01

    Roč. 270, č. 1 (2015), s. 413-424 ISSN 0096-3003 R&D Projects: GA ČR GA13-20433S Institutional support: RVO:67985556 Keywords : Hyperchaotic encryption * Piecewise linear systems * Stream cipher * Pseudo - random bit generator * Chaos theory * Multi-scrollattractors Subject RIV: BC - Control Systems Theory Impact factor: 1.345, year: 2015 http://library.utia.cas.cz/separaty/2015/TR/celikovsky-0446895.pdf

  4. Design and performance of the Stanford Linear Collider Control System

    Energy Technology Data Exchange (ETDEWEB)

    Melen, R.E.

    1984-10-01

    The success of the Stanford Linear Collider (SLC) will be dependent upon the implementation of a very large advanced computer-based instrumentation and control system. This paper describes the architectural design of this system as well as a critique of its performance. This critique is based on experience obtained from its use in the control and monitoring of 1/3 of the SLAC linac and in support of an expensive experimental machine physics experimental program. 11 references, 3 figures.

  5. Identification of single-input-single-output quantum linear systems

    Science.gov (United States)

    Levitt, Matthew; GuÅ£ǎ, Mǎdǎlin

    2017-03-01

    The purpose of this paper is to investigate system identification for single-input-single-output general (active or passive) quantum linear systems. For a given input we address the following questions: (1) Which parameters can be identified by measuring the output? (2) How can we construct a system realization from sufficient input-output data? We show that for time-dependent inputs, the systems which cannot be distinguished are related by symplectic transformations acting on the space of system modes. This complements a previous result of Guţă and Yamamoto [IEEE Trans. Autom. Control 61, 921 (2016), 10.1109/TAC.2015.2448491] for passive linear systems. In the regime of stationary quantum noise input, the output is completely determined by the power spectrum. We define the notion of global minimality for a given power spectrum, and characterize globally minimal systems as those with a fully mixed stationary state. We show that in the case of systems with a cascade realization, the power spectrum completely fixes the transfer function, so the system can be identified up to a symplectic transformation. We give a method for constructing a globally minimal subsystem direct from the power spectrum. Restricting to passive systems the analysis simplifies so that identifiability may be completely understood from the eigenvalues of a particular system matrix.

  6. Universal Linear Precoding for NBI-Proof Widely Linear Equalization in MC Systems

    Directory of Open Access Journals (Sweden)

    Donatella Darsena

    2007-09-01

    Full Text Available In multicarrier (MC systems, transmitter redundancy, which is introduced by means of finite-impulse response (FIR linear precoders, allows for perfect or zero-forcing (ZF equalization of FIR channels (in the absence of noise. Recently, it has been shown that the noncircular or improper nature of some symbol constellations offers an intrinsic source of redundancy, which can be exploited to design efficient FIR widely-linear (WL receiving structures for MC systems operating in the presence of narrowband interference (NBI. With regard to both cyclic-prefixed and zero-padded transmission techniques, it is shown in this paper that, with appropriately designed precoders, it is possible to synthesize in both cases WL-ZF universal equalizers, which guarantee perfect symbol recovery for any FIR channel. Furthermore, it is theoretically shown that the intrinsic redundancy of the improper symbol sequence also enables WL-ZF equalization, based on the minimum mean output-energy criterion, with improved NBI suppression capabilities. Finally, results of numerical simulations are presented, which assess the merits of the proposed precoding designs and validate the theoretical analysis carried out.

  7. Robust observability for regular linear systems under nonlinear perturbation

    Directory of Open Access Journals (Sweden)

    Weisheng Jiang

    2015-08-01

    Full Text Available In this article, we consider the admissibility and exact observability of a class of semilinear systems obtained by nonlinear perturbation for regular linear systems. We obtain the well-posedness of the semilinear system and the admissibility of the observation operator for the nonlinear semigroup, the solution semigroup of the semilinear system. Further, we obtain the robustness of the exact observability with respect to nonlinear perturbations when the Lipschitz constant is small enough. Finally, we give two examples to illustrate the obtained results.

  8. Algorithmic Approach to Abstracting Linear Systems by Timed Automata

    DEFF Research Database (Denmark)

    Sloth, Christoffer; Wisniewski, Rafael

    2011-01-01

    This paper proposes an LMI-based algorithm for abstracting dynamical systems by timed automata, which enables automatic formal verification of linear systems. The proposed abstraction is based on partitioning the state space of the system using positive invariant sets, generated by Lyapunov...... functions. This partitioning ensures that the vector field of the dynamical system is transversal to all facets of the cells, which induces some desirable properties of the abstraction. The algorithm is based on identifying intersections of level sets of quadratic Lyapunov functions, and determining...

  9. Fundamentals of linear systems for physical scientists and engineers

    CERN Document Server

    Puri, N N

    2009-01-01

    Thanks to the advent of inexpensive computing, it is possible to analyze, compute, and develop results that were unthinkable in the '60s. Control systems, telecommunications, robotics, speech, vision, and digital signal processing are but a few examples of computing applications. While there are many excellent resources available that focus on one or two topics, few books cover most of the mathematical techniques required for a broader range of applications. Fundamentals of Linear Systems for Physical Scientists and Engineers is such a resource. The book draws from diverse areas of engineering and the physical sciences to cover the fundamentals of linear systems. Assuming no prior knowledge of complex mathematics on the part of the reader, the author uses his nearly 50 years of teaching experience to address all of the necessary mathematical techniques. Original proofs, hundreds of examples, and proven theorems illustrate and clarify the material. An extensive table provides Lyapunov functions for differentia...

  10. Linear and nonlinear dynamic systems in financial time series prediction

    Directory of Open Access Journals (Sweden)

    Salim Lahmiri

    2012-10-01

    Full Text Available Autoregressive moving average (ARMA process and dynamic neural networks namely the nonlinear autoregressive moving average with exogenous inputs (NARX are compared by evaluating their ability to predict financial time series; for instance the S&P500 returns. Two classes of ARMA are considered. The first one is the standard ARMA model which is a linear static system. The second one uses Kalman filter (KF to estimate and predict ARMA coefficients. This model is a linear dynamic system. The forecasting ability of each system is evaluated by means of mean absolute error (MAE and mean absolute deviation (MAD statistics. Simulation results indicate that the ARMA-KF system performs better than the standard ARMA alone. Thus, introducing dynamics into the ARMA process improves the forecasting accuracy. In addition, the ARMA-KF outperformed the NARX. This result may suggest that the linear component found in the S&P500 return series is more dominant than the nonlinear part. In sum, we conclude that introducing dynamics into the ARMA process provides an effective system for S&P500 time series prediction.

  11. A parallel solver for huge dense linear systems

    Science.gov (United States)

    Badia, J. M.; Movilla, J. L.; Climente, J. I.; Castillo, M.; Marqués, M.; Mayo, R.; Quintana-Ortí, E. S.; Planelles, J.

    2011-11-01

    HDSS (Huge Dense Linear System Solver) is a Fortran Application Programming Interface (API) to facilitate the parallel solution of very large dense systems to scientists and engineers. The API makes use of parallelism to yield an efficient solution of the systems on a wide range of parallel platforms, from clusters of processors to massively parallel multiprocessors. It exploits out-of-core strategies to leverage the secondary memory in order to solve huge linear systems O(100.000). The API is based on the parallel linear algebra library PLAPACK, and on its Out-Of-Core (OOC) extension POOCLAPACK. Both PLAPACK and POOCLAPACK use the Message Passing Interface (MPI) as the communication layer and BLAS to perform the local matrix operations. The API provides a friendly interface to the users, hiding almost all the technical aspects related to the parallel execution of the code and the use of the secondary memory to solve the systems. In particular, the API can automatically select the best way to store and solve the systems, depending of the dimension of the system, the number of processes and the main memory of the platform. Experimental results on several parallel platforms report high performance, reaching more than 1 TFLOP with 64 cores to solve a system with more than 200 000 equations and more than 10 000 right-hand side vectors. New version program summaryProgram title: Huge Dense System Solver (HDSS) Catalogue identifier: AEHU_v1_1 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEHU_v1_1.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 87 062 No. of bytes in distributed program, including test data, etc.: 1 069 110 Distribution format: tar.gz Programming language: Fortran90, C Computer: Parallel architectures: multiprocessors, computer clusters Operating system

  12. Galerkin projection methods for solving multiple related linear systems

    Energy Technology Data Exchange (ETDEWEB)

    Chan, T.F.; Ng, M.; Wan, W.L.

    1996-12-31

    We consider using Galerkin projection methods for solving multiple related linear systems A{sup (i)}x{sup (i)} = b{sup (i)} for 1 {le} i {le} s, where A{sup (i)} and b{sup (i)} are different in general. We start with the special case where A{sup (i)} = A and A is symmetric positive definite. The method generates a Krylov subspace from a set of direction vectors obtained by solving one of the systems, called the seed system, by the CG method and then projects the residuals of other systems orthogonally onto the generated Krylov subspace to get the approximate solutions. The whole process is repeated with another unsolved system as a seed until all the systems are solved. We observe in practice a super-convergence behaviour of the CG process of the seed system when compared with the usual CG process. We also observe that only a small number of restarts is required to solve all the systems if the right-hand sides are close to each other. These two features together make the method particularly effective. In this talk, we give theoretical proof to justify these observations. Furthermore, we combine the advantages of this method and the block CG method and propose a block extension of this single seed method. The above procedure can actually be modified for solving multiple linear systems A{sup (i)}x{sup (i)} = b{sup (i)}, where A{sup (i)} are now different. We can also extend the previous analytical results to this more general case. Applications of this method to multiple related linear systems arising from image restoration and recursive least squares computations are considered as examples.

  13. Neural Network for Combining Linear and Non-Linear Modelling of Dynamic Systems

    DEFF Research Database (Denmark)

    Madsen, Per Printz

    1994-01-01

    The purpose of this paper is to develop a method to combine linear models with MLP networks. In other words to find a method to make a non-linear and multivariable model that performs at least as good as a linear model, when the training data lacks information.......The purpose of this paper is to develop a method to combine linear models with MLP networks. In other words to find a method to make a non-linear and multivariable model that performs at least as good as a linear model, when the training data lacks information....

  14. Technological Singularity: What Do We Really Know?

    Directory of Open Access Journals (Sweden)

    Alexey Potapov

    2018-04-01

    Full Text Available The concept of the technological singularity is frequently reified. Futurist forecasts inferred from this imprecise reification are then criticized, and the reified ideas are incorporated in the core concept. In this paper, I try to disentangle the facts related to the technological singularity from more speculative beliefs about the possibility of creating artificial general intelligence. I use the theory of metasystem transitions and the concept of universal evolution to analyze some misconceptions about the technological singularity. While it may be neither purely technological, nor truly singular, we can predict that the next transition will take place, and that the emerged metasystem will demonstrate exponential growth in complexity with a doubling time of less than half a year, exceeding the complexity of the existing cybernetic systems in few decades.

  15. A quasi-linear parabolic system of chemotaxis

    Directory of Open Access Journals (Sweden)

    2006-01-01

    Full Text Available We consider a quasi-linear parabolic system with respect to unknown functions u and v on a bounded domain of n -dimensional Euclidean space. We assume that the diffusion coefficient of u is a positive smooth function A ( u , and that the diffusion coefficient of v is a positive constant. If A ( u is a positive constant, the system is referred to as so-called Keller-Segel system. In the case where the domain is a bounded domain of two-dimensional Euclidean space, it is shown that some solutions to Keller-Segel system blow up in finite time. In three and more dimensional cases, it is shown that solutions to so-called Nagai system blow up in finite time. Nagai system is introduced by Nagai. The diffusion coefficients of Nagai system are positive constants. In this paper, we describe that solutions to the quasi-linear parabolic system exist globally in time, if the positive function A ( u rapidly increases with respect to u .

  16. Coherent versus Measurement Feedback: Linear Systems Theory for Quantum Information

    Directory of Open Access Journals (Sweden)

    Naoki Yamamoto

    2014-11-01

    Full Text Available To control a quantum system via feedback, we generally have two options in choosing a control scheme. One is the coherent feedback, which feeds the output field of the system, through a fully quantum device, back to manipulate the system without involving any measurement process. The other one is measurement-based feedback, which measures the output field and performs a real-time manipulation on the system based on the measurement results. Both schemes have advantages and disadvantages, depending on the system and the control goal; hence, their comparison in several situations is important. This paper considers a general open linear quantum system with the following specific control goals: backaction evasion, generation of a quantum nondemolished variable, and generation of a decoherence-free subsystem, all of which have important roles in quantum information science. Some no-go theorems are proven, clarifying that those goals cannot be achieved by any measurement-based feedback control. On the other hand, it is shown that, for each control goal there exists a coherent feedback controller accomplishing the task. The key idea to obtain all the results is system theoretic characterizations of the above three notions in terms of controllability and observability properties or transfer functions of linear systems, which are consistent with their standard definitions.

  17. Optimal policies for identification of stochastic linear systems

    Science.gov (United States)

    Lopez-Toledo, A. A.; Athans, M.

    1975-01-01

    The problem of designing closed-loop policies for identification of multiinput-multioutput linear discrete-time systems with random time-varying parameters is considered in this paper using a Bayesian approach. A sensitivity index gives a measure of performance for the closed-loop laws. The computation of the optimal laws is shown to be nontrivial, an exercise in stochastic control, but open-loop, affine, and open-loop feedback optimal inputs are shown to yield tractable problems. Numerical examples are given. For time-invariant systems, the criterion considered is shown to be related to the trace of the information matrix associated with the system.

  18. The new control system of the Saclay linear accelerator

    International Nuclear Information System (INIS)

    Gournay, J.F.; Gourcy, G.; Garreau, F.; Giraud, A.; Rouault, J.

    1985-05-01

    A new control system for the Safety Linear Accelerator is now being designed. The computer control architecture is based on 3 dedicated VME crates with MC68000 micro-processors: one crate with a disk-based operating system will run the high level application programs and the data base management facilities, another one will manage the man-machine communications and the third one will interface the system to the linac equipments. Communications between the VME microcomputers will be done through 16 bit parallel links. The software is modular and organized in specific layers, the data base is fully distributed. About 90% of the code is written in Fortran

  19. Fundamental Matrix for a Class of Point Delay Linear Systems

    International Nuclear Information System (INIS)

    Sen, M. de la; Alastruey, C. F.

    1998-01-01

    It is difficult to establish explicit analytic forms for fundamental matrices of delayed linear systems. In this paper, an explicit form of exponential type is given for such a matrix in the case of punctual delays. The existence of real and complex fundamental matrices, for the case of real parameterizations of the differential system, is studied and discussed. Some additional commutativity properties involving the matrices parameters and the fundamental matrices as well as explicit expressions for the solution of the delayed differential system are also given. (Author)

  20. Singularities in FLRW spacetimes

    Science.gov (United States)

    het Lam, Huibert; Prokopec, Tomislav

    2017-12-01

    We point out that past-incompleteness of geodesics in FLRW spacetimes does not necessarily imply that these spacetimes start from a singularity. Namely, if a test particle that follows such a trajectory has a non-vanishing velocity, its energy was super-Planckian at some time in the past if it kept following that geodesic. That indicates a breakdown of the particle's description, which is why we should not consider those trajectories for the definition of an initial singularity. When one only considers test particles that do not have this breakdown of their trajectory, it turns out that the only singular FLRW spacetimes are the ones that have a scale parameter that vanishes at some initial time.

  1. Neural Network for Combining Linear and Non-Linear Modelling of Dynamic Systems

    DEFF Research Database (Denmark)

    Madsen, Per Printz

    1994-01-01

    The purpose of this paper is to develop a method to combine linear models with MLP networks. In other words to find a method to make a non-linear and multivariable model that performs at least as good as a linear model, when the training data lacks information....

  2. Competitiveness of nonstationary states in linear kinetic systems

    Science.gov (United States)

    Teslenko, Victor I.; Kapitanchuk, Oleksiy L.

    2018-01-01

    The master equation formalism is used to describe the possibility for peak population amplitudes of two nonstationary states in a 3-stage linear kinetic system to be endowed with an untraditional physical quantity — competitiveness — established in regard to the differences for the degree of the peak responses to a change in the input rate constants. Calculated coefficients of competitiveness are found to agree with observations of performance for the three optical materials with respect to their reliability in different operating windows. It is concluded that, for a non-equilibrium linear kinetic system, the competitiveness constitutes a common dynamic property of its nonstationary states and, in the case of their directed irreversible evolution, comprises the property of a system’s anti-cooperativity.

  3. Nonautonomous linear Hamiltonian systems oscillation, spectral theory and control

    CERN Document Server

    Johnson, Russell; Novo, Sylvia; Núñez, Carmen; Fabbri, Roberta

    2016-01-01

    This monograph contains an in-depth analysis of the dynamics given by a linear Hamiltonian system of general dimension with nonautonomous bounded and uniformly continuous coefficients, without other initial assumptions on time-recurrence. Particular attention is given to the oscillation properties of the solutions as well as to a spectral theory appropriate for such systems. The book contains extensions of results which are well known when the coefficients are autonomous or periodic, as well as in the nonautonomous two-dimensional case. However, a substantial part of the theory presented here is new even in those much simpler situations. The authors make systematic use of basic facts concerning Lagrange planes and symplectic matrices, and apply some fundamental methods of topological dynamics and ergodic theory. Among the tools used in the analysis, which include Lyapunov exponents, Weyl matrices, exponential dichotomy, and weak disconjugacy, a fundamental role is played by the rotation number for linear Hami...

  4. Solving Systems of Linear Equations with a Superconducting Quantum Processor.

    Science.gov (United States)

    Zheng, Yarui; Song, Chao; Chen, Ming-Cheng; Xia, Benxiang; Liu, Wuxin; Guo, Qiujiang; Zhang, Libo; Xu, Da; Deng, Hui; Huang, Keqiang; Wu, Yulin; Yan, Zhiguang; Zheng, Dongning; Lu, Li; Pan, Jian-Wei; Wang, H; Lu, Chao-Yang; Zhu, Xiaobo

    2017-05-26

    Superconducting quantum circuits are a promising candidate for building scalable quantum computers. Here, we use a four-qubit superconducting quantum processor to solve a two-dimensional system of linear equations based on a quantum algorithm proposed by Harrow, Hassidim, and Lloyd [Phys. Rev. Lett. 103, 150502 (2009)PRLTAO0031-900710.1103/PhysRevLett.103.150502], which promises an exponential speedup over classical algorithms under certain circumstances. We benchmark the solver with quantum inputs and outputs, and characterize it by nontrace-preserving quantum process tomography, which yields a process fidelity of 0.837±0.006. Our results highlight the potential of superconducting quantum circuits for applications in solving large-scale linear systems, a ubiquitous task in science and engineering.

  5. Optimal linear precoding for indoor visible light communication system

    KAUST Repository

    Sifaou, Houssem

    2017-07-31

    Visible light communication (VLC) is an emerging technique that uses light-emitting diodes (LED) to combine communication and illumination. It is considered as a promising scheme for indoor wireless communication that can be deployed at reduced costs while offering high data rate performance. In this paper, we focus on the design of the downlink of a multi-user VLC system. Inherent to multi-user systems is the interference caused by the broadcast nature of the medium. Linear precoding based schemes are among the most popular solutions that have recently been proposed to mitigate inter-user interference. This paper focuses on the design of the optimal linear precoding scheme that solves the max-min signal-to-interference-plus-noise ratio (SINR) problem. The performance of the proposed precoding scheme is studied under different working conditions and compared with the classical zero-forcing precoding. Simulations have been provided to illustrate the high gain of the proposed scheme.

  6. Large linear magnetoresistivity in strongly inhomogeneous planar and layered systems

    International Nuclear Information System (INIS)

    Bulgadaev, S.A.; Kusmartsev, F.V.

    2005-01-01

    Explicit expressions for magnetoresistance R of planar and layered strongly inhomogeneous two-phase systems are obtained, using exact dual transformation, connecting effective conductivities of in-plane isotropic two-phase systems with and without magnetic field. These expressions allow to describe the magnetoresistance of various inhomogeneous media at arbitrary concentrations x and magnetic fields H. All expressions show large linear magnetoresistance effect with different dependencies on the phase concentrations. The corresponding plots of the x- and H-dependencies of R(x,H) are represented for various values, respectively, of magnetic field and concentrations at some values of inhomogeneity parameter. The obtained results show a remarkable similarity with the existing experimental data on linear magnetoresistance in silver chalcogenides Ag 2+δ Se. A possible physical explanation of this similarity is proposed. It is shown that the random, stripe type, structures of inhomogeneities are the most suitable for a fabrication of magnetic sensors and a storage of information at room temperatures

  7. SSNN toolbox for non-linear system identification

    Science.gov (United States)

    Luzar, Marcel; Czajkowski, Andrzej

    2015-11-01

    The aim of this paper is to develop and design a State Space Neural Network toolbox for a non-linear system identification with an artificial state-space neural networks, which can be used in a model-based robust fault diagnosis and control. Such toolbox is implemented in the MATLAB environment and it uses some of its predefined functions. It is designed in the way that any non-linear multi-input multi-output system is identified and represented in the classical state-space form. The novelty of the proposed approach is that the final result of the identification process is the state, input and output matrices, not only the neural network parameters. Moreover, the toolbox is equipped with the graphical user interface, which makes it useful for the users not familiar with the neural networks theory.

  8. AZTEC: A parallel iterative package for the solving linear systems

    Energy Technology Data Exchange (ETDEWEB)

    Hutchinson, S.A.; Shadid, J.N.; Tuminaro, R.S. [Sandia National Labs., Albuquerque, NM (United States)

    1996-12-31

    We describe a parallel linear system package, AZTEC. The package incorporates a number of parallel iterative methods (e.g. GMRES, biCGSTAB, CGS, TFQMR) and preconditioners (e.g. Jacobi, Gauss-Seidel, polynomial, domain decomposition with LU or ILU within subdomains). Additionally, AZTEC allows for the reuse of previous preconditioning factorizations within Newton schemes for nonlinear methods. Currently, a number of different users are using this package to solve a variety of PDE applications.

  9. Dynamic logic architecture based on piecewise-linear systems

    International Nuclear Information System (INIS)

    Peng Haipeng; Liu Fei; Li Lixiang; Yang Yixian; Wang Xue

    2010-01-01

    This Letter explores piecewise-linear systems to construct dynamic logic architecture. The proposed schemes can discriminate the two input signals and obtain 16 kinds of logic operations by different combinations of parameters and conditions for determining the output. Each logic cell performs more flexibly, that makes it possible to achieve complex logic operations more simply and construct computing architecture with less logic cells. We also analyze the various performances of our schemes under different conditions and the characteristics of these schemes.

  10. Bounding the error of a continuous approximation for linear systems ...

    African Journals Online (AJOL)

    We present preconditioned interval Gauss-Siedel method and interval LU decomposition for finding solution to the interval linear system of equation Ad=b where the nxn coefficient matrix A lies between two bounds A and A and b„¡ƒËb,b ƒÍ. It is found out that preconditioned interval methods of Gauss-Siedel and LU have ...

  11. Feedback Linearization Controller for a Wind Energy Power System

    Directory of Open Access Journals (Sweden)

    Muthana Alrifai

    2016-09-01

    Full Text Available This paper deals with the control of a doubly-fed induction generator (DFIG-based variable speed wind turbine power system. A system of eight ordinary differential equations is used to model the wind energy conversion system. The generator has a wound rotor type with back-to-back three-phase power converter bridges between its rotor and the grid; it is modeled using the direct-quadrature rotating reference frame with aligned stator flux. An input-state feedback linearization controller is proposed for the wind energy power system. The controller guarantees that the states of the system track the desired states. Simulation results are presented to validate the proposed control scheme. Moreover, further simulation results are shown to investigate the robustness of the proposed control scheme to changes in some of the parameters of the system.

  12. Stochastic Reformulations of Linear Systems: Algorithms and Convergence Theory

    KAUST Repository

    Richtarik, Peter

    2017-06-04

    We develop a family of reformulations of an arbitrary consistent linear system into a stochastic problem. The reformulations are governed by two user-defined parameters: a positive definite matrix defining a norm, and an arbitrary discrete or continuous distribution over random matrices. Our reformulation has several equivalent interpretations, allowing for researchers from various communities to leverage their domain specific insights. In particular, our reformulation can be equivalently seen as a stochastic optimization problem, stochastic linear system, stochastic fixed point problem and a probabilistic intersection problem. We prove sufficient, and necessary and sufficient conditions for the reformulation to be exact. Further, we propose and analyze three stochastic algorithms for solving the reformulated problem---basic, parallel and accelerated methods---with global linear convergence rates. The rates can be interpreted as condition numbers of a matrix which depends on the system matrix and on the reformulation parameters. This gives rise to a new phenomenon which we call stochastic preconditioning, and which refers to the problem of finding parameters (matrix and distribution) leading to a sufficiently small condition number. Our basic method can be equivalently interpreted as stochastic gradient descent, stochastic Newton method, stochastic proximal point method, stochastic fixed point method, and stochastic projection method, with fixed stepsize (relaxation parameter), applied to the reformulations.

  13. Linear circuits, systems and signal processing: theory and application

    International Nuclear Information System (INIS)

    Byrnes, C.I.; Saeks, R.E.; Martin, C.F.

    1988-01-01

    In part because of its universal role as a first approximation of more complicated behaviour and in part because of the depth and breadth of its principle paradigms, the study of linear systems continues to play a central role in control theory and its applications. Enhancing more traditional applications to aerospace and electronics, application areas such as econometrics, finance, and speech and signal processing have contributed to a renaissance in areas such as realization theory and classical automatic feedback control. Thus, the last few years have witnessed a remarkable research effort expended in understanding both new algorithms and new paradigms for modeling and realization of linear processes and in the analysis and design of robust control strategies. The papers in this volume reflect these trends in both the theory and applications of linear systems and were selected from the invited and contributed papers presented at the 8th International Symposium on the Mathematical Theory of Networks and Systems held in Phoenix on June 15-19, 1987

  14. Identification of Nonlinear Dynamic Systems Possessing Some Non-linearities

    Directory of Open Access Journals (Sweden)

    Y. N. Pavlov

    2015-01-01

    Full Text Available The subject of this work is the problem of identification of nonlinear dynamic systems based on the experimental data obtained by applying test signals to the system. The goal is to determinate coefficients of differential equations of systems by experimental frequency hodographs and separate similar, but different, in essence, forces: dissipative forces with the square of the first derivative in the motion equations and dissipative force from the action of dry friction. There was a proposal to use the harmonic linearization method to approximate each of the nonlinearity of "quadratic friction" and "dry friction" by linear friction with the appropriate harmonic linearization coefficient.Assume that a frequency transfer function of the identified system has a known form. Assume as well that there are disturbances while obtaining frequency characteristics of the realworld system. As a result, the points of experimentally obtained hodograph move randomly. Searching for solution of the identification problem was in the hodograph class, specified by the system model, which has the form of the frequency transfer function the same as the form of the frequency transfer function of the system identified. Minimizing a proximity criterion (measure of the experimentally obtained system hodograph and the system hodograph model for all the experimental points described and previously published by one of the authors allowed searching for the unknown coefficients of the frequenc ransfer function of the system model. The paper shows the possibility to identify a nonlinear dynamic system with multiple nonlinearities, obtained on the experimental samples of the frequency system hodograph. The proposed algorithm allows to select the nonlinearity of the type "quadratic friction" and "dry friction", i.e. also in the case where the nonlinearity is dependent on the same dynamic parameter, in particular, on the derivative of the system output value. For the dynamic

  15. Linear filtering of systems with memory and application to finance

    Directory of Open Access Journals (Sweden)

    2006-01-01

    Full Text Available We study the linear filtering problem for systems driven by continuous Gaussian processes V ( 1 and V ( 2 with memory described by two parameters. The processes V ( j have the virtue that they possess stationary increments and simple semimartingale representations simultaneously. They allow for straightforward parameter estimations. After giving the semimartingale representations of V ( j by innovation theory, we derive Kalman-Bucy-type filtering equations for the systems. We apply the result to the optimal portfolio problem for an investor with partial observations. We illustrate the tractability of the filtering algorithm by numerical implementations.

  16. Tracking studies of the Compact Linear Collider collimation system

    International Nuclear Information System (INIS)

    Agapov, I.; Burkhardt, H.; Schulte, D.; Latina, A.; Blair, G.A.; Malton, S.; Resta-Lopez, J.

    2009-01-01

    A collimation system performance study includes several types of computations performed by different codes. Optics calculations are performed with codes such as MADX, tracking studies including additional effects such as wakefields, halo and tail generation, and dynamical machine alignment are done with codes such as PLACET, and energy deposition can be studied with BDSIM. More detailed studies of hadron production in the beam halo interaction with collimators are better performed with GEANT4 and FLUKA. A procedure has been developed that allows one to perform a single tracking study using several codes simultaneously. In this paper we study the performance of the Compact Linear Collider collimation system using such a procedure

  17. Parametric Linear Hybrid Automata for Complex Environmental Systems Modeling

    Directory of Open Access Journals (Sweden)

    Samar Hayat Khan Tareen

    2015-07-01

    Full Text Available Environmental systems, whether they be weather patterns or predator-prey relationships, are dependent on a number of different variables, each directly or indirectly affecting the system at large. Since not all of these factors are known, these systems take on non-linear dynamics, making it difficult to accurately predict meaningful behavioral trends far into the future. However, such dynamics do not warrant complete ignorance of different efforts to understand and model close approximations of these systems. Towards this end, we have applied a logical modeling approach to model and analyze the behavioral trends and systematic trajectories that these systems exhibit without delving into their quantification. This approach, formalized by René Thomas for discrete logical modeling of Biological Regulatory Networks (BRNs and further extended in our previous studies as parametric biological linear hybrid automata (Bio-LHA, has been previously employed for the analyses of different molecular regulatory interactions occurring across various cells and microbial species. As relationships between different interacting components of a system can be simplified as positive or negative influences, we can employ the Bio-LHA framework to represent different components of the environmental system as positive or negative feedbacks. In the present study, we highlight the benefits of hybrid (discrete/continuous modeling which lead to refinements among the fore-casted behaviors in order to find out which ones are actually possible. We have taken two case studies: an interaction of three microbial species in a freshwater pond, and a more complex atmospheric system, to show the applications of the Bio-LHA methodology for the timed hybrid modeling of environmental systems. Results show that the approach using the Bio-LHA is a viable method for behavioral modeling of complex environmental systems by finding timing constraints while keeping the complexity of the model

  18. Singularities in a Teacup

    Indian Academy of Sciences (India)

    Home; Journals; Resonance – Journal of Science Education; Volume 19; Issue 9. Singularities in a Teacup: Good Mathematics from Bad Lenses. Rajaram Nityananda. General Article Volume 19 Issue 9 September 2014 pp 787-796. Fulltext. Click here to view fulltext PDF. Permanent link:

  19. Singularities in a Teacup

    Indian Academy of Sciences (India)

    Home; Journals; Resonance – Journal of Science Education; Volume 19; Issue 9. Singularities in a Teacup: Good ... Author Affiliations. Rajaram Nityananda1. Azim Premji University, PES Institute of Technology Campus, Pixel Park, B Block, Electronics City, Hosur Road (Beside NICE Road) Bangalore – 560100 ...

  20. Stochastic singular optics

    CSIR Research Space (South Africa)

    Roux, FS

    2013-09-01

    Full Text Available Roux Presented at the International Conference on Correlation Optics 2013 Chernivtsi, Ukraine 18-20 September 2013 CSIR National Laser Centre, Pretoria, South Africa – p. 1/24 Contents ⊲ Defining Stochastic Singular Optics (SSO) ⊲ Tools of Stochastic...

  1. Pseudospherical surfaces with singularities

    DEFF Research Database (Denmark)

    Brander, David

    2017-01-01

    We study a generalization of constant Gauss curvature −1 surfaces in Euclidean 3-space, based on Lorentzian harmonic maps, that we call pseudospherical frontals. We analyse the singularities of these surfaces, dividing them into those of characteristic and non-characteristic type. We give methods...

  2. Singularities in FLRW Spacetimes

    NARCIS (Netherlands)

    Lam, Huibert het; Prokopec, Tom

    2017-01-01

    We point out that past-incompleteness of geodesics in FLRW spacetimes does not necessarily imply that these spacetimes start from a singularity. Namely, if a test particle that follows such a trajectory has a non-vanishing velocity, its energy was super-Planckian at some time in the past if it kept

  3. Demultiplexing of photonic temporal modes by a linear system

    Science.gov (United States)

    Xu, Shuang; Shen, H. Z.; Yi, X. X.

    2018-03-01

    Temporally and spatially overlapping but field-orthogonal photonic temporal modes (TMs) that intrinsically span a high-dimensional Hilbert space are recently suggested as a promising means of encoding information on photons. Presently, the realization of photonic TM technology, particularly to retrieve the information it carries, i.e., demultiplexing of photonic TMs, is mostly dependent on nonlinear medium and frequency conversion. Meanwhile, its miniaturization, simplification, and optimization remain the focus of research. In this paper, we propose a scheme of TM demultiplexing using linear systems consisting of resonators with linear couplings. Specifically, we examine a unidirectional array of identical resonators with short environment correlations. For both situations with and without tunable couplers, propagation formulas are derived to demonstrate photonic TM demultiplexing capabilities. The proposed scheme, being entirely feasible with current technologies, might find potential applications in quantum information processing.

  4. Singular potentials in quantum mechanics

    Energy Technology Data Exchange (ETDEWEB)

    Aguilera-Navarro, V.C. [Instituto de Fisica Teorica (IFT), Sao Paulo, SP (Brazil); Koo, E. Ley [Universidad Nacional Autonoma de Mexico, Mexico City (Mexico). Inst. de Fisica

    1995-10-01

    This paper is a review of some mathematical methods as recently developed and applied to deal with singular potentials in Quantum Mechanics. Regular and singular perturbative methods as well as variational treatments are considered. (author). 25 refs.

  5. Control of Linear Parameter Varying Systems with Applications

    CERN Document Server

    Mohammadpour, Javad

    2012-01-01

    Control of Linear Parameter Varying Systems with Applications compiles state-of-the-art contributions on novel analytical and computational methods to address system modeling and identification, complexity reduction, performance analysis and control design for time-varying and nonlinear systems in the LPV framework. The book has an interdisciplinary character by emphasizing techniques that can be commonly applied in various engineering fields. It also includes a rich collection of illustrative applications in diverse domains to substantiate the effectiveness of the design methodologies and provide pointers to open research directions. The book is divided into three parts. The first part collects chapters of a more tutorial character on the background of LPV systems modeling and control. The second part gathers chapters devoted to the theoretical advancement of LPV analysis and synthesis methods to cope with the design constraints such as uncertainties and time delay. The third part of the volume showcases con...

  6. The new control system of the Saclay linear accelerator

    International Nuclear Information System (INIS)

    Gournay, J.F.

    1985-10-01

    A new control system for the Saclay Linear Accelerator designed during the two past years is now in operation. The computer control architecture is based on 3 dedicated VME crates: one crate with a disk-based operating system runs the high level application programs and the database management facilities, another one manages the man-machine communications and the third one interfaces the system to the linac equipments. At the present time, communications between the VME micro-computers are done through 16 bit parallel links. The software is modular and organized in specific layers, the database is fully distributed. About 90% of the code is written in Fortran. The present status of the system is discussed and the hardware and software developments are described

  7. Linearization Technologies for Broadband Radio-Over-Fiber Transmission Systems

    Directory of Open Access Journals (Sweden)

    Xiupu Zhang

    2014-11-01

    Full Text Available Linearization technologies that can be used for linearizing RoF transmission are reviewed. Three main linearization methods, i.e. electrical analog linearization, optical linearization, and electrical digital linearization are presented and compared. Analog linearization can be achieved using analog predistortion circuits, and can be used for suppression of odd order nonlinear distortion components, such as third and fifth order. Optical linearization includes mixed-polarization, dual-wavelength, optical channelization and the others, implemented in optical domain, to suppress both even and odd order nonlinear distortion components, such as second and third order. Digital predistortion has been a widely used linearization method for RF power amplifiers. However, digital linearization that requires analog to digital converter is severely limited to hundreds of MHz bandwidth. Instead, analog and optical linearization provide broadband linearization with up to tens of GHz. Therefore, for broadband radio over fiber transmission that can be used for future broadband cloud radio access networks, analog and optical linearization are more appropriate than digital linearization. Generally speaking, both analog and optical linearization are able to improve spur-free dynamic range greater than 10 dB over tens of GHz. In order for current digital linearization to be used for broadband radio over fiber transmission, the reduced linearization complexity and increased linearization bandwidth are required. Moreover, some digital linearization methods in which the complexity can be reduced, such as Hammerstein type, may be more promising and require further investigation.

  8. Singularities: the Brieskorn anniversary volume

    National Research Council Canada - National Science Library

    Brieskorn, Egbert; Arnolʹd, V. I; Greuel, G.-M; Steenbrink, J. H. M

    1998-01-01

    ...... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Main theorem ... 3 Ideals of ideal-unimodal plane curve singularities. . . . . . . . . . . . . . . . References ... Gert-Martin Greuel and Gerhard Pfister...

  9. String theory and cosmological singularities

    Indian Academy of Sciences (India)

    Well-known examples are singularities inside black holes and initial or final singularities in expanding or contracting universes. In recent times, string theory is providing new perspectives of such singularities which may lead to an understanding of these in the standard framework of time evolution in quantum mechanics.

  10. Holographic complexity and spacetime singularities

    International Nuclear Information System (INIS)

    Barbón, José L.F.; Rabinovici, Eliezer

    2016-01-01

    We study the evolution of holographic complexity in various AdS/CFT models containing cosmological crunch singularities. We find that a notion of complexity measured by extremal bulk volumes tends to decrease as the singularity is approached in CFT time, suggesting that the corresponding quantum states have simpler entanglement structure at the singularity.

  11. Control of stage by stage changing linear dynamic systems

    Directory of Open Access Journals (Sweden)

    Barseghyan V.R.

    2012-01-01

    Full Text Available In this paper, the control problems of linear dynamic systems stage by stage changing and the optimal control with the criteria of quality set for the whole range of time intervals are considered. The necessary and sufficient conditions of total controllability are also stated. The constructive solving method of a control problem is offered, as well as the definitions of conditions for the existence of programmed control and motions. The explicit form of control action for a control problem is constructed. The method for solving optimal control problem is offered, and the solution of optimal control of a specific target is brought.

  12. A RECIPE FOR LINEAR COLLIDER FINAL FOCUS SYSTEM DESIGN

    International Nuclear Information System (INIS)

    Seryi, Andrei

    2003-01-01

    The design of Final Focus systems for linear colliders is challenging because of the large demagnifications needed to produce nanometer-sized beams at the interaction point. Simple first- and second-order matrix matching have proven insufficient for this task, and minimization of third- and higher-order aberrations is essential. An appropriate strategy is required for the latter to be successful. A recipe for Final Focus design, and a set of computational tools used to implement this approach, are described herein. An example of the use of this procedure is given

  13. Tuning of the Compact Linear Collider Beam Delivery System

    CERN Document Server

    Garcia, H; Inntjore Levinsen, Y; Latina, A; Tomas, R; Snuverink, J

    2014-01-01

    Tuning the Compact Linear Collider (CLIC) BeamDelivery System (BDS), and in particular the Final Focus (FF), is a challenging task. In simulations without misalignments, the goal is to reach 120%o f the nominal luminosity target, in order to allow for 10% loss due to static imperfections, and another 10% loss from dynamic imperfections. Various approaches have been considered to correct the magnet misalignments, including 1-1 correction, Dispersion Free Steering (DFS), and several minimization methods utilizing multipole movers. In this paper we report on the recent advancements towards a feasible tuning approach that reaches the required luminosity target.

  14. Considering system non-linearity in transmission pricing

    International Nuclear Information System (INIS)

    Oloomi-Buygi, M.; Salehizadeh, M. Reza

    2008-01-01

    In this paper a new approach for transmission pricing is presented. The contribution of a contract on power flow of a transmission line is used as extent-of-use criterion for transmission pricing. In order to determine the contribution of each contract on power flow of each transmission line, first the contribution of each contract on each voltage angle is determined, which is called voltage angle decomposition. To this end, DC power flow is used to compute a primary solution for voltage angle decomposition. To consider the impacts of system non-linearity on voltage angle decomposition, a method is presented to determine the share of different terms of sine argument in sine value. Then the primary solution is corrected in different iterations of decoupled Newton-Raphson power flow using the presented sharing method. The presented approach is applied to a 4-bus test system and IEEE 30-bus test system and the results are analyzed. (author)

  15. Memristive non-linear system and hidden attractor

    Science.gov (United States)

    Saha, P.; Saha, D. C.; Ray, A.; Chowdhury, A. R.

    2015-07-01

    Effects of memristor on non-linear dynamical systems exhibiting chaos are analysed both form the view point of theory and experiment. It is observed that the memristive system has always fewer number of fixed points than the original one. Sometimes there is no fixed point in the memristive system. But its chaotic properties are retained. As such we have a situation known as hidden attractor because if it is a stable fixed point then the attractor does not evolve from its basin of attraction(obtained from its stable fixed point) or if there is no fixed point, the question of basin of attraction from fixed point does not arise at all [1, 2]. Our analysis gives a detailed accounts of properties related to its chaotic behavior. Important observations are also obtained with the help of electronic circuits to support the numerical simulations.

  16. Infinitesimal Structure of Singularities

    Directory of Open Access Journals (Sweden)

    Michael Heller

    2017-02-01

    Full Text Available Some important problems of general relativity, such as the quantisation of gravity or classical singularity problems, crucially depend on geometry on very small scales. The so-called synthetic differential geometry—a categorical counterpart of the standard differential geometry—provides a tool to penetrate infinitesimally small portions of space-time. We use this tool to show that on any “infinitesimal neighbourhood” the components of the curvature tensor are themselves infinitesimal, and construct a simplified model in which the curvature singularity disappears, owing to this effect. However, one pays a price for this result. Using topoi as a generalisation of spaces requires a weakening of arithmetic (the existence of infinitesimals and of logic (to the intuitionistic logic. Is this too high a price to pay for acquiring a new method of solving unsolved problems in physics? Without trying, we shall never know the answer.

  17. Deformations of surface singularities

    CERN Document Server

    Szilárd, ágnes

    2013-01-01

    The present publication contains a special collection of research and review articles on deformations of surface singularities, that put together serve as an introductory survey of results and methods of the theory, as well as open problems, important examples and connections to other areas of mathematics. The aim is to collect material that will help mathematicians already working or wishing to work in this area to deepen their insight and eliminate the technical barriers in this learning process. This also is supported by review articles providing some global picture and an abundance of examples. Additionally, we introduce some material which emphasizes the newly found relationship with the theory of Stein fillings and symplectic geometry.  This links two main theories of mathematics: low dimensional topology and algebraic geometry. The theory of normal surface singularities is a distinguished part of analytic or algebraic geometry with several important results, its own technical machinery, and several op...

  18. The cosmological singularity

    CERN Document Server

    Belinski, Vladimir

    2018-01-01

    Written for researchers focusing on general relativity, supergravity, and cosmology, this is a self-contained exposition of the structure of the cosmological singularity in generic solutions of the Einstein equations, and an up-to-date mathematical derivation of the theory underlying the Belinski–Khalatnikov–Lifshitz (BKL) conjecture on this field. Part I provides a comprehensive review of the theory underlying the BKL conjecture. The generic asymptotic behavior near the cosmological singularity of the gravitational field, and fields describing other kinds of matter, is explained in detail. Part II focuses on the billiard reformulation of the BKL behavior. Taking a general approach, this section does not assume any simplifying symmetry conditions and applies to theories involving a range of matter fields and space-time dimensions, including supergravities. Overall, this book will equip theoretical and mathematical physicists with the theoretical fundamentals of the Big Bang, Big Crunch, Black Hole singula...

  19. Fault Diagnosis and Fault Tolerant Control for Non-Gaussian Singular Time-Delayed Stochastic Distribution Systems with Disturbance Based on the Rational Square-Root Model

    Directory of Open Access Journals (Sweden)

    Yuancheng Sun

    2016-01-01

    Full Text Available For the non-Gaussian singular time-delayed stochastic distribution control (SDC system with unknown external disturbance where the output probability density function (PDF is approximated by the rational square-root B-spline basis function, a robust fault diagnosis and fault tolerant control algorithm is presented. A full-order observer is constructed to estimate the exogenous disturbance and an adaptive observer is used to estimate the fault size. A fault tolerant tracking controller is designed using the feedback of distribution tracking error, fault, and disturbance estimation to let the postfault output PDF still track desired distribution. Finally, a simulation example is included to illustrate the effectiveness of the proposed algorithms and encouraging results have been obtained.

  20. Final focus system tuning studies towards Compact Linear Collider feasibility

    Directory of Open Access Journals (Sweden)

    E. Marin

    2018-01-01

    Full Text Available In this paper we present the latest results regarding the tuning study of the baseline design of the final focus system of the Compact Linear Collider (CLIC-FFS. CLIC aims to provide collisions to the experiments at a luminosity above 10^{34}  cm^{-2} s^{-1}. In order to deliver such luminosity in a single pass machine, the vertical beam size at the interaction point (IP is reduced to about 1 nm, which imposes unprecedented tuning difficulties to the system. In previous studies, 90% of the machines reached 90% of the nominal luminosity at the expense of 18 000 luminosity measurements, when considering beam position monitor errors and transverse misalignments of magnets for a single beam case. In the present study, additional static imperfections such as roll misalignments and strength errors are included. Moreover both e^{-} and e^{+} beamlines are properly simulated. A new tuning procedure based on linear and nonlinear knobs is implemented to effectively cure the most relevant beam size aberrations at the IP. The obtained results for single and double beam studies under solely static imperfections are presented.

  1. Final focus system tuning studies towards Compact Linear Collider feasibility

    Science.gov (United States)

    Marin, E.; Latina, A.; Tomás, R.; Schulte, D.

    2018-01-01

    In this paper we present the latest results regarding the tuning study of the baseline design of the final focus system of the Compact Linear Collider (CLIC-FFS). CLIC aims to provide collisions to the experiments at a luminosity above 1034 c m-2 s-1 . In order to deliver such luminosity in a single pass machine, the vertical beam size at the interaction point (IP) is reduced to about 1 nm, which imposes unprecedented tuning difficulties to the system. In previous studies, 90% of the machines reached 90% of the nominal luminosity at the expense of 18 000 luminosity measurements, when considering beam position monitor errors and transverse misalignments of magnets for a single beam case. In the present study, additional static imperfections as, roll misalignments, strength v2.epss are included. Moreover both e- and e+ beamlines are properly simulated. A new tuning procedure based on linear and nonlinear knobs is implemented to effectively cure the most relevant beam size aberrations at the IP. The obtained results for single and double beam studies under solely static imperfections are presented.

  2. Multiscale singularity trees

    DEFF Research Database (Denmark)

    Somchaipeng, Kerawit; Sporring, Jon; Johansen, Peter

    2007-01-01

    We propose MultiScale Singularity Trees (MSSTs) as a structure to represent images, and we propose an algorithm for image comparison based on comparing MSSTs. The algorithm is tested on 3 public image databases and compared to 2 state-of-theart methods. We conclude that the computational complexity...... of our algorithm only allows for the comparison of small trees, and that the results of our method are comparable with state-of-the-art using much fewer parameters for image representation....

  3. Efficient Feedforward Linearization Technique Using Genetic Algorithms for OFDM Systems

    Directory of Open Access Journals (Sweden)

    García Paloma

    2010-01-01

    Full Text Available Feedforward is a linearization method that simultaneously offers wide bandwidth and good intermodulation distortion suppression; so it is a good choice for Orthogonal Frequency Division Multiplexing (OFDM systems. Feedforward structure consists of two loops, being necessary an accurate adjustment between them along the time, and when temperature, environmental, or operating changes are produced. Amplitude and phase imbalances of the circuit elements in both loops produce mismatched effects that lead to degrade its performance. A method is proposed to compensate these mismatches, introducing two complex coefficients calculated by means of a genetic algorithm. A full study is carried out to choose the optimal parameters of the genetic algorithm applied to wideband systems based on OFDM technologies, which are very sensitive to nonlinear distortions. The method functionality has been verified by means of simulation.

  4. A type system for PSPACE derived from light linear logic

    Directory of Open Access Journals (Sweden)

    Lucien Capedevielle

    2012-01-01

    Full Text Available We present a polymorphic type system for lambda calculus ensuring that well-typed programs can be executed in polynomial space: dual light affine logic with booleans (DLALB. To build DLALB we start from DLAL (which has a simple type language with a linear and an intuitionistic type arrow, as well as one modality which characterizes FPTIME functions. In order to extend its expressiveness we add two boolean constants and a conditional constructor in the same way as with the system STAB. We show that the value of a well-typed term can be computed by an alternating machine in polynomial time, thus such a term represents a program of PSPACE (given that PSPACE = APTIME. We also prove that all polynomial space decision functions can be represented in DLALB. Therefore DLALB characterizes PSPACE predicates.

  5. Tracking studies of the Compact Linear Collider collimation system

    Directory of Open Access Journals (Sweden)

    I. Agapov

    2009-08-01

    Full Text Available A collimation system performance study includes several types of computations performed by different codes. Optics calculations are performed with codes such as MADX, tracking studies including additional effects such as wakefields, halo and tail generation, and dynamical machine alignment are done with codes such as PLACET, and energy deposition can be studied with BDSIM. More detailed studies of hadron production in the beam halo interaction with collimators are better performed with Geant4 and FLUKA. A procedure has been developed that allows one to perform a single tracking study using several codes simultaneously. In this paper we study the performance of the Compact Linear Collider collimation system using such a procedure.

  6. Thermodynamic Optimality criteria for biological systems in linear irreversible thermodynamics

    International Nuclear Information System (INIS)

    Chimal, J C; Sánchez, N; Ramírez, PR

    2017-01-01

    In this paper the methodology of the so-called Linear Irreversible Thermodynamics (LIT) is applied; although traditionally used locally to study general systems in non-equilibrium states in which it is consider both internal and external contributions to the entropy increments in order to analyze the efficiency of two coupled processes with generalized fluxes J 1 , J 2 and their corresponding forces X 1 , X 2 . We extend the former analysis to takes into account two different operating regimes namely: Omega Function and Efficient Power criterion, respectively. Results show analogies in the optimal performance between and we can say that there exist a criteria of optimization which can be used specially for biological systems where a good design of the biological parameters made by nature at maximum efficient power conditions lead to more efficient engines than those at the maximum power conditions or ecological conditions. (paper)

  7. Control methods to improve non-linear HVAC system operations

    Science.gov (United States)

    Phalak, Kaustubh Pradeep

    The change of weather conditions and occupancy schedules makes heating ventilating and air-conditioning (HVAC) systems heavily dynamic. The mass and thermal inertia, nonlinear characteristics and interactions in HVAC systems make the control more complicated. As a result, some conventional control methods often cannot provide desired control performance under variable operating conditions. The purpose of this study is to develop control methods to improve the control performance of HVAC systems. This study focuses on optimizing the airflow-pressure control method of air side economizers, identifying robust building pressurization controls, developing a control method to control outdoor air and building pressure in absence of flow and pressure sensors, stabilizing the cooling coil valve operation and, return fan speed control. The improvements can be achieved by identifying and selecting a method with relatively linear performance characteristics out of the available options, applying fans rather than dampers to control building pressure, and improving the controller's stability range using cascade control method. A steady state nonlinear network model, for an air handling unit (AHU), air distribution system and conditioned space, is applied to analyze the system control performance of air-side economizers and building pressurization. The study shows that traditional controls with completely interlinked outdoor air, recirculated air, relief air dampers have the best control performance. The decoupled relief damper control may result in negative building static pressure at lower outdoor airflow ratio and excessively positive building static pressure at higher outdoor airflow ratio. On the other hand, return fan speed control has a better controllability on building pressurization. In absence of flow and pressure sensors fixed interlinked damper and linear return fan speed tracking control can maintain constant outside air ratio and positive building pressure. The

  8. Radii of Solvability and Unsolvability of Linear Systems

    Czech Academy of Sciences Publication Activity Database

    Hladík, M.; Rohn, Jiří

    2016-01-01

    Roč. 503, 15 August (2016), s. 120-134 ISSN 0024-3795 Institutional support: RVO:67985807 Keywords : interval matrix * linear equations * linear inequalities * matrix norm Subject RIV: BA - General Mathematics Impact factor: 0.973, year: 2016

  9. Linear IFMIF Prototype Accelerator (LIPAc) Control System: Design and development

    Energy Technology Data Exchange (ETDEWEB)

    Calvo Pinto, J.

    2014-07-01

    Distributed real time control systems in scientific instruments, such as particle accelerators or telescopes, have emerged as a solution to control multiple interconnected devices, which required constant attention and observation, along with a complete integration of each of its parts. This enhancement is provided by the intense technological development that control devices have suffered in recent years. With respect to the control software, libraries and applications have also emerged in recent times. These sets of tools have been developed collaboratively in various laboratories and research centers worldwide. Experimental Physics and Industrial Control System (EPICS), a set of open source tools capable of controlling most of the devices necessary to operate a particle accelerator, can be pointed as a prime example of this progress. This thesis presents the design and development of the EPICS based control system for Linear IFMIF1 Prototype Accelerator (LIPAc), which construction involves several countries and it is currently being carried out in Rokkasho, Japan. LIPAc comprises a succession of devices and systems that focus and accelerate deuteron beam to an energy of 9 MeV with a current of 125mA, developing a previously unobtainable power of 1.125MW for that given energy...(Author)

  10. Periodic inventory system in cafeteria using linear programming

    Science.gov (United States)

    Usop, Mohd Fais; Ishak, Ruzana; Hamdan, Ahmad Ridhuan

    2017-11-01

    Inventory management is an important factor in running a business. It plays a big role of managing the stock in cafeteria. If the inventories are failed to be managed wisely, it will affect the profit of the cafeteria. Therefore, the purpose of this study is to find the solution of the inventory management in cafeteria. Most of the cafeteria in Malaysia did not manage their stock well. Therefore, this study is to propose a database system of inventory management and to develop the inventory model in cafeteria management. In this study, new database system to improve the management of the stock in a weekly basis will be provided using Linear Programming Model to get the optimal range of the inventory needed for selected categories. Data that were collected by using the Periodic Inventory System at the end of the week within three months period being analyzed by using the Food Stock-take Database. The inventory model was developed from the collected data according to the category of the inventory in the cafeteria. Results showed the effectiveness of using the Periodic Inventory System and will be very helpful to the cafeteria management in organizing the inventory. Moreover, the findings in this study can reduce the cost of operation and increased the profit.

  11. Linear Temporal Logic (LTL) Based Monitoring of Smart Manufacturing Systems.

    Science.gov (United States)

    Heddy, Gerald; Huzaifa, Umer; Beling, Peter; Haimes, Yacov; Marvel, Jeremy; Weiss, Brian; LaViers, Amy

    2015-01-01

    The vision of Smart Manufacturing Systems (SMS) includes collaborative robots that can adapt to a range of scenarios. This vision requires a classification of multiple system behaviors, or sequences of movement, that can achieve the same high-level tasks. Likewise, this vision presents unique challenges regarding the management of environmental variables in concert with discrete, logic-based programming. Overcoming these challenges requires targeted performance and health monitoring of both the logical controller and the physical components of the robotic system. Prognostics and health management (PHM) defines a field of techniques and methods that enable condition-monitoring, diagnostics, and prognostics of physical elements, functional processes, overall systems, etc. PHM is warranted in this effort given that the controller is vulnerable to program changes, which propagate in unexpected ways, logical runtime exceptions, sensor failure, and even bit rot. The physical component's health is affected by the wear and tear experienced by machines constantly in motion. The controller's source of faults is inherently discrete, while the latter occurs in a manner that builds up continuously over time. Such a disconnect poses unique challenges for PHM. This paper presents a robotic monitoring system that captures and resolves this disconnect. This effort leverages supervisory robotic control and model checking with linear temporal logic (LTL), presenting them as a novel monitoring system for PHM. This methodology has been demonstrated in a MATLAB-based simulator for an industry inspired use-case in the context of PHM. Future work will use the methodology to develop adaptive, intelligent control strategies to evenly distribute wear on the joints of the robotic arms, maximizing the life of the system.

  12. Compressive System Identification in the Linear Time-Invariant framework

    KAUST Repository

    Toth, Roland

    2011-12-01

    Selection of an efficient model parametrization (model order, delay, etc.) has crucial importance in parametric system identification. It navigates a trade-off between representation capabilities of the model (structural bias) and effects of over-parametrization (variance increase of the estimates). There exists many approaches to this widely studied problem in terms of statistical regularization methods and information criteria. In this paper, an alternative ℓ 1 regularization scheme is proposed for estimation of sparse linear-regression models based on recent results in compressive sensing. It is shown that the proposed scheme provides consistent estimation of sparse models in terms of the so-called oracle property, it is computationally attractive for large-scale over-parameterized models and it is applicable in case of small data sets, i.e., underdetermined estimation problems. The performance of the approach w.r.t. other regularization schemes is demonstrated in an extensive Monte Carlo study. © 2011 IEEE.

  13. The Cosmic Linear Anisotropy Solving System (CLASS) II: Approximation schemes

    CERN Document Server

    Blas, Diego; Tram, Thomas

    2011-01-01

    Boltzmann codes are used extensively by several groups for constraining cosmological parameters with Cosmic Microwave Background and Large Scale Structure data. This activity is computationally expensive, since a typical project requires from 10'000 to 100'000 Boltzmann code executions. The newly released code CLASS (Cosmic Linear Anisotropy Solving System) incorporates improved approximation schemes leading to a simultaneous gain in speed and precision. We describe here the three approximations used by CLASS for basic LambdaCDM models, namely: a baryon-photon tight-coupling approximation which can be set to first order, second order or to a compromise between the two; an ultra-relativistic fluid approximation which had not been implemented in public distributions before; and finally a radiation streaming approximation taking reionisation into account.

  14. Entanglement production in bosonic systems: Linear and logarithmic growth

    Science.gov (United States)

    Hackl, Lucas; Bianchi, Eugenio; Modak, Ranjan; Rigol, Marcos

    2018-03-01

    We study the time evolution of the entanglement entropy in bosonic systems with time-independent, or time-periodic, Hamiltonians. In the first part, we focus on quadratic Hamiltonians and Gaussian initial states. We show that all quadratic Hamiltonians can be decomposed into three parts: (a) unstable, (b) stable, and (c) metastable. If present, each part contributes in a characteristic way to the time dependence of the entanglement entropy: (a) linear production, (b) bounded oscillations, and (c) logarithmic production. In the second part, we use numerical calculations to go beyond Gaussian states and quadratic Hamiltonians. We provide numerical evidence for the conjecture that entanglement production through quadratic Hamiltonians has the same asymptotic behavior for non-Gaussian initial states as for Gaussian ones. Moreover, even for nonquadratic Hamiltonians, we find a similar behavior at intermediate times. Our results are of relevance to understanding entanglement production for quantum fields in dynamical backgrounds and ultracold atoms in optical lattices.

  15. Adaptive neuro-fuzzy inference system multi-objective optimization using the genetic algorithm/singular value decomposition method for modelling the discharge coefficient in rectangular sharp-crested side weirs

    Science.gov (United States)

    Khoshbin, Fatemeh; Bonakdari, Hossein; Hamed Ashraf Talesh, Seyed; Ebtehaj, Isa; Zaji, Amir Hossein; Azimi, Hamed

    2016-06-01

    In the present article, the adaptive neuro-fuzzy inference system (ANFIS) is employed to model the discharge coefficient in rectangular sharp-crested side weirs. The genetic algorithm (GA) is used for the optimum selection of membership functions, while the singular value decomposition (SVD) method helps in computing the linear parameters of the ANFIS results section (GA/SVD-ANFIS). The effect of each dimensionless parameter on discharge coefficient prediction is examined in five different models to conduct sensitivity analysis by applying the above-mentioned dimensionless parameters. Two different sets of experimental data are utilized to examine the models and obtain the best model. The study results indicate that the model designed through GA/SVD-ANFIS predicts the discharge coefficient with a good level of accuracy (mean absolute percentage error = 3.362 and root mean square error = 0.027). Moreover, comparing this method with existing equations and the multi-layer perceptron-artificial neural network (MLP-ANN) indicates that the GA/SVD-ANFIS method has superior performance in simulating the discharge coefficient of side weirs.

  16. Comparison of linear, mixed integer and non-linear programming methods in energy system dispatch modelling

    DEFF Research Database (Denmark)

    Ommen, Torben Schmidt; Markussen, Wiebke Brix; Elmegaard, Brian

    2014-01-01

    of selected units by 23%, while for a non-linear approach the increase can be higher than 39%. The results indicate a higher coherence between the two latter approaches, and that the MLP (mixed integer programming) optimisation is most appropriate from a viewpoint of accuracy and runtime. © 2014 Elsevier Ltd...

  17. Modified Differential Transform Method for Two Singular Boundary Values Problems

    Directory of Open Access Journals (Sweden)

    Yinwei Lin

    2014-01-01

    Full Text Available This paper deals with the two singular boundary values problems of second order. Two singular points are both boundary values points of the differential equation. The numerical solutions are developed by modified differential transform method (DTM for expanded point. Linear and nonlinear models are solved by this method to get more reliable and efficient numerical results. It can also solve ordinary differential equations where the traditional one fails. Besides, we give the convergence of this new method.

  18. A pipeline VLSI design of fast singular value decomposition processor for real-time EEG system based on on-line recursive independent component analysis.

    Science.gov (United States)

    Huang, Kuan-Ju; Shih, Wei-Yeh; Chang, Jui Chung; Feng, Chih Wei; Fang, Wai-Chi

    2013-01-01

    This paper presents a pipeline VLSI design of fast singular value decomposition (SVD) processor for real-time electroencephalography (EEG) system based on on-line recursive independent component analysis (ORICA). Since SVD is used frequently in computations of the real-time EEG system, a low-latency and high-accuracy SVD processor is essential. During the EEG system process, the proposed SVD processor aims to solve the diagonal, inverse and inverse square root matrices of the target matrices in real time. Generally, SVD requires a huge amount of computation in hardware implementation. Therefore, this work proposes a novel design concept for data flow updating to assist the pipeline VLSI implementation. The SVD processor can greatly improve the feasibility of real-time EEG system applications such as brain computer interfaces (BCIs). The proposed architecture is implemented using TSMC 90 nm CMOS technology. The sample rate of EEG raw data adopts 128 Hz. The core size of the SVD processor is 580×580 um(2), and the speed of operation frequency is 20MHz. It consumes 0.774mW of power during the 8-channel EEG system per execution time.

  19. Sampled-data models for linear and nonlinear systems

    CERN Document Server

    Yuz, Juan I

    2014-01-01

    Sampled-data Models for Linear and Nonlinear Systems provides a fresh new look at a subject with which many researchers may think themselves familiar. Rather than emphasising the differences between sampled-data and continuous-time systems, the authors proceed from the premise that, with modern sampling rates being as high as they are, it is becoming more appropriate to emphasise connections and similarities. The text is driven by three motives: ·      the ubiquity of computers in modern control and signal-processing equipment means that sampling of systems that really evolve continuously is unavoidable; ·      although superficially straightforward, sampling can easily produce erroneous results when not treated properly; and ·      the need for a thorough understanding of many aspects of sampling among researchers and engineers dealing with applications to which they are central. The authors tackle many misconceptions which, although appearing reasonable at first sight, are in fact either p...

  20. Phantom cosmology without Big Rip singularity

    Energy Technology Data Exchange (ETDEWEB)

    Astashenok, Artyom V. [Baltic Federal University of I. Kant, Department of Theoretical Physics, 236041, 14, Nevsky st., Kaliningrad (Russian Federation); Nojiri, Shin' ichi, E-mail: nojiri@phys.nagoya-u.ac.jp [Department of Physics, Nagoya University, Nagoya 464-8602 (Japan); Kobayashi-Maskawa Institute for the Origin of Particles and the Universe, Nagoya University, Nagoya 464-8602 (Japan); Odintsov, Sergei D. [Department of Physics, Nagoya University, Nagoya 464-8602 (Japan); Institucio Catalana de Recerca i Estudis Avancats - ICREA and Institut de Ciencies de l' Espai (IEEC-CSIC), Campus UAB, Facultat de Ciencies, Torre C5-Par-2a pl, E-08193 Bellaterra (Barcelona) (Spain); Tomsk State Pedagogical University, Tomsk (Russian Federation); Yurov, Artyom V. [Baltic Federal University of I. Kant, Department of Theoretical Physics, 236041, 14, Nevsky st., Kaliningrad (Russian Federation)

    2012-03-23

    We construct phantom energy models with the equation of state parameter w which is less than -1, w<-1, but finite-time future singularity does not occur. Such models can be divided into two classes: (i) energy density increases with time ('phantom energy' without 'Big Rip' singularity) and (ii) energy density tends to constant value with time ('cosmological constant' with asymptotically de Sitter evolution). The disintegration of bound structure is confirmed in Little Rip cosmology. Surprisingly, we find that such disintegration (on example of Sun-Earth system) may occur even in asymptotically de Sitter phantom universe consistent with observational data. We also demonstrate that non-singular phantom models admit wormhole solutions as well as possibility of Big Trip via wormholes.

  1. Cosmological models without singularities

    International Nuclear Information System (INIS)

    Petry, W.

    1981-01-01

    A previously studied theory of gravitation in flat space-time is applied to homogeneous and isotropic cosmological models. There exist two different classes of models without singularities: (i) ever-expanding models, (ii) oscillating models. The first class contains models with hot big bang. For these models there exist at the beginning of the universe-in contrast to Einstein's theory-very high but finite densities of matter and radiation with a big bang of very short duration. After short time these models pass into the homogeneous and isotropic models of Einstein's theory with spatial curvature equal to zero and cosmological constant ALPHA >= O. (author)

  2. Supersymmetric quantum mechanics under point singularities

    International Nuclear Information System (INIS)

    Uchino, Takashi; Tsutsui, Izumi

    2003-01-01

    We provide a systematic study on the possibility of supersymmetry (SUSY) for one-dimensional quantum mechanical systems consisting of a pair of lines R or intervals [-l, l] each having a point singularity. We consider the most general singularities and walls (boundaries) at x = ±l admitted quantum mechanically, using a U(2) family of parameters to specify one singularity and similarly a U(1) family of parameters to specify one wall. With these parameter freedoms, we find that for a certain subfamily the line systems acquire an N = 1 SUSY which can be enhanced to N = 4 if the parameters are further tuned, and that these SUSY are generically broken except for a special case. The interval systems, on the other hand, can accommodate N = 2 or N = 4 SUSY, broken or unbroken, and exhibit a rich variety of (degenerate) spectra. Our SUSY systems include the familiar SUSY systems with the Dirac δ(x)-potential, and hence are extensions of the known SUSY quantum mechanics to those with general point singularities and walls. The self-adjointness of the supercharge in relation to the self-adjointness of the Hamiltonian is also discussed

  3. Plane waves with weak singularities

    International Nuclear Information System (INIS)

    David, Justin R.

    2003-03-01

    We study a class of time dependent solutions of the vacuum Einstein equations which are plane waves with weak null singularities. This singularity is weak in the sense that though the tidal forces diverge at the singularity, the rate of divergence is such that the distortion suffered by a freely falling observer remains finite. Among such weak singular plane waves there is a sub-class which does not exhibit large back reaction in the presence of test scalar probes. String propagation in these backgrounds is smooth and there is a natural way to continue the metric beyond the singularity. This continued metric admits string propagation without the string becoming infinitely excited. We construct a one parameter family of smooth metrics which are at a finite distance in the space of metrics from the extended metric and a well defined operator in the string sigma model which resolves the singularity. (author)

  4. 2-D linear motion system. Innovative technology summary report

    International Nuclear Information System (INIS)

    1998-11-01

    The US Department of Energy's (DOE's) nuclear facility decontamination and decommissioning (D and D) program requires buildings to be decontaminated, decommissioned, and surveyed for radiological contamination in an expeditious and cost-effective manner. Simultaneously, the health and safety of personnel involved in the D and D activities is of primary concern. D and D workers must perform duties high off the ground, requiring the use of manlifts or scaffolding, often, in radiologically or chemically contaminated areas or in areas with limited access. Survey and decontamination instruments that are used are sometimes heavy or awkward to use, particularly when the worker is operating from a manlift or scaffolding. Finding alternative methods of performing such work on manlifts or scaffolding is important. The 2-D Linear Motion System (2-D LMS), also known as the Wall Walker trademark, is designed to remotely position tools and instruments on walls for use in such activities as radiation surveys, decontamination, and painting. Traditional (baseline) methods for operating equipment for these tasks require workers to perform duties on elevated platforms, sometimes several meters above the ground surface and near potential sources of contamination. The Wall Walker 2-D LMS significantly improves health and safety conditions by facilitating remote operation of equipment. The Wall Walker 2-D LMS performed well in a demonstration of its precision, accuracy, maneuverability, payload capacity, and ease of use. Thus, this innovative technology is demonstrated to be a viable alternative to standard methods of performing work on large, high walls, especially those that have potential contamination concerns. The Wall Walker was used to perform a final release radiological survey on over 167 m 2 of walls. In this application, surveying using a traditional (baseline) method that employs an aerial lift for manual access was 64% of the total cost of the improved technology. However

  5. Linear System Models for Ultrasonic Imaging: Intensity Signal Statistics.

    Science.gov (United States)

    Abbey, Craig K; Zhu, Yang; Bahramian, Sara; Insana, Michael F

    2017-04-01

    Despite a great deal of work characterizing the statistical properties of radio frequency backscattered ultrasound signals, less is known about the statistical properties of demodulated intensity signals. Analysis of intensity is made more difficult by a strong nonlinearity that arises in the process of demodulation. This limits our ability to characterize the spatial resolution and noise properties of B-mode ultrasound images. In this paper, we generalize earlier results on two-point intensity covariance using a multivariate systems approach. We derive the mean and autocovariance function of the intensity signal under Gaussian assumptions on both the object scattering function and acquisition noise, and with the assumption of a locally shift-invariant pulse-echo system function. We investigate the limiting cases of point statistics and a uniform scattering field with a stationary distribution. Results from validation studies using simulation and data from a real system applied to a uniform scattering phantom are presented. In the simulation studies, we find errors less than 10% between the theoretical mean and variance, and sample estimates of these quantities. Prediction of the intensity power spectrum (PS) in the real system exhibits good qualitative agreement (errors less than 3.5 dB for frequencies between 0.1 and 10 cyc/mm, but with somewhat higher error outside this range that may be due to the use of a window in the PS estimation procedure). We also replicate the common finding that the intensity mean is equal to its standard deviation (i.e., signal-to-noise ratio = 1) for fully developed speckle. We show how the derived statistical properties can be used to characterize the quality of an ultrasound linear array for low-contrast patterns using generalized noise-equivalent quanta directly on the intensity signal.

  6. Stochastic linear hybrid systems: Modeling, estimation, and application

    Science.gov (United States)

    Seah, Chze Eng

    Hybrid systems are dynamical systems which have interacting continuous state and discrete state (or mode). Accurate modeling and state estimation of hybrid systems are important in many applications. We propose a hybrid system model, known as the Stochastic Linear Hybrid System (SLHS), to describe hybrid systems with stochastic linear system dynamics in each mode and stochastic continuous-state-dependent mode transitions. We then develop a hybrid estimation algorithm, called the State-Dependent-Transition Hybrid Estimation (SDTHE) algorithm, to estimate the continuous state and discrete state of the SLHS from noisy measurements. It is shown that the SDTHE algorithm is more accurate or more computationally efficient than existing hybrid estimation algorithms. Next, we develop a performance analysis algorithm to evaluate the performance of the SDTHE algorithm in a given operating scenario. We also investigate sufficient conditions for the stability of the SDTHE algorithm. The proposed SLHS model and SDTHE algorithm are illustrated to be useful in several applications. In Air Traffic Control (ATC), to facilitate implementations of new efficient operational concepts, accurate modeling and estimation of aircraft trajectories are needed. In ATC, an aircraft's trajectory can be divided into a number of flight modes. Furthermore, as the aircraft is required to follow a given flight plan or clearance, its flight mode transitions are dependent of its continuous state. However, the flight mode transitions are also stochastic due to navigation uncertainties or unknown pilot intents. Thus, we develop an aircraft dynamics model in ATC based on the SLHS. The SDTHE algorithm is then used in aircraft tracking applications to estimate the positions/velocities of aircraft and their flight modes accurately. Next, we develop an aircraft conformance monitoring algorithm to detect any deviations of aircraft trajectories in ATC that might compromise safety. In this application, the SLHS

  7. Popov–Belevitch–Hautus type tests for the controllability of linear complementarity systems

    NARCIS (Netherlands)

    Camlibel, M. Kanat

    2007-01-01

    It is well-known that checking certain controllability properties of very simple piecewise linear systems are undecidable problems. This paper deals with the controllability problem of a class of piecewise linear systems, known as linear complementarity systems. By exploiting the underlying

  8. Residues and duality for singularity categories of isolated Gorenstein singularities

    OpenAIRE

    Murfet, Daniel

    2009-01-01

    We study Serre duality in the singularity category of an isolated Gorenstein singularity and find an explicit formula for the duality pairing in terms of generalised fractions and residues. For hypersurfaces we recover the residue formula of the string theorists Kapustin and Li. These results are obtained from an explicit construction of complete injective resolutions of maximal Cohen-Macaulay modules.

  9. Stability and Linear Quadratic Differential Games of Discrete-Time Markovian Jump Linear Systems with State-Dependent Noise

    Directory of Open Access Journals (Sweden)

    Huiying Sun

    2014-01-01

    Full Text Available We mainly consider the stability of discrete-time Markovian jump linear systems with state-dependent noise as well as its linear quadratic (LQ differential games. A necessary and sufficient condition involved with the connection between stochastic Tn-stability of Markovian jump linear systems with state-dependent noise and Lyapunov equation is proposed. And using the theory of stochastic Tn-stability, we give the optimal strategies and the optimal cost values for infinite horizon LQ stochastic differential games. It is demonstrated that the solutions of infinite horizon LQ stochastic differential games are concerned with four coupled generalized algebraic Riccati equations (GAREs. Finally, an iterative algorithm is presented to solve the four coupled GAREs and a simulation example is given to illustrate the effectiveness of it.

  10. Fractal analysis of hyperbolic and nonhyperbolic fixed points and singularities of dynamical systems in $\\mathbb{R}^{n}$

    OpenAIRE

    Dmitrović, Lana Horvat

    2017-01-01

    The main purpose of this article is to study box dimension of orbits near hyperbolic and nonhyperbolic fixed points of discrete dynamical systems in higher dimensions. We generalize the known results for one-dimensional systems, that is, the orbits near the hyperbolic fixed point in one-dimensional discrete dynamical system has the box dimension equal to zero and the orbits near nonhyperbolic fixed point has positive box dimension. In the process of studying box dimensions, we use the stable,...

  11. A constraint algorithm for singular Lagrangians subjected to nonholonomic constraints

    Energy Technology Data Exchange (ETDEWEB)

    de Leon, M. [Instituto de Matematicas y Fisica Fundamental, Consejo Superior de Investigaciones Cientificas, Serrano 123, 28006 Madrid (Spain); de Diego, D.M. [Departamento de Economia Aplicada Cuantitativa, Facultad de Ciencias Economicas y Empresariales, UNED, 28040 Madrid (Spain)

    1997-06-01

    We construct a constraint algorithm for singular Lagrangian systems subjected to nonholonomic constraints which generalizes that of Dirac for constrained Hamiltonian systems. {copyright} {ital 1997 American Institute of Physics.}

  12. Direct linear driving systems; Les entrainements lineaires directs

    Energy Technology Data Exchange (ETDEWEB)

    Favre, E.; Brunner, C.; Piaget, D. [ETEL SA (France)

    1999-11-01

    The linear motor is one of the most important developments in electrical drive technology. However, it only, began to be adopted on a large scale at the beginning of the 1990's and will not be considered a mature technology until well into the next millennium. Actuators based on linear motor technology have a number of technical advantages including high speed, high positional accuracy and fine resolution. They also require fewer component parts. Some precautions are necessary when using linear motors. Care must be taken to avoid overheating and excessive vibration, and the magnetic components must be protected.

  13. On bifurcations of a system of cubic differential equations with an integrating multiplier singular along a second-order curve

    Directory of Open Access Journals (Sweden)

    Aleksandr Alekseev

    2015-07-01

    Full Text Available We establish necessary and sufficient conditions for existence of an integrating multiplier of a special form for systems of two cubic differential equations of the first order. We further study bifurcations of such systems with the change of parameters of their integrating multipliers.

  14. Gravitational collapse and naked singularities

    Indian Academy of Sciences (India)

    Recent developments have revealed that there are examples of naked singularity formation in the collapse of physically reasonable matter fields, although the stability of these examples is still uncertain. We propose the concept of `effective naked singularities', which will be quite helpful because general relativity has ...

  15. String theory and cosmological singularities

    Indian Academy of Sciences (India)

    recent times, string theory is providing new perspectives of such singularities which may lead to an understanding of these in the standard framework of time evolution in quantum mechanics. In this article, we describe some of these approaches. Keywords. String theory; cosmological singularities. PACS Nos 11.25.

  16. Linear algebra

    CERN Document Server

    Liesen, Jörg

    2015-01-01

    This self-contained textbook takes a matrix-oriented approach to linear algebra and presents a complete theory, including all details and proofs, culminating in the Jordan canonical form and its proof. Throughout the development, the applicability of the results is highlighted. Additionally, the book presents special topics from applied linear algebra including matrix functions, the singular value decomposition, the Kronecker product and linear matrix equations. The matrix-oriented approach to linear algebra leads to a better intuition and a deeper understanding of the abstract concepts, and therefore simplifies their use in real world applications. Some of these applications are presented in detailed examples. In several ‘MATLAB-Minutes’ students can comprehend the concepts and results using computational experiments. Necessary basics for the use of MATLAB are presented in a short introduction. Students can also actively work with the material and practice their mathematical skills in more than 300 exerc...

  17. First-order systems of linear partial differential equations: normal forms, canonical systems, transform methods

    Directory of Open Access Journals (Sweden)

    Heinz Toparkus

    2014-04-01

    Full Text Available In this paper we consider first-order systems with constant coefficients for two real-valued functions of two real variables. This is both a problem in itself, as well as an alternative view of the classical linear partial differential equations of second order with constant coefficients. The classification of the systems is done using elementary methods of linear algebra. Each type presents its special canonical form in the associated characteristic coordinate system. Then you can formulate initial value problems in appropriate basic areas, and you can try to achieve a solution of these problems by means of transform methods.

  18. Estimation of failure probabilities of linear dynamic systems by ...

    Indian Academy of Sciences (India)

    variant reliability problems has been developed. In the paper, the focus is on the displacement response of a linear oscillator driven by white noise. Failure is then assumed to occur when the displacement response exceeds a critical thresh-.

  19. Lag synchronization of chaotic systems with time-delayed linear ...

    Indian Academy of Sciences (India)

    delayed linear terms via impulsive control is investigated. Based on the stability theory of impulsive delayed differen- tial equations, some sufficient conditions are obtained guaranteeing the synchronized behaviours between two delayed chaotic ...

  20. Forecasting the EMU inflation rate: Linear econometric vs. non-linear computational models using genetic neural fuzzy systems

    DEFF Research Database (Denmark)

    Kooths, Stefan; Mitze, Timo Friedel; Ringhut, Eric

    2004-01-01

    to a battery of parametric and non-parametric test statistics to measure their performance in one- and four-step ahead forecasts of quarterly data. Using genetic-neural fuzzy systems we find the computational approach superior to some degree and show how to combine both techniques successfully.......This paper compares the predictive power of linear econometric and non-linear computational models for forecasting the inflation rate in the European Monetary Union (EMU). Various models of both types are developed using different monetary and real activity indicators. They are compared according...

  1. Robustness of Linear Systems towards Multi-Dissipative Pertubations

    DEFF Research Database (Denmark)

    Thygesen, Uffe Høgsbro; Poulsen, Niels Kjølstad

    1997-01-01

    We consider the question of robust stability of a linear time invariant plant subject to dynamic perturbations, which are dissipative in the sense of Willems with respect to several quadratic supply rates. For instance, parasitic dynamics are often both small gain and passive. We reduce several...... robustness analysis questions to linear matrix inequalities: robust stability, robust H2 performance and robust performance in presence of disturbances with finite signal-to-noise ratios...

  2. Daily Average Wind Power Interval Forecasts Based on an Optimal Adaptive-Network-Based Fuzzy Inference System and Singular Spectrum Analysis

    Directory of Open Access Journals (Sweden)

    Zhongrong Zhang

    2016-01-01

    Full Text Available Wind energy has increasingly played a vital role in mitigating conventional resource shortages. Nevertheless, the stochastic nature of wind poses a great challenge when attempting to find an accurate forecasting model for wind power. Therefore, precise wind power forecasts are of primary importance to solve operational, planning and economic problems in the growing wind power scenario. Previous research has focused efforts on the deterministic forecast of wind power values, but less attention has been paid to providing information about wind energy. Based on an optimal Adaptive-Network-Based Fuzzy Inference System (ANFIS and Singular Spectrum Analysis (SSA, this paper develops a hybrid uncertainty forecasting model, IFASF (Interval Forecast-ANFIS-SSA-Firefly Alogorithm, to obtain the upper and lower bounds of daily average wind power, which is beneficial for the practical operation of both the grid company and independent power producers. To strengthen the practical ability of this developed model, this paper presents a comparison between IFASF and other benchmarks, which provides a general reference for this aspect for statistical or artificially intelligent interval forecast methods. The comparison results show that the developed model outperforms eight benchmarks and has a satisfactory forecasting effectiveness in three different wind farms with two time horizons.

  3. Fuzzy Saturated Output Feedback Tracking Control for Robot Manipulators: A Singular Perturbation Theory Based Approach

    Directory of Open Access Journals (Sweden)

    Huashan Liu

    2011-09-01

    Full Text Available To deal with the problem of the output feedback tracking (OFT control with bounded torque inputs of robot manipulators, we propose a generalized fuzzy saturated OFT controller based on singular perturbation theory. First, considering the fact that the output toque of joint actuators is limited, a general expression for a class of saturation functions is given to be applied in the control law. Second, to carry out the whole closed‐loop control with only position measurements, linear and nonlinear filters are optionally involved to generate a pseudo signal to surrogate the actual velocity tracking error. As a third contribution, a fuzzy regulator is added to obtain a self‐tuning performance in tackling the disturbances. Moreover, an explicit but strict stability proof of the system based on the stability theory of singularly perturbed systems is presented. Finally, numerical simulations on several sample controllers are implemented to verify the effectiveness of the proposed approach.

  4. Fuzzy Saturated Output Feedback Tracking Control for Robot Manipulators: A Singular Perturbation Theory Based Approach

    Directory of Open Access Journals (Sweden)

    Huashan Liu

    2011-09-01

    Full Text Available To deal with the problem of the output feedback tracking (OFT control with bounded torque inputs of robot manipulators, we propose a generalized fuzzy saturated OFT controller based on singular perturbation theory. First, considering the fact that the output toque of joint actuators is limited, a general expression for a class of saturation functions is given to be applied in the control law. Second, to carry out the whole closed-loop control with only position measurements, linear and nonlinear filters are optionally involved to generate a pseudo signal to surrogate the actual velocity tracking error. As a third contribution, a fuzzy regulator is added to obtain a self-tuning performance in tackling the disturbances. Moreover, an explicit but strict stability proof of the system based on the stability theory of singularly perturbed systems is presented. Finally, numerical simulations on several sample controllers are implemented to verify the effectiveness of the proposed approach.

  5. Composite-step product methods for solving nonsymmetric linear systems

    Energy Technology Data Exchange (ETDEWEB)

    Chan, T.F.; Szeto, T. [Univ. of California, Los Angeles, CA (United States)

    1994-12-31

    The Biconjugate Gradient (BCG) algorithm is the {open_quotes}natural{close_quotes} generalization of the classical Conjugate Gradient method to nonsymmetric linear systems. It is an attractive method because of its simplicity and its good convergence properties. Unfortunately, BCG suffers from two kinds of breakdowns (divisions by 0): one due to the non-existence of the residual polynomial, and the other due to a breakdown in the recurrence relationship used. There are many look-ahead techniques in existence which are designed to handle these breakdowns. Although the step size needed to overcome an exact breakdown can be computed in principle, these methods can unfortunately be quite complicated for handling near breakdowns since the sizes of the look-ahead steps are variable (indeed, the breakdowns can be incurable). Recently, Bank and Chan introduced the Composite Step Biconjugate Gradient (CSBCG) algorithm, an alternative which cures only the first of the two breakdowns mentioned by skipping over steps for which the BCG iterate is not defined. This is done with a simple modification of BCG which needs only a maximum look-ahead step size of 2 to eliminate the (near) breakdown and to smooth the sometimes erratic convergence of BCG. Thus, instead of a more complicated (but less prone to breakdown) version, CSBCG cures only one kind of breakdown, but does so with a minimal modification to the usual implementation of BCG in the hope that its empirically observed stability will be inherited. The authors note, then, that the Composite Step idea can be incorporated anywhere the BCG polynomial is used; in particular, in product methods such as CGS, Bi-CGSTAB, and TFQMR. Doing this not only cures the breakdown mentioned above, but also takes on the advantages of these product methods, namely, no multiplications by the transpose matrix and a faster convergence rate than BCG.

  6. Multifractal signal reconstruction based on singularity power spectrum

    International Nuclear Information System (INIS)

    Xiong, Gang; Yu, Wenxian; Xia, Wenxiang; Zhang, Shuning

    2016-01-01

    Highlights: • We propose a novel multifractal reconstruction method based on singularity power spectrum analysis (MFR-SPS). • The proposed MFR-SPS method has better power characteristic than the algorithm in Fraclab. • Further, the SPS-ISE algorithm performs better than the SPS-MFS algorithm. • Based on the proposed MFR-SPS method, we can restructure singularity white fractal noise (SWFN) and linear singularity modulation (LSM) multifractal signal, in equivalent sense, similar with the linear frequency modulation(LFM) signal and WGN in the Fourier domain. - Abstract: Fractal reconstruction (FR) and multifractal reconstruction (MFR) can be considered as the inverse problem of singularity spectrum analysis, and it is challenging to reconstruct fractal signal in accord with multifractal spectrum (MFS). Due to the multiple solutions of fractal reconstruction, the traditional methods of FR/MFR, such as FBM based method, wavelet based method, random wavelet series, fail to reconstruct fractal signal deterministically, and besides, those methods neglect the power spectral distribution in the singular domain. In this paper, we propose a novel MFR method based singularity power spectrum (SPS). Supposing the consistent uniform covering of multifractal measurement, we control the traditional power law of each scale of wavelet coefficients based on the instantaneous singularity exponents (ISE) or MFS, simultaneously control the singularity power law based on the SPS, and deduce the principle and algorithm of MFR based on SPS. Reconstruction simulation and error analysis of estimated ISE, MFS and SPS show the effectiveness and the improvement of the proposed methods compared to those obtained by the Fraclab package.

  7. Cold atoms in singular potentials

    International Nuclear Information System (INIS)

    Denschlag, J. P.

    1998-09-01

    We studied both theoretically and experimentally the interaction between cold Li atoms from a magnetic-optical trap (MOT) and a charged or current-carrying wire. With this system, we were able to realize 1/r 2 and 1/r potentials in two dimensions and to observe the motion of cold atoms in both potentials. For an atom in an attractive 1/r 2 potential, there exist no stable trajectories, instead there is a characteristic class of trajectories for which atoms fall into the singularity. We were able to observe this falling of atoms into the center of the potential. Moreover, by probing the singular 1/r 2 potential with atomic clouds of varying size and temperature we extracted scaling properties of the atom-wire interaction. For very cold atoms, and very thin wires the motion of the atoms must be treated quantum mechanically. Here we predict that the absorption cross section for the 1/r 2 potential should exhibit quantum steps. These quantum steps are a manifestation of the quantum mechanical decomposition of plane waves into partial waves. For the second part of this work, we realized a two dimensional 1/r potential for cold atoms. If the potential is attractive, the atoms can be bound and follow Kepler-like orbits around the wire. The motion in the third dimension along the wire is free. We were able to exploit this property and constructed a novel cold atom guide, the 'Kepler guide'. We also demonstrated another type of atom guide (the 'side guide'), by combining the magnetic field of the wire with a homogeneous offset magnetic field. In this case, the atoms are held in a potential 'tube' on the side of the wire. The versatility, simplicity, and scaling properties of this guide make it an interesting technique. (author)

  8. Nonlinear singularly perturbed optimal control problems with singular arcs. [flight mechanics application

    Science.gov (United States)

    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.

  9. Homogeneous piecewise polynomial Lyapunov function for robust stability of uncertain piecewise linear system

    International Nuclear Information System (INIS)

    BenAbdallah, Abdallah; Hammami, Mohamed Ali; Kallel, Jalel

    2009-01-01

    In this paper we present some sufficient conditions for the robust stability and stabilization of time invariant uncertain piecewise linear system using homogenous piecewise polynomial Lyapunov function. The proposed conditions are given in terms of linear matrix inequalities which can be numerically solved. An application of the obtained result is given. It consists in resolving the stabilization of piecewise uncertain linear control systems by using a state piecewise linear feedback.

  10. Design, dynamics and control of an Adaptive Singularity-Free Control Moment Gyroscope actuator for microspacecraft Attitude Determination and Control System

    Science.gov (United States)

    Viswanathan, Sasi Prabhakaran

    how they lead to CMG singularities, are described. General ideas on control of the angular momentum of the spacecraft using changes in the momentum variables of a finite number of ASCMGs, are provided. Control schemes for agile and precise attitude maneuvers using ASCMG cluster in the absence of external torques and when the total angular momentum of the spacecraft is zero, is presented for both constant speed and variable speed modes. A Geometric Variational Integrator (GVI) that preserves the geometry of the state space and the conserved norm of the total angular momentum is constructed for numerical simulation and microcontroller implementation of the control scheme. The GVI is obtained by discretizing the Lagrangian of the rnultibody systems, in which the rigid body attitude is globally represented on the Lie group of rigid body rotations. Hardware and software architecture of a novel spacecraft Attitude Determination and Control System (ADCS) based on commercial smartphones and a bare minimum hardware prototype of an ASCMG using low cost COTS components is also described. A lightweight, dynamics model-free Variational Attitude Estimator (VAE) suitable for smartphone implementation is employed for attitude determination and the attitude control is performed by ASCMG actuators. The VAE scheme presented here is implemented and validated onboard an Unmanned Aerial Vehicle (UAV) platform and the real time performance is analyzed. On-board sensing, data acquisition, data uplink/downlink, state estimation and real-time feedback control objectives can be performed using this novel spacecraft ADCS. The mechatronics realization of the attitude determination through variational attitude estimation scheme and control implementation using ASCMG actuators are presented here. Experimental results of the attitude estimation (filtering) scheme using smartphone sensors as an Inertial Measurement Unit (IMU) on the Hardware In the Loop (HIL) simulator testbed are given. These

  11. Singularities of n-fold integrals of the Ising class and the theory of elliptic curves

    International Nuclear Information System (INIS)

    Boukraa, S; Hassani, S; Maillard, J-M; Zenine, N

    2007-01-01

    We introduce some multiple integrals that are expected to have the same singularities as the singularities of the n-particle contributions χ (n) to the susceptibility of the square lattice Ising model. We find the Fuchsian linear differential equation satisfied by these multiple integrals for n = 1, 2, 3, 4 and only modulo some primes for n = 5 and 6, thus providing a large set of (possible) new singularities of χ (n) . We discuss the singularity structure for these multiple integrals by solving the Landau conditions. We find that the singularities of the associated ODEs identify (up to n = 6) with the leading pinch Landau singularities. The second remarkable obtained feature is that the singularities of the ODEs associated with the multiple integrals reduce to the singularities of the ODEs associated with a finite number of one-dimensional integrals. Among the singularities found, we underline the fact that the quadratic polynomial condition 1 + 3w + 4w 2 = 0, that occurs in the linear differential equation of χ (3) , actually corresponds to a remarkable property of selected elliptic curves, namely the occurrence of complex multiplication. The interpretation of complex multiplication for elliptic curves as complex fixed points of the selected generators of the renormalization group, namely isogenies of elliptic curves, is sketched. Most of the other singularities occurring in our multiple integrals are not related to complex multiplication situations, suggesting an interpretation in terms of (motivic) mathematical structures beyond the theory of elliptic curves

  12. Loop quantum cosmology and singularities.

    Science.gov (United States)

    Struyve, Ward

    2017-08-15

    Loop quantum gravity is believed to eliminate singularities such as the big bang and big crunch singularity. This belief is based on studies of so-called loop quantum cosmology which concerns symmetry-reduced models of quantum gravity. In this paper, the problem of singularities is analysed in the context of the Bohmian formulation of loop quantum cosmology. In this formulation there is an actual metric in addition to the wave function, which evolves stochastically (rather than deterministically as the case of the particle evolution in non-relativistic Bohmian mechanics). Thus a singularity occurs whenever this actual metric is singular. It is shown that in the loop quantum cosmology for a homogeneous and isotropic Friedmann-Lemaître-Robertson-Walker space-time with arbitrary constant spatial curvature and cosmological constant, coupled to a massless homogeneous scalar field, a big bang or big crunch singularity is never obtained. This should be contrasted with the fact that in the Bohmian formulation of the Wheeler-DeWitt theory singularities may exist.

  13. Object detection with a multistatic array using singular value decomposition

    Science.gov (United States)

    Hallquist, Aaron T.; Chambers, David H.

    2014-07-01

    A method and system for detecting the presence of subsurface objects within a medium is provided. In some embodiments, the detection system operates in a multistatic mode to collect radar return signals generated by an array of transceiver antenna pairs that is positioned across a surface and that travels down the surface. The detection system converts the return signals from a time domain to a frequency domain, resulting in frequency return signals. The detection system then performs a singular value decomposition for each frequency to identify singular values for each frequency. The detection system then detects the presence of a subsurface object based on a comparison of the identified singular values to expected singular values when no subsurface object is present.

  14. A novel linear direct drive system for textile winding applications

    OpenAIRE

    Jakeman, N; Bullough, W; Bingham, Chris; Mellor, Phillip

    2003-01-01

    The paper describes the specification, modelling, magnetic design, thermal characteristics and control of a novel, high acceleration (up to 82g) brushless PM linear actuator with Halbach array, for textile package winding applications. Experimental results demonstrate the realisation of the actuator and induced performance advantages afforded to the phase lead, closed-loop position control scheme.

  15. Estimation of failure probabilities of linear dynamic systems by ...

    Indian Academy of Sciences (India)

    An iterative method for estimating the failure probability for certain time-variant reliability problems has been developed. In the paper, the focus is on the displacement response of a linear oscillator driven by white noise. Failure is then assumed to occur when the displacement response exceeds a critical threshold.

  16. Smoothing identification of systems with small non-linearities

    Czech Academy of Sciences Publication Activity Database

    Kozánek, Jan; Piranda, J.

    2003-01-01

    Roč. 38, č. 1 (2003), s. 71-84 ISSN 0025-6455 R&D Projects: GA ČR GA101/00/1471 Institutional research plan: CEZ:AV0Z2076919 Keywords : identification * small non-linearities * smoothing methods Subject RIV: BI - Acoustics Impact factor: 0.237, year: 2003

  17. Kinetics of clusters in a binary linear system

    NARCIS (Netherlands)

    Hilhorst, H.J.

    We consider the stochastically time-dependent behaviour of a binary linear chain of N units at temperature T and in an external field H. The kinetics is described in terms of clusters (sequences) of specified numbers of units in the same state. A coarse-grained master equation for the cluster

  18. Riccati transformations and principal solutions of discrete linear systems

    International Nuclear Information System (INIS)

    Ahlbrandt, C.D.; Hooker, J.W.

    1984-01-01

    Consider a second-order linear matrix difference equation. A definition of principal and anti-principal, or recessive and dominant, solutions of the equation are given and the existence of principal and anti-principal solutions and the essential uniqueness of principal solutions is proven

  19. Iterative linear system solvers with approximate matrix-vector products

    NARCIS (Netherlands)

    Eshof, J. van den; Sleijpen, G.L.G.; Gijzen, M.B. van

    2003-01-01

    There are classes of linear problems for which a matrix-vector product is a time consuming operation because an expensive approximation method is required to compute it to a given accuracy. One important example is simulations in lattice QCD with Neuberger fermions where a matrix multiply

  20. Linearization of systems of four second-order ordinary differential ...

    Indian Academy of Sciences (India)

    found and proved to be cubically semi-linear in the dependent variables [3]. Separately, the geometric .... and all three parameters in (4) are complex functions of the real independent variable. Thus we obtain .... coupling as above but whose coefficients involve the dependent and independent variables, f1 − f1( f 2. 1 − f 2.

  1. Multi-domain boundary element method for axi-symmetric layered linear acoustic systems

    Science.gov (United States)

    Reiter, Paul; Ziegelwanger, Harald

    2017-12-01

    Homogeneous porous materials like rock wool or synthetic foam are the main tool for acoustic absorption. The conventional absorbing structure for sound-proofing consists of one or multiple absorbers placed in front of a rigid wall, with or without air-gaps in between. Various models exist to describe these so called multi-layered acoustic systems mathematically for incoming plane waves. However, there is no efficient method to calculate the sound field in a half space above a multi layered acoustic system for an incoming spherical wave. In this work, an axi-symmetric multi-domain boundary element method (BEM) for absorbing multi layered acoustic systems and incoming spherical waves is introduced. In the proposed BEM formulation, a complex wave number is used to model absorbing materials as a fluid and a coordinate transformation is introduced which simplifies singular integrals of the conventional BEM to non-singular radial and angular integrals. The radial and angular part are integrated analytically and numerically, respectively. The output of the method can be interpreted as a numerical half space Green's function for grounds consisting of layered materials.

  2. A singular value sensitivity approach to robust eigenstructure assignment

    DEFF Research Database (Denmark)

    Søgaard-Andersen, Per; Trostmann, Erik; Conrad, Finn

    1986-01-01

    A design technique for improving the feedback properties of multivariable state feedback systems designed using eigenstructure assignment is presented. Based on a singular value analysis of the feedback properties a design parameter adjustment procedure is outlined. This procedure allows...

  3. The duality in the topological vector spaces and the linear physical system theory

    International Nuclear Information System (INIS)

    Oliveira Castro, F.M. de.

    1980-01-01

    The excitation-response relation in a linear, passive, and causal physical system who has the property of this relation be invariant for a time translation is univocally determined by the general form of the linear and continuous functionals defined on the linear topological space chosen for the representation of the excitations. (L.C.) [pt

  4. Amplitude Linearizers for PEP-II 1.2 MW Klystrons and LLRF Systems

    Energy Technology Data Exchange (ETDEWEB)

    Van Winkle, D.; Browne, J.; Fox, J.D.; Mastorides, T.; Rivetta, C.; Teytelman, D.; /SLAC

    2006-07-18

    The PEP-II B-factory has aggressive current increases planned for luminosity through 2008. At 2.2A (HER) on 4A (LER) currents, we estimate that longitudinal growth rates will be comparable to the damping rates currently achieved in the existing low level RF and longitudinal feedback systems. Prior to having a good non-linear time domain model [1] it was postulated that klystron small signal gain non-linearity may be contributing to measured longitudinal growth rates being higher than linearly predicted growth rates. Five prototype klystron amplitude modulation linearizers have been developed to explore improved linearity in the LLRF system. The linearizers operate at 476 MHz with 15 dB dynamic range and 1 MHz linear control bandwidth. Results from lab measurements and high current beam tests are presented. Future development plans, conclusions from beam testing and ideas for future use of this linearization technique are presented.

  5. A final focus system for the Next Linear Collider

    International Nuclear Information System (INIS)

    Zimmermann, F.; Brown, K.; Emma, P.; Helm, R.; Irwin, J.; Tenenbaum, P.; Wilson, P.

    1995-06-01

    The final focus of the Next Linear Collider (NLC) demagnifies electron and positron beams of 250--750 GeV energy down to a transverse size of about 2.5 x 350 nm 2 at the interaction point (IP). The basic layout, momentum bandwidth, vibration tolerances, wakefield effects, and the tunability of the proposed final focus design are discussed. Also a perspective is given on the crab cavity and on effects of the solenoid field in the interaction region

  6. Adaptive ensemble Kalman filtering of non-linear systems

    Directory of Open Access Journals (Sweden)

    Tyrus Berry

    2013-07-01

    Full Text Available A necessary ingredient of an ensemble Kalman filter (EnKF is covariance inflation, used to control filter divergence and compensate for model error. There is an on-going search for inflation tunings that can be learned adaptively. Early in the development of Kalman filtering, Mehra (1970, 1972 enabled adaptivity in the context of linear dynamics with white noise model errors by showing how to estimate the model error and observation covariances. We propose an adaptive scheme, based on lifting Mehra's idea to the non-linear case, that recovers the model error and observation noise covariances in simple cases, and in more complicated cases, results in a natural additive inflation that improves state estimation. It can be incorporated into non-linear filters such as the extended Kalman filter (EKF, the EnKF and their localised versions. We test the adaptive EnKF on a 40-dimensional Lorenz96 model and show the significant improvements in state estimation that are possible. We also discuss the extent to which such an adaptive filter can compensate for model error, and demonstrate the use of localisation to reduce ensemble sizes for large problems.

  7. Solution of systems of linear algebraic equations by the method of summation of divergent series

    International Nuclear Information System (INIS)

    Kirichenko, G.A.; Korovin, Ya.S.; Khisamutdinov, M.V.; Shmojlov, V.I.

    2015-01-01

    A method for solving systems of linear algebraic equations has been proposed on the basis on the summation of the corresponding continued fractions. The proposed algorithm for solving systems of linear algebraic equations is classified as direct algorithms providing an exact solution in a finite number of operations. Examples of solving systems of linear algebraic equations have been presented and the effectiveness of the algorithm has been estimated [ru

  8. Complexity in Linear Systems: A Chaotic Linear Operator on the Space of Odd 2π-Periodic Functions

    Directory of Open Access Journals (Sweden)

    Tamás Kalmár-Nagy

    2017-01-01

    Full Text Available Not just nonlinear systems but infinite-dimensional linear systems can exhibit complex behavior. It has long been known that twice the backward shift on the space of square-summable sequences l2 displays chaotic dynamics. Here we construct the corresponding operator C on the space of 2π-periodic odd functions and provide its representation involving a Principal Value Integral. We explicitly calculate the eigenfunction of this operator, as well as its periodic points. We also provide examples of chaotic and unbounded trajectories of C.

  9. An Explicit Formulation of Singularity-Free Dynamic Equations of Mechanical Systems in Lagrangian Form---Part one: Single Rigid Bodies

    Directory of Open Access Journals (Sweden)

    Pål Johan From

    2012-04-01

    differential geometry to implement the dynamic equations of rigid bodies without the presence of singularities. Presenting the explicit dynamic equations also allows for more insight into the dynamic structure of the system. Another motivation is to correct some errors commonly found in the literature. Unfortunately, the formulation of the Boltzmann-Hamel equations used here are presented incorrectly. This has been corrected by the authors, but we present here, for the first time, the detailed mathematical details on how to arrive at the correct equations. We also show through examples that using the equations presented here, the dynamics of a single rigid body is reduced to the standard equations on a Lagrangian form, for example Euler's equations for rotational motion and Euler--Lagrange equations for free motion.

  10. Singular traces theory and applications

    CERN Document Server

    Sukochev, Fedor; Zanin, Dmitriy

    2012-01-01

    This text is the first complete study and monograph dedicated to singular traces. For mathematical readers the text offers, due to Nigel Kalton's contribution, a complete theory of traces on symmetrically normed ideals of compact operators. For mathematical physicists and other users of Connes' noncommutative geometry the text offers a complete reference to Dixmier traces and the deeper mathematical features of singular traces. An application section explores the consequences of these features, which previously were not discussed in general texts on noncommutative geometry.

  11. Quality control of virtual wedge in a linear electron accelerator with a computerized radiography system (CR)

    International Nuclear Information System (INIS)

    Ordiales, J. M.; Alvarez, F. J.; Falero, B.

    2011-01-01

    For quality control of the virtual wedge there are several systems on the market as arrays of detectors or ionization chambers, linear or 2D configuration, radiochromic films or digital imaging systems incorporated in electron linear accelerators (ALE ). The present work aims at implementing a system of Computed Radiography (CR) for a routine check of the virtual wedge.

  12. New approach to solve fully fuzzy system of linear equations using ...

    Indian Academy of Sciences (India)

    This paper proposes two new methods to solve fully fuzzy system of linear equations. The fuzzy system has been converted to a crisp system of linear equations by using single and double parametric form of fuzzy numbers to obtain the non-negative solution. Double parametric form of fuzzy numbers is defined and applied ...

  13. New approach to solve fully fuzzy system of linear equations using ...

    Indian Academy of Sciences (India)

    Abstract. This paper proposes two new methods to solve fully fuzzy system of linear equations. The fuzzy system has been converted to a crisp system of linear equations by using single and double parametric form of fuzzy numbers to obtain the non-negative solution. Double parametric form of fuzzy numbers is defined and.

  14. Dynkin graphs and quadrilateral singularities

    CERN Document Server

    Urabe, Tohsuke

    1993-01-01

    The study of hypersurface quadrilateral singularities can be reduced to the study of elliptic K3 surfaces with a singular fiber of type I * 0 (superscript *, subscript 0), and therefore these notes consider, besides the topics of the title, such K3 surfaces too. The combinations of rational double points that can occur on fibers in the semi-universal deformations of quadrilateral singularities are examined, to show that the possible combinations can be described by a certain law from the viewpoint of Dynkin graphs. This is equivalent to saying that the possible combinations of singular fibers in elliptic K3 surfaces with a singular fiber of type I * 0 (superscript *, subscript 0) can be described by a certain law using classical Dynkin graphs appearing in the theory of semi-simple Lie groups. Further, a similar description for thecombination of singularities on plane sextic curves is given. Standard knowledge of algebraic geometry at the level of graduate students is expected. A new method based on graphs wil...

  15. Application of linear systems theory to characterize coherence scanning interferometry

    Science.gov (United States)

    Mandal, Rahul; Palodhi, Kanik; Coupland, Jeremy; Leach, Richard; Mansfield, Daniel

    2012-04-01

    This paper considers coherence scanning interferometry as a linear filtering operation that is characterised by a point spread function in the space domain or equivalently a transfer function in the frequency domain. The applicability of the theory is discussed and the effects of these functions on the measured interferograms, and their influence on the resulting surface measurements, are described. The practical characterisation of coherence scanning interferometers using a spherical reference artefact is then considered and a new method to compensate measurement errors, based on a modified inverse filter, is demonstrated.

  16. Local and nonlocal space-time singularities

    International Nuclear Information System (INIS)

    Konstantinov, M.Yu.

    1985-01-01

    The necessity to subdivide the singularities into two classes: local and nonlocal, each of them to be defined independently, is proved. Both classes of the singularities are defined, and the relation between the definitions introduced and the standard definition of singularities, based on space-time, incompleteness, is established. The relation between definitions introduced and theorems on the singularity existence is also established

  17. Singular structure of polarization images of bile secret in diagnostics of human physiological state

    Science.gov (United States)

    Ushenko, A. G.; Fediv, A. I.; Marchuk, Yu. F.

    2009-07-01

    There have been theoretically analyzed the ways of the formation of the polarization singularities of the biological tissues images of various morphological structures. There have been also experimentally examined the coordinate distributions of a single and doubly degenerated polarization singularities of the physiologically normal and pathologically changed biological tissues. There have been determined the statistical criteria of diagnostics of the kidney tissue collagenous disease (the 3rd and the 4th statistical moments of the linear density singularity points). It was found out that the process of the pathological change of the kidney tissue morphology leads to the formation of the self-similar (fractal) distribution of the polarization singularities of its image.

  18. Dissipative open systems theory as a foundation for the thermodynamics of linear systems.

    Science.gov (United States)

    Delvenne, Jean-Charles; Sandberg, Henrik

    2017-03-06

    In this paper, we advocate the use of open dynamical systems, i.e. systems sharing input and output variables with their environment, and the dissipativity theory initiated by Jan Willems as models of thermodynamical systems, at the microscopic and macroscopic level alike. We take linear systems as a study case, where we show how to derive a global Lyapunov function to analyse networks of interconnected systems. We define a suitable notion of dynamic non-equilibrium temperature that allows us to derive a discrete Fourier law ruling the exchange of heat between lumped, discrete-space systems, enriched with the Maxwell-Cattaneo correction. We complete these results by a brief recall of the steps that allow complete derivation of the dissipation and fluctuation in macroscopic systems (i.e. at the level of probability distributions) from lossless and deterministic systems.This article is part of the themed issue 'Horizons of cybernetical physics'. © 2017 The Author(s).

  19. Application of singular eigenfunctions method of neutron transport theory

    International Nuclear Information System (INIS)

    Simovicj, R.

    1974-11-01

    A possibility of applying analitical method of neutron transport theory was investigated in research of processes governed by linearized Boltzmann equation, especially in semiconducting media. Analitical singular eigenfunctions method was developed and improved. It was applied in solving the electron transport equation for nonpolar semiconductors in case of constant high electrical field. Energy and angular distribution of high energy electrons was obtained

  20. How to Use Linear Programming for Information System Performances Optimization

    Directory of Open Access Journals (Sweden)

    Hell Marko

    2014-09-01

    Full Text Available Background: Organisations nowadays operate in a very dynamic environment, and therefore, their ability of continuously adjusting the strategic plan to the new conditions is a must for achieving their strategic objectives. BSC is a well-known methodology for measuring performances enabling organizations to learn how well they are doing. In this paper, “BSC for IS” will be proposed in order to measure the IS impact on the achievement of organizations’ business goals. Objectives: The objective of this paper is to present the original procedure which is used to enhance the BSC methodology in planning the optimal targets of IS performances value in order to maximize the organization's effectiveness. Methods/Approach: The method used in this paper is the quantitative methodology - linear programming. In the case study, linear programming is used for optimizing organization’s strategic performance. Results: Results are shown on the example of a case study national park. An optimal performance value for the strategic objective has been calculated, as well as an optimal performance value for each DO (derived objective. Results are calculated in Excel, using Solver Add-in. Conclusions: The presentation of methodology through the case study of a national park shows that this methodology, though it requires a high level of formalisation, provides a very transparent performance calculation.

  1. Storage functions for dissipative linear systems are quadratic state functions

    NARCIS (Netherlands)

    Trentelman, Harry L.; Willems, Jan C.

    1997-01-01

    This paper deals with dissipative dynamical systems. Dissipative dynamical systems can be used as models for physical phenomena in which energy exchange with their environment plays a role. In a dissipative dynamical system, the book-keeping of energy is done via the supply rate and a storage

  2. Reliability modelling and simulation of switched linear system ...

    African Journals Online (AJOL)

    Thus, constructing a subsystem Markov model and matching its parameters with the specified safety factors provides the basis for the entire system analysis. For the system simulation, temporal databases and predictive control algorithm are designed. The simulation results are analyzed to assess the reliability of the system ...

  3. Attractor reconstruction for non-linear systems: a methodological note

    Science.gov (United States)

    Nichols, J.M.; Nichols, J.D.

    2001-01-01

    Attractor reconstruction is an important step in the process of making predictions for non-linear time-series and in the computation of certain invariant quantities used to characterize the dynamics of such series. The utility of computed predictions and invariant quantities is dependent on the accuracy of attractor reconstruction, which in turn is determined by the methods used in the reconstruction process. This paper suggests methods by which the delay and embedding dimension may be selected for a typical delay coordinate reconstruction. A comparison is drawn between the use of the autocorrelation function and mutual information in quantifying the delay. In addition, a false nearest neighbor (FNN) approach is used in minimizing the number of delay vectors needed. Results highlight the need for an accurate reconstruction in the computation of the Lyapunov spectrum and in prediction algorithms.

  4. Practical Implementations of Advanced Process Control for Linear Systems

    DEFF Research Database (Denmark)

    Knudsen, Jørgen K . H.; Huusom, Jakob Kjøbsted; Jørgensen, John Bagterp

    This paper describes some practical problems encountered, when implementing Advanced Process Control, APC, schemes on linear processes. The implemented APC controllers discussed will be LQR, Riccati MPC and Condensed MPC controllers illustrated by simulation of the Four Tank Process...... cannot be achieved without violation of process constraints. A target calculation function can be used to calculate the optimal achievable target for the process. The use of hard and soft constraints for process input constraints in the MPC controllers, ensures feasible solutions. The computational load...... as function of controllers type, Model dimension and constraint type will be discussed. Finally the special requirements set by processes including a pure integration dynamics will be illustrated by a linearised CSTR process. The simulated results presented, will later on be implemented on and demonstrated...

  5. Linear and/or curvilinear rail mount system

    Science.gov (United States)

    Thomas, Jackie D. (Inventor); Harris, Lawanna L. (Inventor)

    2012-01-01

    One or more linear and/or curvilinear mounting rails are coupled to a structure. Each mounting rail defines a channel and at least one cartridge assembly is engaged in the channel. Each cartridge assembly includes a housing that slides within the channel. The housing defines a curvilinearly-shaped recess longitudinally aligned with the channel when the housing is in engagement therewith. The cartridge assembly also includes a cleat fitted in the recess for sliding engagement therealong. The cleat can be coupled to a fastener that passes through the mounting rail and the housing when the housing is so-engaged in the channel. The cleat is positioned in the recess by a position of the fastener.

  6. Dynamic Performance of Subway Vehicle with Linear Induction Motor System

    Science.gov (United States)

    Wu, Pingbo; Luo, Ren; Hu, Yan; Zeng, Jing

    The light rail vehicle with Linear Induction Motor (LIM) bogie, which is a new type of urban rail traffic tool, has the advantages of low costs, wide applicability, low noise, simple maintenance and better dynamic behavior. This kind of vehicle, supported and guided by the wheel and rail, is not driven by the wheel/rail adhesion force, but driven by the electromagnetic force between LIM and reaction plate. In this paper, three different types of suspensions and their characteristic are discussed with considering the interactions both between wheel and rail and between LIM and reaction plate. A nonlinear mathematical model of the vehicle with LIM bogie is set up by using the software SIMPACK, and the electromechanical model is also set up on Simulink roof. Then the running behavior of the LIM vehicle is simulated, and the influence of suspension on the vehicle dynamic performance is investigated.

  7. Tunnel radio communications system at Stanford Linear Accelerator Center

    Energy Technology Data Exchange (ETDEWEB)

    Struven, W.C.

    1980-07-01

    A unique single frequency, dual daisy chain tunnel radio communication system has been developed for use in our new Positron-Electron Storage Ring. Communications are possible between portables in the underground ring and between a portable in the ring and all control rooms on the site. The system is designed as a wide band facility and therefore can carry many simplex and duplex transmissions. This system utilizes TV twinlead as a distributed antenna and repeater amplifiers to cover more than 7000 feet of underground tunnel. The design philosophy, tests and initial design are discussed and contrasted with the final implementation of the system. Future uses of the system are discussed.

  8. Stability analysis and controller design for a linear system with Duhem hysteresis nonlinearity

    NARCIS (Netherlands)

    Ouyang, Ruiyue; Jayawardhana, Bayu

    2012-01-01

    In this paper, we investigate the stability of feedback interconnections between a linear system and a Duhem hysteresis operator, where the linear system satisfies either counter-clockwise (CCW) or clockwise (CW) inputoutput dynamics [1], [13]. More precisely, depending on the input-output dynamics

  9. Weak regularizability and pole assignment for non-square linear systems

    Czech Academy of Sciences Publication Activity Database

    Korotka, Tetiana; Loiseau, J. J.; Zagalak, Petr

    2012-01-01

    Roč. 48, č. 6 (2012), s. 1065-1088 ISSN 0023-5954 R&D Projects: GA ČR GAP103/12/2431 Keywords : linear systems * linear state feedback * pole assignment Subject RIV: BC - Control Systems Theory Impact factor: 0.619, year: 2012 http://library.utia.cas.cz/separaty/2013/AS/korotka-0386325.pdf

  10. Singularity confinement for maps with the Laurent property

    International Nuclear Information System (INIS)

    Hone, A.N.W.

    2007-01-01

    The singularity confinement test is very useful for isolating integrable cases of discrete-time dynamical systems, but it does not provide a sufficient criterion for integrability. Quite recently a new property of the bilinear equations appearing in discrete soliton theory has been noticed: The iterates of such equations are Laurent polynomials in the initial data. A large class of non-integrable mappings of the plane are presented which both possess this Laurent property and have confined singularities

  11. Resonance scattering and singularities of the scattering function

    Energy Technology Data Exchange (ETDEWEB)

    Heiss, W.D. [National Institute for Theoretical Physics, Stellenbosch Institute for Advanced Study, and Institute of Theoretical Physics, University of Stellenbosch (South Africa); Nazmitdinov, R.G. [Department de Fisica, Universitat de les Illes Balears, Palma de Mallorca (Spain); Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna (Russian Federation)

    2010-05-15

    Recent studies of transport phenomena with complex potentials are explained by generic square root singularities of spectrum and eigenfunctions of non-Hermitian Hamiltonians. Using a two channel problem we demonstrate that such singularities produce a significant effect upon the pole behaviour of the scattering matrix, and more significantly upon the associated residues. This mechanism explains why by proper choice of the system parameters the resonance cross section is increased drastically in one channel and suppressed in the other channel. (authors)

  12. Brane singularities and their avoidance

    International Nuclear Information System (INIS)

    Antoniadis, Ignatios; Cotsakis, Spiros; Klaoudatou, Ifigeneia

    2010-01-01

    The singularity structure and the corresponding asymptotic behavior of a 3-brane coupled to a scalar field or to a perfect fluid in a five-dimensional bulk is analyzed in full generality using the method of asymptotic splittings. In the case of the scalar field, it is shown that the collapse singularity at a finite distance from the brane can be avoided only at the expense of making the brane world-volume positively or negatively curved. In the case where the bulk field content is parametrized by an analog of perfect fluid with an arbitrary equation of state P = γρ between the 'pressure' P and the 'density' ρ, our results depend crucially on the constant fluid parameter γ. (i) For γ > -1/2, the flat brane solution suffers from a collapse singularity at a finite distance that disappears in the curved case. (ii) For γ < -1, the singularity cannot be avoided and it becomes of the big rip type for a flat brane. (iii) For -1 < γ ≤ -1/2, the surprising result is found that while the curved brane solution is singular, the flat brane is not, opening the possibility for a revival of the self-tuning proposal.

  13. Conservation laws for multidimensional systems and related linear algebra problems

    NARCIS (Netherlands)

    Igonine, Sergei

    2002-01-01

    We consider multidimensional systems of PDEs of generalized evolution form with t-derivatives of arbitrary order on the left-hand side and with the right-hand side dependent on lower order t-derivatives and arbitrary space derivatives. For such systems we find an explicit necessary condition for the

  14. Conservation laws for multidimensional systems and related linear algebra problems

    NARCIS (Netherlands)

    Igonin, S.

    2002-01-01

    We consider multidimensional systems of PDEs of generalized evolution form with $t$-derivatives of arbitrary order on the left-hand side and with the right-hand side dependent on lower order $t$-derivatives and arbitrary space derivatives. For such systems we find an explicit necessary condition for

  15. Static linear Fresnel lenses as LCPV system in a greenhouse

    NARCIS (Netherlands)

    Sonneveld, P.J.; Swinkels, G.L.A.M.; Tuijl, van B.A.J.; Janssen, H.J.J.; Zwart, de H.F.

    2011-01-01

    A low concentrating PV system with water cooling (LCPVT system) will result in electrical and thermal energy output from the solar energy excess entering a building or greenhouse. All the direct radiation could be converted, which corresponds to 75% of the incoming solar energy. This will

  16. Linear time heteronymous damping in nonlinear parametric systems

    Czech Academy of Sciences Publication Activity Database

    Hortel, Milan; Škuderová, Alena; Houfek, Martin

    2016-01-01

    Roč. 40, 23-24 (2016), s. 10038-10051 ISSN 0307-904X Institutional support: RVO:61388998 Keywords : nonlinear dynamics of system s * parametric system s * time heteronymous damping * gears Subject RIV: JT - Propulsion, Motors ; Fuels Impact factor: 2.350, year: 2016

  17. Conservation laws for multidimensional systems and related linear algebra problems

    International Nuclear Information System (INIS)

    Igonin, Sergei

    2002-01-01

    We consider multidimensional systems of PDEs of generalized evolution form with t-derivatives of arbitrary order on the left-hand side and with the right-hand side dependent on lower order t-derivatives and arbitrary space derivatives. For such systems we find an explicit necessary condition for the existence of higher conservation laws in terms of the system's symbol. For systems that violate this condition we give an effective upper bound on the order of conservation laws. Using this result, we completely describe conservation laws for viscous transonic equations, for the Brusselator model and the Belousov-Zhabotinskii system. To achieve this, we solve over an arbitrary field the matrix equations SA=A t S and SA=-A t S for a quadratic matrix A and its transpose A t , which may be of independent interest

  18. Mathematical models of non-linear phenomena, processes and systems: from molecular scale to planetary atmosphere

    CERN Document Server

    2013-01-01

    This book consists of twenty seven chapters, which can be divided into three large categories: articles with the focus on the mathematical treatment of non-linear problems, including the methodologies, algorithms and properties of analytical and numerical solutions to particular non-linear problems; theoretical and computational studies dedicated to the physics and chemistry of non-linear micro-and nano-scale systems, including molecular clusters, nano-particles and nano-composites; and, papers focused on non-linear processes in medico-biological systems, including mathematical models of ferments, amino acids, blood fluids and polynucleic chains.

  19. Phase and amplitude control system for Stanford Linear Accelerator

    International Nuclear Information System (INIS)

    Yoo, S.J.

    1983-01-01

    The computer controlled phase and amplitude detection system measures the instantaneous phase and amplitude of a 1 micro-second 2856 MHz rf pulse at a 180 Hz rate. This will be used for phase feedback control, and also for phase and amplitude jitter measurement. The program, which was originally written by John Fox and Keith Jobe, has been modified to improve the function of the system. The software algorithms used in the measurement are described, as is the performance of the prototype phase and amplitude detector system

  20. Stability Tests of Positive Fractional Continuous-time Linear Systems with Delays

    Directory of Open Access Journals (Sweden)

    Tadeusz Kaczorek

    2013-06-01

    Full Text Available Necessary and sufficient conditions for the asymptotic stability of positive fractional continuous-time linear systems with many delays are established. It is shown that: 1 the asymptotic stability of the positive fractional system is independent of their delays, 2 the checking of the asymptotic stability of the positive fractional systems with delays can be reduced to checking of the asymptotic stability of positive standard linear systems without delays.

  1. Discontinuous Galerkin Methods for NonLinear Differential Systems

    Science.gov (United States)

    Barth, Timothy; Mansour, Nagi (Technical Monitor)

    2001-01-01

    This talk considers simplified finite element discretization techniques for first-order systems of conservation laws equipped with a convex (entropy) extension. Using newly developed techniques in entropy symmetrization theory, simplified forms of the discontinuous Galerkin (DG) finite element method have been developed and analyzed. The use of symmetrization variables yields numerical schemes which inherit global entropy stability properties of the PDE (partial differential equation) system. Central to the development of the simplified DG methods is the Eigenvalue Scaling Theorem which characterizes right symmetrizers of an arbitrary first-order hyperbolic system in terms of scaled eigenvectors of the corresponding flux Jacobian matrices. A constructive proof is provided for the Eigenvalue Scaling Theorem with detailed consideration given to the Euler equations of gas dynamics and extended conservation law systems derivable as moments of the Boltzmann equation. Using results from kinetic Boltzmann moment closure theory, we then derive and prove energy stability for several approximate DG fluxes which have practical and theoretical merit.

  2. Adaptive Non-linear Control of Hydraulic Actuator Systems

    DEFF Research Database (Denmark)

    Hansen, Poul Erik; Conrad, Finn

    1998-01-01

    Presentation of two new developed adaptive non-liner controllers for hydraulic actuator systems to give stable operation and improved performance.Results from the IMCIA project supported by the Danish Technical Research Council (STVF).......Presentation of two new developed adaptive non-liner controllers for hydraulic actuator systems to give stable operation and improved performance.Results from the IMCIA project supported by the Danish Technical Research Council (STVF)....

  3. Analysis, control and optimal operations in hybrid power systems advanced techniques and applications for linear and nonlinear systems

    CERN Document Server

    Bizon, Nicu; Mahdavi Tabatabaei, Naser

    2014-01-01

    This book explains and analyzes the dynamic performance of linear and nonlinear systems, particularly for Power Systems including Hybrid Power Sources. Offers a detailed description of system stability using state space energy conservation principle, and more.

  4. On non-linear dynamics of a coupled electro-mechanical system

    DEFF Research Database (Denmark)

    Darula, Radoslav; Sorokin, Sergey

    2012-01-01

    , for mechanical system, is of the second order. The governing equations are coupled via linear and weakly non-linear terms. A classical perturbation method, a method of multiple scales, is used to find a steadystate response of the electro-mechanical system exposed to a harmonic close-resonance mechanical......Electro-mechanical devices are an example of coupled multi-disciplinary weakly non-linear systems. Dynamics of such systems is described in this paper by means of two mutually coupled differential equations. The first one, describing an electrical system, is of the first order and the second one...... excitation. The results are verified using a numerical model created in MATLAB Simulink environment. Effect of non-linear terms on dynamical response of the coupled system is investigated; the backbone and envelope curves are analyzed. The two phenomena, which exist in the electro-mechanical system: (a...

  5. Singular Perturbation Analysis and Gene Regulatory Networks with Delay

    Science.gov (United States)

    Shlykova, Irina; Ponosov, Arcady

    2009-09-01

    There are different ways of how to model gene regulatory networks. Differential equations allow for a detailed description of the network's dynamics and provide an explicit model of the gene concentration changes over time. Production and relative degradation rate functions used in such models depend on the vector of steeply sloped threshold functions which characterize the activity of genes. The most popular example of the threshold functions comes from the Boolean network approach, where the threshold functions are given by step functions. The system of differential equations becomes then piecewise linear. The dynamics of this system can be described very easily between the thresholds, but not in the switching domains. For instance this approach fails to analyze stationary points of the system and to define continuous solutions in the switching domains. These problems were studied in [2], [3], but the proposed model did not take into account a time delay in cellular systems. However, analysis of real gene expression data shows a considerable number of time-delayed interactions suggesting that time delay is essential in gene regulation. Therefore, delays may have a great effect on the dynamics of the system presenting one of the critical factors that should be considered in reconstruction of gene regulatory networks. The goal of this work is to apply the singular perturbation analysis to certain systems with delay and to obtain an analog of Tikhonov's theorem, which provides sufficient conditions for constracting the limit system in the delay case.

  6. Soliton-like behavior in fast two-pulse collisions in weakly perturbed linear physical systems

    Science.gov (United States)

    Peleg, Avner; Nguyen, Quan M.; Huynh, Toan T.

    2017-12-01

    We demonstrate that pulses of linear physical systems, weakly perturbed by nonlinear dissipation, exhibit soliton-like behavior in fast collisions. The behavior is demonstrated for linear waveguides with weak cubic loss and for systems described by linear diffusion-advection models with weak quadratic loss. We show that in both systems, the expressions for the collision-induced amplitude shifts due to the nonlinear loss have the same form as the expression for the amplitude shift in a fast collision between two solitons of the cubic nonlinear Schrödinger equation in the presence of weak cubic loss. Our analytic predictions are confirmed by numerical simulations with the corresponding coupled linear evolution models with weak nonlinear loss. These results open the way for studying dynamics of fast collisions between pulses of weakly perturbed linear physical systems in an arbitrary spatial dimension.

  7. A Linear Active Disturbance Rejection Control for a Ball and Rigid Triangle System

    Directory of Open Access Journals (Sweden)

    Carlos Aguilar-Ibanez

    2016-01-01

    Full Text Available This paper proposes an application of linear flatness control along with active disturbance rejection control (ADRC for the local stabilization and trajectory tracking problems in the underactuated ball and rigid triangle system. To this end, an observer-based linear controller of the ADRC type is designed based on the flat tangent linearization of the system around its corresponding unstable equilibrium rest position. It was accomplished through two decoupled linear extended observers and a single linear output feedback controller, with disturbance cancelation features. The controller guarantees locally exponentially asymptotic stability for the stabilization problem and practical local stability in the solution of the tracking error. An advantage of combining the flatness and the ADRC methods is that it possible to perform online estimates and cancels the undesirable effects of the higher-order nonlinearities discarded by the linearization approximation. Simulation indicates that the proposed controller behaves remarkably well, having an acceptable domain of attraction.

  8. A 1 + 5-dimensional gravitational-wave solution. Curvature singularity and spacetime singularity

    International Nuclear Information System (INIS)

    Chen, Yu-Zhu; Li, Wen-Du; Dai, Wu-Sheng

    2017-01-01

    We solve a 1 + 5-dimensional cylindrical gravitational-wave solution of the Einstein equation, in which there are two curvature singularities. Then we show that one of the curvature singularities can be removed by an extension of the spacetime. The result exemplifies that the curvature singularity is not always a spacetime singularity; in other words, the curvature singularity cannot serve as a criterion for spacetime singularities. (orig.)

  9. A 1 + 5-dimensional gravitational-wave solution. Curvature singularity and spacetime singularity

    Energy Technology Data Exchange (ETDEWEB)

    Chen, Yu-Zhu [Tianjin University, Department of Physics, Tianjin (China); Li, Wen-Du [Tianjin University, Department of Physics, Tianjin (China); Nankai University, Theoretical Physics Division, Chern Institute of Mathematics, Tianjin (China); Dai, Wu-Sheng [Nankai University, Theoretical Physics Division, Chern Institute of Mathematics, Tianjin (China); Nankai University and Tianjin University, LiuHui Center for Applied Mathematics, Tianjin (China)

    2017-12-15

    We solve a 1 + 5-dimensional cylindrical gravitational-wave solution of the Einstein equation, in which there are two curvature singularities. Then we show that one of the curvature singularities can be removed by an extension of the spacetime. The result exemplifies that the curvature singularity is not always a spacetime singularity; in other words, the curvature singularity cannot serve as a criterion for spacetime singularities. (orig.)

  10. Estimation of Physical Parameters in Linear and Nonlinear Dynamic Systems

    DEFF Research Database (Denmark)

    Knudsen, Morten

    for certain input in the time or frequency domain, are emphasised. Consequently, some special techniques are required, in particular for input signal design and model validation. The model structure containing physical parameters is constructed from basic physical laws (mathematical modelling). It is possible......Estimation of physical parameters is an important subclass of system identification. The specific objective is to obtain accurate estimates of the model parameters, while the objective of other aspects of system identification might be to determine a model where other properties, such as responses...... and essential to utilise this physical insight in the input design and validation procedures. This project has two objectives: 1. To develop and apply theories and techniques that are compatible with physical insight and robust to violation of assumptions and approximations, for system identification in general...

  11. Development Of Linear Quadratic Regulator Design For Small UAV System

    Directory of Open Access Journals (Sweden)

    Cho Zin Myint

    2015-08-01

    Full Text Available The aim of this paper is to know the importance role of stability analysis for both unmanned aircraft system and for all control system. The objective of paper is to develop a method for dynamic stability analysis of the design process. These are categorized intoTo design model and stability analysis of UAV based on the forces and moment equations of aircraft dynamic model To choose the suitable controller for desired altitude of a particular UAV model To analyze the stability condition for aircraft using mathematical modeling and MATLAB. In this paper the analytical model of the longitudinal dynamic of flying wing UAV has been developed using aerodynamic data. The stability characteristics of UAV can be achieved from the system transfer function with LQR controller.

  12. Improving the energy efficiency of sparse linear system solvers on multicore and manycore systems.

    Science.gov (United States)

    Anzt, H; Quintana-Ortí, E S

    2014-06-28

    While most recent breakthroughs in scientific research rely on complex simulations carried out in large-scale supercomputers, the power draft and energy spent for this purpose is increasingly becoming a limiting factor to this trend. In this paper, we provide an overview of the current status in energy-efficient scientific computing by reviewing different technologies used to monitor power draft as well as power- and energy-saving mechanisms available in commodity hardware. For the particular domain of sparse linear algebra, we analyse the energy efficiency of a broad collection of hardware architectures and investigate how algorithmic and implementation modifications can improve the energy performance of sparse linear system solvers, without negatively impacting their performance. © 2014 The Author(s) Published by the Royal Society. All rights reserved.

  13. Polarization singularity anarchy in three dimensional ellipse fields

    Science.gov (United States)

    Freund, Isaac

    2004-11-01

    Lines of circular polarization, C lines, and lines of linear polarization, L lines, are studied in a computer simulated random three-dimensional ellipse field. Although we verify existing predictions for the location of particular points on these lines at which the sign of the topological index of the line inverts, we show that from the point of view of foliations of the field such points are better described as points of pair production. We find a new set of true sign inversion points, and show that when all possible foliations are considered this set includes all points on the line. We also find three new families of polarization singularities whose members include all polarization ellipses. The recently described polarization singularity democracy in two-dimensional fields evidently explodes into polarization singularity anarchy in three-dimensional fields.

  14. Two-scale approach to oscillatory singularly perturbed transport equations

    CERN Document Server

    Frénod, Emmanuel

    2017-01-01

    This book presents the classical results of the two-scale convergence theory and explains – using several figures – why it works. It then shows how to use this theory to homogenize ordinary differential equations with oscillating coefficients as well as oscillatory singularly perturbed ordinary differential equations. In addition, it explores the homogenization of hyperbolic partial differential equations with oscillating coefficients and linear oscillatory singularly perturbed hyperbolic partial differential equations. Further, it introduces readers to the two-scale numerical methods that can be built from the previous approaches to solve oscillatory singularly perturbed transport equations (ODE and hyperbolic PDE) and demonstrates how they can be used efficiently. This book appeals to master’s and PhD students interested in homogenization and numerics, as well as to the Iter community.

  15. Symmetry breaking and singularity structure in Bose-Einstein condensates

    Science.gov (United States)

    Commeford, K. A.; Garcia-March, M. A.; Ferrando, A.; Carr, Lincoln D.

    2012-08-01

    We determine the trajectories of vortex singularities that arise after a single vortex is broken by a discretely symmetric impulse in the context of Bose-Einstein condensates in a harmonic trap. The dynamics of these singularities are analyzed to determine the form of the imprinted motion. We find that the symmetry-breaking process introduces two effective forces: a repulsive harmonic force that causes the daughter trajectories to be ejected from the parent singularity and a Magnus force that introduces a torque about the axis of symmetry. For the analytical noninteracting case we find that the parent singularity is reconstructed from the daughter singularities after one period of the trapping frequency. The interactions between singularities in the weakly interacting system do not allow the parent vortex to be reconstructed. Analytic trajectories were compared to the actual minima of the wave function, showing less than 0.5% error for an impulse strength of v=0.00005. We show that these solutions are valid within the impulse regime for various impulse strengths using numerical integration of the Gross-Pitaevskii equation. We also show that the actual duration of the symmetry-breaking potential does not significantly change the dynamics of the system as long as the strength is below v=0.0005.

  16. Ambient cosmology and spacetime singularities

    CERN Document Server

    Antoniadis, Ignatios

    2015-01-01

    We present a new approach to the issues of spacetime singularities and cosmic censorship in general relativity. This is based on the idea that standard 4-dimensional spacetime is the conformal infinity of an ambient metric for the 5-dimensional Einstein equations with fluid sources. We then find that the existence of spacetime singularities in four dimensions is constrained by asymptotic properties of the ambient 5-metric, while the non-degeneracy of the latter crucially depends on cosmic censorship holding on the boundary.

  17. Ambient cosmology and spacetime singularities

    Energy Technology Data Exchange (ETDEWEB)

    Antoniadis, Ignatios [Bern University, Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, Bern (Switzerland); Ecole Polytechnique, Palaiseau (France); Cotsakis, Spiros [CERN, Theory Division, Department of Physics, Geneva 23 (Switzerland); National Technical University, School of Applied Mathematics and Physical Sciences, Athens (Greece)

    2015-01-01

    We present a new approach to the issues of spacetime singularities and cosmic censorship in general relativity. This is based on the idea that standard 4-dimensional spacetime is the conformal infinity of an ambient metric for the 5-dimensional Einstein equations with fluid sources. We then find that the existence of spacetime singularities in four dimensions is constrained by asymptotic properties of the ambient 5-metric, while the non-degeneracy of the latter crucially depends on cosmic censorship holding on the boundary. (orig.)

  18. Application of Quadratic Linearization for the Control of Permanent Magnet Synchronous Motor

    Directory of Open Access Journals (Sweden)

    Parvathy Ayalur Krishnamoorthy

    2011-01-01

    Full Text Available Many of the existing control methods for the permanent magnet synchronous motor (PMSM either deal with steady state models or consider dynamic models under particular cases. A dynamic model of the PM machine allows powerful control-theoretic techniques such as linearization to be applied to the system. Existing exact feedback linearization of dynamic model of PMSM suffers from singularity issues. In this paper, we propose a quadratic linearization approach for PMSM based on the approximate linearization technique which does not introduce singularities. A MATLAB simulation is used to verify the effectiveness of the linearization technique proposed. Also, to account for higher-order and unmodelled dynamics of PMSM, tuning of the linearizing transformation is proposed and verified using simulation.

  19. Downlink SINR Distribution of Linearly Precoded Multiuser MIMO Systems

    DEFF Research Database (Denmark)

    Lin, Zihuai; Sørensen, Troels Bundgaard; Mogensen, Preben

    2007-01-01

    is confined to 3GPP downlink transmission in which we specifically investigate the Single User (SU) and Multi-user (MU) Spatial Divsion Multiplexing (SDM) MIMO schemes. From the analytical results we find that the outage probability for systems using the SU-MIMO scheme is larger than the one for the MU...

  20. Stability and response bounds of non-conservative linear systems

    DEFF Research Database (Denmark)

    Kliem, Wolfhard; Pommer, Christian

    2004-01-01

    This paper develops a stability theorem and response bounds for non-conservative systems of the form MX + (D + G)x + (K + N)x = f(t), with hermitian positive-definite matrices M, D and K, and skew-hermitian matrices G and N. To this end, we first find a Lyapunov function by solving the Lyapunov m...

  1. Stability and stabilization of linear systems with saturating actuators

    CERN Document Server

    Tarbouriech, Sophie; Gomes da Silva Jr, João Manoel; Queinnec, Isabelle

    2011-01-01

    Gives the reader an in-depth understanding of the phenomena caused by the more-or-less ubiquitous problem of actuator saturation. Proposes methods and algorithms designed to avoid, manage or overcome the effects of actuator saturation. Uses a state-space approach to ensure local and global stability of the systems considered. Compilation of fifteen years' worth of research results.

  2. Linear and branching metrics for quantitative transition systems

    NARCIS (Netherlands)

    de Alfaro, L.; Faella, M.; Stoelinga, Mariëlle Ida Antoinette; Díaz, J.; Karhumäki, J.; Lepistö, A.; Sannella, D.

    2004-01-01

    We extend the basic system relations of trace inclusion, trace equivalence, simulation, and bisimulation to a quantitative setting in which propositions are interpreted not as boolean values, but as real values in the interval [0,1]. Trace inclusion and equivalence give rise to asymmetrical and

  3. Identification of linear error-models with projected dynamical systems

    Czech Academy of Sciences Publication Activity Database

    Krejčí, Pavel; Kuhnen, K.

    2004-01-01

    Roč. 10, č. 1 (2004), s. 59-91 ISSN 1387-3954 Keywords : identification * error models * projected dynamical systems Subject RIV: BA - General Mathematics Impact factor: 0.292, year: 2004 http://www.informaworld.com/smpp/content~db=all~content=a713682517

  4. cauchy problems for semi-linear hyperbolic systems with their ...

    African Journals Online (AJOL)

    DJFLEX

    is given. We apply this solution approached to establish the solution representation for any isentropic fluid flow. KEYWORDS: Hyperbolic Systems, Characteristic curves, eigenvalues, eigenvectors, isentropic fluid. 1.0. INTRODUCTION. Cauchy problems arose naturally from physical phenomena and are of great interest.

  5. A laser-wire system for the International Linear Collider

    Indian Academy of Sciences (India)

    Laser-wire; accelerator test facility; laser; optical system; Compton; beam emittance; MOPA; fiber laser. Abstract. A new laser-wire has been installed in the extraction line of the ATF at KEK. It aims at demonstrating that laser-wires can be used to measure micrometre scale beam size. In parallel, studies have been made to ...

  6. A laser-wire system for the International Linear Collider

    Indian Academy of Sciences (India)

    ... line of the ATF at KEK. It aims at demonstrating that laser-wires can be used to measure micrometre scale beam size. In parallel, studies have been made to specify a laser suitable for the ILC laser-wires. Keywords. Laser-wire; accelerator test facility; laser; optical system; Compton; beam emittance; MOPA; fiber laser.

  7. Sparse symmetric preconditioners for dense linear systems in electromagnetism

    NARCIS (Netherlands)

    Carpentieri, Bruno; Duff, Iain S.; Giraud, Luc; Monga Made, M. Magolu

    2004-01-01

    We consider symmetric preconditioning strategies for the iterative solution of dense complex symmetric non-Hermitian systems arising in computational electromagnetics. In particular, we report on the numerical behaviour of the classical incomplete Cholesky factorization as well as some of its recent

  8. Computational Experiments with ABS Algorithms for KKT Linear Systems

    Czech Academy of Sciences Publication Activity Database

    Bodon, E.; Del Popolo, A.; Lukšan, Ladislav; Spedicato, E.

    2001-01-01

    Roč. 16, č. 1-4 (2001), s. 85-99 ISSN 1055-6788 R&D Projects: GA ČR GA201/00/0080 Institutional research plan: AV0Z1030915 Keywords : ABS algorithms * KKT systems Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 0.623, year: 2001

  9. Linear Motion Systems. A Modular Approach for Improved Straightness Performance

    NARCIS (Netherlands)

    Nijsse, G.J.P.

    2001-01-01

    This thesis deals with straight motion systems. A modular approach has been applied in order to find ways to improve the performance. The main performance parameters that are considered are position accuracy, repeatability and, to a lesser extent, cost. Because of the increasing requirements to

  10. Quadratic theory and feedback controllers for linear time delay systems

    International Nuclear Information System (INIS)

    Lee, E.B.

    1976-01-01

    Recent research on the design of controllers for systems having time delays is discussed. Results for the ''open loop'' and ''closed loop'' designs will be presented. In both cases results for minimizing a quadratic cost functional are given. The usefulness of these results is not known, but similar results for the non-delay case are being routinely applied. (author)

  11. Linear Optimization of Frequency Spectrum Assignments Across System

    Science.gov (United States)

    2016-03-01

    ELECTROMAGNETIC MANEUVER WARFARE .............................5  B.  THE SPECTRUM AS THE NEWEST DOMAIN ..................................6  C.  A FULL...environment EMI electromagnetic interference EMS electromagnetic spectrum EMW electromagnetic maneuver warfare EP electronic protect ES electronic...warships’ electromagnetic systems to operate dynamically across the spectrum (Carter 2013). Bureaucratic and administrative spectrum allocations

  12. Linear and Branching Metrics for Quantitative Transition Systems

    NARCIS (Netherlands)

    de Alfaro, Luca; Faella, Marco; Stoelinga, Mariëlle Ida Antoinette

    2004-01-01

    We extend the basic system relations of trace inclusion, trace equivalence, simulation, and bisimulation to a quantitative setting in which propositions are interpreted not as boolean values, but as real values in the interval [0,1]. Trace inclusion and equivalence give rise to asymmetrical and

  13. Extending the COVAD toolbox to accommodate system non-linearities

    NARCIS (Netherlands)

    Bucco, D.; Weiss, M.

    2009-01-01

    The COVAD toolbox is a MATLAB/Simulink based tool conceived and developed for the rapid analysis and simulation of stochastically driven dynamic systems. In addition to a generic Monte Carlo capability, the toolbox is also supported by traditional analytical techniques such as the adjoint and

  14. Linear algebra

    CERN Document Server

    Shilov, Georgi E

    1977-01-01

    Covers determinants, linear spaces, systems of linear equations, linear functions of a vector argument, coordinate transformations, the canonical form of the matrix of a linear operator, bilinear and quadratic forms, Euclidean spaces, unitary spaces, quadratic forms in Euclidean and unitary spaces, finite-dimensional space. Problems with hints and answers.

  15. An energy analysis of a linear concentrating photovoltaic system with an active cooling system

    Science.gov (United States)

    Kerzmann, Tony L.; Schaefer, Laura A.

    2010-08-01

    The recent focus on renewable energy has lead to an increased awareness of solar energy. Concentrating photovoltaic systems have seen a resurgence in research interest since their earlier pilot plant origins in the 1970s and 1980s. The use of concentration reduces the amount of expensive photovoltaic materials while maintaining a high level of incident solar radiation. This research combines the advantage of concentrating solar energy with high efficiency multijunction cells and an active cooling system to create a system that efficiently produces both electricity and heat. A linear concentrating photovoltaic system model was developed in order to simulate the system under actual solar and climatic conditions, where a number of different system variables can be adjusted. This simulation was used to evaluate the effects of domestic hot water use on a 6.2 kWp system. The results show the changes in solar cell efficiency, electricity produced, thermal energy produced, dollar value displaced, and global warming potential displaced as the domestic hot water use of the system is varied. This simulation can be used to find an optimal system for given input conditions and can be used to find optimal operating conditions for a given system size.

  16. Krylov Subspace Methods for Complex Non-Hermitian Linear Systems. Thesis

    Science.gov (United States)

    Freund, Roland W.

    1991-01-01

    We consider Krylov subspace methods for the solution of large sparse linear systems Ax = b with complex non-Hermitian coefficient matrices. Such linear systems arise in important applications, such as inverse scattering, numerical solution of time-dependent Schrodinger equations, underwater acoustics, eddy current computations, numerical computations in quantum chromodynamics, and numerical conformal mapping. Typically, the resulting coefficient matrices A exhibit special structures, such as complex symmetry, or they are shifted Hermitian matrices. In this paper, we first describe a Krylov subspace approach with iterates defined by a quasi-minimal residual property, the QMR method, for solving general complex non-Hermitian linear systems. Then, we study special Krylov subspace methods designed for the two families of complex symmetric respectively shifted Hermitian linear systems. We also include some results concerning the obvious approach to general complex linear systems by solving equivalent real linear systems for the real and imaginary parts of x. Finally, numerical experiments for linear systems arising from the complex Helmholtz equation are reported.

  17. Non-linear and adaptive control of a refrigeration system

    DEFF Research Database (Denmark)

    Rasmussen, Henrik; Larsen, Lars F. S.

    2011-01-01

    are capable of adapting to variety of systems. This paper proposes a novel method for superheat and capacity control of refrigeration systems; namely by controlling the superheat by the compressor speed and capacity by the refrigerant flow. A new low order nonlinear model of the evaporator is developed......In a refrigeration process heat is absorbed in an evaporator by evaporating a flow of liquid refrigerant at low pressure and temperature. Controlling the evaporator inlet valve and the compressor in such a way that a high degree of liquid filling in the evaporator is obtained at all compressor...... capacities ensures a high energy efficiency. The level of liquid filling is indirectly measured by the superheat. Introduction of variable speed compressors and electronic expansion valves enables the use of more sophisticated control algorithms, giving a higher degree of performance and just as important...

  18. Portable linear-focused solar thermal energy collecting system

    Science.gov (United States)

    Miller, C. G.; Pohl, J. G. (Inventor)

    1977-01-01

    A solar heat collection system is provided by utilizing a line-focusing device that is effectively a cylindrically curved concentrator within a protected environment formed by a transparent inflatable casing. A target, such as a fluid or gas carrying conduit is positioned within or near the casing containing the concentrator, at the line focus of the concentrator. The casing can be inflated at the site of use by a low pressure air supply to form a unitary light weight structure. The collector, including casing, concentrator and target, is readily transportable and can be used either at ground level or on rooftops. The inflatable concentrator can be replaced with a rigid metal or other concentrator while maintaining the novel advantages of the whole solar heat collection system.

  19. Effective solution of a linear system with Chebyshev coefficients

    Czech Academy of Sciences Publication Activity Database

    Kujan, Petr; Hromčík, M.; Šebek, Michael

    2009-01-01

    Roč. 20, č. 8 (2009), s. 619-628 ISSN 1065-2469 R&D Projects: GA MŠk(CZ) 1M0567 Institutional research plan: CEZ:AV0Z10750506 Keywords : orthogonal Chebyshev polynomials * hypergeometric functions * optimal PWM problem Subject RIV: BC - Control Systems Theory Impact factor: 0.756, year: 2009 http://dx.doi.org/10.1080/10652460902727938

  20. Decentralized linear quadratic power system stabilizers for multi ...

    Indian Academy of Sciences (India)

    Now consider a single generator connected to the external system through a power transformer as shown in figure 1 (Gurunath & Sen 2010). The rotor angle with respect to the voltage Vs θs of the high voltage bus is defined as δs = δ − θs. The expressions for δs, Eq, id and iq are as follows (Gurunath & Sen 2010; Gurunath ...

  1. Static Linear Fresnel Lenses as LCPV System in a Greenhouse

    Science.gov (United States)

    Sonneveld, P. J.; Swinkels, G. L. A. M.; van Tuijl, B. A. J.; Janssen, H. J. J.; de Zwart, H. F.

    2011-12-01

    A low concentrating PV system with water cooling (LCPVT system) will result in electrical and thermal energy output from the solar energy excess entering a building or greenhouse. All the direct radiation could be converted, which corresponds to 75% of the incoming solar energy. This will significantly reduce the demand of cooling of the building. For an optimal performance it is beneficial to construct asymmetric roof elements with a steep inclination at the north side (the exact angle of course depends on the latitude of the building site). The Fresnel lens structure is oriented in upwards direction. In the current design, two of them are placed between an AR-coated double glass structure to prevent pollution and condensation on the lenses. Compared with a previous system, the number of lenses is reduced from 3 to 2 lenses, which reduces the costs of the system by limiting the number of receivers. By the upward facing of the lens structure, the focus quality is preserved over a much broader range of angles of incidence compared to a lens with downward facing structures. Each PMMA lens with a size of 1.20 m×1.60 m is composed of 12 `tiles' for easy production. The focal distance of the lens is 1,875 m and the concentration factor 50x. In most cases the focus line is thinner than 3 cm and the transmission is above 80%. The performance of these lenses with respect of the shape of the focal area and the position of the focal line has been analyzed with ray tracing techniques. From this analyses it was concluded that tracking of the receiver module is possible with two motors. One motor controls the distance between lens and receiver and one motor controls the translocation of the receivers parallel to the lens. The second conclusion was that the positions of the focal line are within the bounds of the greenhouse construction for almost the whole year. Only in winter, the focal line will be unreachable from time to time. A 480 m2 greenhouse with the LCPVT system

  2. Left Atrial Linear Ablation of Paroxysmal Atrial Fibrillation Guided by Three-dimensional Electroanatomical System

    DEFF Research Database (Denmark)

    Zhang, Dai-Fu; Li, Ying; Qi, Wei-Gang

    2005-01-01

    Objective To investigate the safety and efficacy of Left atrial linear ablation of paroxysmal atrial fibrillation guided by three-dimensional electroanatomical system. Methods 29 patients with paroxysmal atrial fibrillation in this study. A nonfluoroscopic mapping system was used to generate a 3D...... attacks unchanged. No pulmonary vein narrowing was observed. Conclusion Left atrial linear ablation of paroxysmal atrial fibrillation guided by three-dimensional electroanatomical system was safe and effective....

  3. Principle and analysis of a linear motor driving system for HTS levitation applications

    International Nuclear Information System (INIS)

    Jin, Jian X.; Guo, You G.; Zhu, Jian G.

    2007-01-01

    High temperature superconductor (HTS) high levitation force density with passive and self-stabilizing features allows a number of special applications to be developed. Linear motor driving systems are commonly required for those applications such as levitated transport systems. In this paper a prototype linear motor driving system with HTS is analyzed with calculation details including its magnetic fields and driving forces presented in the paper

  4. Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control.

    Science.gov (United States)

    Brunton, Steven L; Brunton, Bingni W; Proctor, Joshua L; Kutz, J Nathan

    2016-01-01

    In this wIn this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control.ork, we explore finite

  5. Linear hydraulic drive system for a Stirling engine

    Science.gov (United States)

    Walsh, Michael M.

    1984-02-21

    A hydraulic drive system operating from the periodic pressure wave produced by a Stirling engine along a first axis thereof and effecting transfer of power from the Stirling engine to a load apparatus therefor and wherein the movable, or working member of the load apparatus is reciprocatingly driven along an axis substantially at right angles to the first axis to achieve an arrangement of a Stirling engine and load apparatus assembly which is much shorter and the components of the load apparatus more readily accessible.

  6. Frequency Interval Cross Gramians for Linear and Bilinear Systems

    DEFF Research Database (Denmark)

    Jazlan, Ahmad; Sreeram, Victor; Shaker, Hamid Reza

    2017-01-01

    the frequency interval cross gramians are derived in order to be used to obtain information regarding controllability and observability within a single matrix. The advantage of the proposed method is that it is computationally more efficient compared to existing gramian-based techniques since only half...... of the number of equations need to be solved in order to obtain information regarding the controllability and observability of a system compared to existing techniques. Numerical examples are provided to demonstrate the computational efficiency of the proposed method which uses frequency interval cross gramians...

  7. A note on the time decay of solutions for the linearized Wigner-Poisson system

    KAUST Repository

    Gamba, Irene

    2009-01-01

    We consider the one-dimensional Wigner-Poisson system of plasma physics, linearized around a (spatially homogeneous) Lorentzian distribution and prove that the solution of the corresponding linearized problem decays to zero in time. We also give an explicit algebraic decay rate.

  8. Linear problems and Baecklund transformations for the Hirota-Ohta system

    International Nuclear Information System (INIS)

    Adler, V.E.; Postnikov, V.V.

    2011-01-01

    The auxiliary linear problems are presented for all discretization levels of the Hirota-Ohta system. The structure of these linear problems coincides essentially with the structure of Nonlinear Schroedinger hierarchy. The squared eigenfunction constraints are found which relate Hirota-Ohta and Kulish-Sklyanin vectorial NLS hierarchies.

  9. FAST modularization framework for wind turbine simulation: full-system linearization

    Science.gov (United States)

    Jonkman, J. M.; Jonkman, B. J.

    2016-09-01

    The wind engineering community relies on multiphysics engineering software to run nonlinear time-domain simulations e.g. for design-standards-based loads analysis. Although most physics involved in wind energy are nonlinear, linearization of the underlying nonlinear system equations is often advantageous to understand the system response and exploit well- established methods and tools for analyzing linear systems. This paper presents the development and verification of the new linearization functionality of the open-source engineering tool FAST v8 for land-based wind turbines, as well as the concepts and mathematical background needed to understand and apply it correctly.

  10. FAST Modularization Framework for Wind Turbine Simulation: Full-System Linearization: Preprint

    Energy Technology Data Exchange (ETDEWEB)

    Jonkman, Jason; Jonkman, Bonnie

    2016-11-01

    The wind engineering community relies on multiphysics engineering software to run nonlinear time-domain simulations e.g. for design-standards-based loads analysis. Although most physics involved in wind energy are nonlinear, linearization of the underlying nonlinear system equations is often advantageous to understand the system response and exploit well-established methods and tools for analyzing linear systems. This paper presents the development and verification of the new linearization functionality of the open-source engineering tool FAST v8 for land-based wind turbines, as well as the concepts and mathematical background needed to understand and apply it correctly.

  11. Modal cost analysis for linear matrix-second-order systems

    Science.gov (United States)

    Skelton, R. E.; Hughes, P. C.

    1980-01-01

    Reduced models and reduced controllers for systems governed by matrix-second-order differential equations are obtained by retaining those modes which make the largest contributions to quadratic control objectives. Such contributions, expressed in terms of modal data, used as mode truncation criteria, allow the statement of the specific control objectives to influence the early model reduction from very high order models which are available, for example, from finite element methods. The relative importance of damping, frequency, and eigenvector in the mode truncation decisions are made explicit for each of these control objectives: attitude control, vibration suppression and figure control. The paper also shows that using modal cost analysis (MCA) on the closed loop modes of the optimally controlled system allows the construction of reduced control policies which feedback only those closed loop modal coordinates which are most critical to the quadratic control performance criterion. In this way, the modes which should be controlled (and hence the modes which must be observable by choice of measurements), are deduced from truncations of the optimal controller.

  12. The Upper Bound for GMRES on Normal Tridiagonal Toeplitz Linear System

    Directory of Open Access Journals (Sweden)

    R. Doostaki∗

    2015-09-01

    Full Text Available The Generalized Minimal Residual method (GMRES is often used to solve a large and sparse system Ax = b. This paper establishes error bound for residuals of GMRES on solving an N × N normal tridiagonal Toeplitz linear system. This problem has been studied previously by Li [R.-C. Li, Convergence of CG and GMRES on a tridiagonal Toeplitz linear system, BIT 47 (3 (2007 577-599.], for two special right-hand sides b = e1, eN . Also, Li and Zhang [R.-C. Li, W. Zhang, The rate of convergence of GMRES on a tridiagonal Toeplitz linear system, Numer. Math. 112 (2009 267-293.] for non-symmetric matrix A, presented upper bound for GMRES residuals. But in this paper we establish the upper bound on normal tridiagonal Toeplitz linear systems for special right-hand sides b = b(lel, for 1  l  N

  13. Fuzzy Lyapunov Reinforcement Learning for Non Linear Systems.

    Science.gov (United States)

    Kumar, Abhishek; Sharma, Rajneesh

    2017-03-01

    We propose a fuzzy reinforcement learning (RL) based controller that generates a stable control action by lyapunov constraining fuzzy linguistic rules. In particular, we attempt at lyapunov constraining the consequent part of fuzzy rules in a fuzzy RL setup. Ours is a first attempt at designing a linguistic RL controller with lyapunov constrained fuzzy consequents to progressively learn a stable optimal policy. The proposed controller does not need system model or desired response and can effectively handle disturbances in continuous state-action space problems. Proposed controller has been employed on the benchmark Inverted Pendulum (IP) and Rotational/Translational Proof-Mass Actuator (RTAC) control problems (with and without disturbances). Simulation results and comparison against a) baseline fuzzy Q learning, b) Lyapunov theory based Actor-Critic, and c) Lyapunov theory based Markov game controller, elucidate stability and viability of the proposed control scheme. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

  14. Analysis of linear dynamic systems of low rank

    DEFF Research Database (Denmark)

    Reinikainen, S.P.; Aaljoki, K.; Høskuldsson, Agnar

    2005-01-01

    to carry out graphic analysis of the dynamic systems. It is shown how score vectors can display the low dimensional variation in data, the loading vectors display the correlation structure, and the transformation vectors how the variables generate the resulting variation in data; these graphic analysis......The objective of this paper is to show how the procedures of traditional chemometrics like stepwise evaluation of the model, graphic analysis of the latent structure, etc., can be applied to common modeling methods in chemical engineering like for instance Kalman filtering. Procedures of how...... have proven their importance in traditional chemometric methods. These graphics methods are important in supervising and controlling the process in light of the variation in data. The algorithms can provide with solutions of models having hundreds or thousands of variables. It is shown here how...

  15. Gravitational collapse and naked singularities

    Indian Academy of Sciences (India)

    We propose the concept of 'effective naked singularities', which will be quite helpful ... If a pressure gradient force is not sufficiently strong, a body can continue collapsing due to its self-gravity. This phenomenon is called gravitational collapse. .... approaches a self-similar solution, which is called a critical solution, and then it.

  16. Interval matrices: Regularity generates singularity

    Czech Academy of Sciences Publication Activity Database

    Rohn, Jiří; Shary, S.P.

    2018-01-01

    Roč. 540, 1 March (2018), s. 149-159 ISSN 0024-3795 Institutional support: RVO:67985807 Keywords : interval matrix * regularity * singularity * P-matrix * absolute value equation * diagonally singilarizable matrix Subject RIV: BA - General Mathematics Impact factor: 0.973, year: 2016

  17. Gravitational collapse and naked singularities

    Indian Academy of Sciences (India)

    Abstract. Gravitational collapse is one of the most striking phenomena in gravitational physics. The cosmic censorship conjecture has provided strong motivation for research in this field. In the absence of a general proof for censorship, many examples have been proposed, in which naked singularity is the outcome of ...

  18. Singularity: Raychaudhuri equation once again

    Indian Academy of Sciences (India)

    birth of the Universe in a Big Bang. Nothing could be happier and more persuasive than the observation verifying the prediction of theory. This gave rise to a general belief that singularities were inevitable in general relativity (GR) so long as the dynamics were governed by Einstein's equations and more over positive energy ...

  19. String theory and cosmological singularities

    Indian Academy of Sciences (India)

    of space and time needs revision near these singularities where quantum effects of gravity become important, it is still not clear what structure could replace space ..... The dimensionful parameter μ is a Lagrange multiplier which ensures that the total number of eigenvalues is fixed. 98. Pramana – J. Phys., Vol. 69, No. 1, July ...

  20. A polynomial approach for generating a monoparametric family of chaotic attractors via switched linear systems

    International Nuclear Information System (INIS)

    Aguirre-Hernández, B.; Campos-Cantón, E.; López-Renteria, J.A.; Díaz González, E.C.

    2015-01-01

    In this paper, we consider characteristic polynomials of n-dimensional systems that determine a segment of polynomials. One parameter is used to characterize this segment of polynomials in order to determine the maximal interval of dissipativity and unstability. Then we apply this result to the generation of a family of attractors based on a class of unstable dissipative systems (UDS) of type affine linear systems. This class of systems is comprised of switched linear systems yielding strange attractors. A family of these chaotic switched systems is determined by the maximal interval of perturbation of the matrix that governs the dynamics for still having scroll attractors