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Conservatism reduction in simultaneous output feedback stabilisation of linear systems

IET CONTROL THEORY AND APPLICATIONS 2016年第17期10卷 2243-2250页

作者： Kohan-Sedgh, Peyman Khayatian, Alireza Asemani, Mohammad H. Shiraz Univ Dept Elect Engn Shiraz Iran

This study concerns with simultaneous output feedback stabiliser for continuous-time linear systems. Two convex methods based on structured slack variable and dilated matrix inequalities are proposed. Both methods are based on non-common Lyapunov approach and designs are independent of controller order. Sufficiency of the first method decreases with increasing the number of system inputs. The second method, namely the dilated method, contains free scalar parameters. These parameters can be used to shape the controller for some performance objectives. In particular, it is proved that the dilated method can give less or at least the same conservative results than existing methods with equality constraints. It is also shown that the feasibility region of these two methods does not coincide and thus combining them can increase the chance of finding simultaneous stabiliser. Extensive numerical studies and benchmark examples are used to reveal the conservatism reduction merit.

关键词： linear systems continuous time systems stability Lyapunov methods simultaneous output feedback stabilisation continuous-time linear systems convex methods structured slack variable dilated matrix inequalities noncommon Lyapunov approach controller order dilated method free scalar parameters conservatism reduction merit

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Optimal guaranteed cost for singular linear systems with random abrupt changes

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OPTIMAL CONTROL APPLICATIONS & METHODS 2010年第4期31卷 335-349页

作者： Boukas, El-Kebir Ecole Polytech Dept Mech Engn Montreal PQ H3C 3A7 Canada

This paper considers the class of continuous-time singular linear Markovian jump systems with totally and partially known transition jump rates. The guaranteed cost control problem of this class of systems is tackled. New sufficient conditions for optimal guaranteed cost are developed A design procedure for the guaranteed cost controller, which guarantees that the closed-loop dynamics will be piecewise regular, impulse-free and stochastically stable is proposed. It is shown that the addressed problem can be solved if the corresponding developed linear matrix inequalities (LMIts) with some constraints are feasible. A numerical example is employed to show the usefulness of the proposed results. Copyright CD (C) 2009 John Wiley & Sons, Ltd

关键词： singular systems descriptor systems continuous-time linear systems linear matrix inequality (LMI) stochastic stability guaranteed cost state feedback controller

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On Parametrization of All the Exact Pole-Assignment State-Feedbacks for LTI systems

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2017年第7期62卷 3436-3441页

作者： Peretz, Y. Jerusalem Coll Technol Lev Acad Ctr Dept Comp Sci POB 16031 Jerusalem Israel

In this technical note, we provide a parametrization of all the exact pole-assignment state-feedbacks for LTI systems, when the set of poles to be assigned contains sufficient number of real eigenvalues. We also refute a recent conjecture concerning the explicit form of all the state-feedbacks assigning a given set of poles to the closed-loop.

关键词： continuous-time linear systems discrete-time linear systems state-space representation feedback stability state feedbacks pole-assignment problem

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Distributed H_∞ filtering over sensor networks with heterogeneous Markovian coupling intercommunication delays

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IET CONTROL THEORY AND APPLICATIONS 2015年第1期9卷 82-90页

作者： Ge, Xiaohua Han, Qing-Long Jiang, Xiefu Cent Queensland Univ Ctr Intelligent & Networked Syst Rockhampton Qld 4702 Australia Griffith Univ Griffith Sch Engn Brisbane Qld 4222 Australia Hangzhou Dianzi Univ Sch Automat Hangzhou 310018 Zhejiang Peoples R China

This study is concerned with distributed H filtering for continuous-time linear systems over sensor networks with heterogeneous Markovian coupling intercommunication delays. The set of sensor nodes forms a sensing and communication network whose topology is modelled by a directed graph that describes the measurement exchanged among neighbouring sensor nodes. Heterogeneous random coupling delays modelled by a Markov process are considered in the intercommunication between interacting sensor nodes. A refined two-step decoupling technique is presented to deal with the complicated coupling of exchanged measurement in the presence of the delays. A sufficient condition on the existence of desired distributed H filters is derived such that the resultant filtering error system is mean square exponentially stable with prescribed weighting average H performance. Two illustrative examples are given to show the effectiveness of the proposed results.

关键词： H filters filtering theory distributed sensors delays Markov processes asymptotic stability linear systems continuous time systems distributed parameter systems distributed H filtering sensor networks heterogeneous Markovian coupling intercommunication delays continuous-time linear systems sensing network communication network neighbouring sensor nodes directed graph heterogeneous random coupling delays Markov process refined two-step decoupling technique resultant filtering error system mean square exponential stability weighting average H performance

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The Kleinman iteration for nonstabilizable systems

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MATHEMATICS OF CONTROL SIGNALS AND systems 2003年第1期16卷 76-93页

作者： Benner, P Hernández, V Pastor, A Tech Univ Berlin Fak Math & Nat Wissensch 2 Inst Math D-10623 Berlin Germany Univ Politecn Valencia Dept Sistemas Informat & Computac E-46071 Valencia Spain Univ Politecn Valencia Dept Matemat Aplicada E-46071 Valencia Spain

We consider the computation of Hermitian nonnegative definite solutions of algebraic Riccati equations. These solutions are the limit, P = lim(i -->infinity) P-i, of a sequence of matrices obtained by solving a sequence of Lyapunov equations. The procedure parallels the well-known Kleinman technique but the stabilizability condition on the underlying linear time-invariant system is removed. The convergence of the constructed sequence {P-i }(igreater than or equal to1) is guaranteed by the minimality of P-i in the set of Hermitian nonnegative definite solutions of the Lyapunov equation in the ith iteration step.

关键词： algebraic Riccati equation Newton's method Kleinman iteration Lyapunov equation continuous-time linear systems nonstabilizable systems linear-quadratic optimal control

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A New Optimal Tracking Controller of linear Strongly Coupled systems and Its Applications

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IEEE TRANSACTIONS ON CIRCUITS AND systems II-EXPRESS BRIEFS 2022年第3期69卷 1387-1391页

作者： Fu, Yue Chen, Wei Fu, Jun Northeastern Univ State Key Lab Synthet Automat Proc Ind Shenyang 110004 Peoples R China

In this brief, for a class of continuous-time multivariable linear systems with strong coupling property, a new optimal tracking controller is proposed, which can simultaneously decouple the closed-loop system in its dynamic, and provide optimal performance. Firstly, a new quadratic performance index considering decoupling design is introduced, and then the optimal tracking controller is derived by minimizing the new index according to the minimum principle. Finally, the weighting matrices are provided, by using which decoupling and tracking can both be realized. Experiments on a Coupled-Tank are conducted, whose results show the superiority of the proposed method comparing with the conventional linear quadratic tracking (LQT) controller.

关键词： Couplings Matrices Closed loop systems Adaptive systems Performance analysis Transfer functions Tracking loops Optimal tracking control continuous-time linear systems multivariable systems

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H-CONTROLLABILITY AND OBSERVABILITY OF linear PERIODIC-systems

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SIAM JOURNAL ON CONTROL AND OPTIMIZATION 1984年第6期22卷 889-893页

作者： BITTANTI, S COLANERI, P GUARDABASSI, G Politecnico di Milano Dipartimento di Elettronica Milan Italy Politecnico di Milano Dipartimento di Elettronica Milan Italy

With reference to linear periodic systems, the classical notion of controllability introduced by Kalman (K-controllability) is shown to be equivalent to the characterization of controllability (H-controllability) first proposed by Hewer as a natural extension to the periodic case of an eigenvalue-eigenvector controllability condition independently introduced by several authors for time-invariant systems only. The proof of such an equivalence also leads to the conclusion that if a T-periodic system S is K-controllable and k is the degree of the minimal polynomial of the monodromy matrix associated with S, then, at any time t, S is controllable over $(t,t + kT)$. Since k is lower than or equal to the system order, a well-known result due to Brunovsky is slightly strengthened. By duality, the corresponding observability results follow.

关键词： continuous-time linear systems periodic systems controllability and observability modal controllability conditions periodic Riccati equation

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On the poles and zeros of linear, time-varying systems

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IEEE TRANSACTIONS ON CIRCUITS AND systems I-REGULAR PAPERS 2001年第5期48卷 565-577页

作者： O'Brien, RT Iglesias, PA USN Acad Dept Syst Engn Annapolis MD 21402 USA Johns Hopkins Univ Dept Elect & Comp Engn Baltimore MD 21218 USA

Definition of poles and zeros are presented for continuous-time, linear, time-varying systems. For a linear, time-varying state equation, a set of time-varying poles defines a stability-preserving variable change relating the original state equation to an upper triangular state equation, A zero is a function of time corresponding to an exponential input whose transmission to the output is blocked. Both definitions are shown to be generalizations of existing definitions of poles and zeros for linear, time-varying systems and are consistent with the definitions for linear, time-invariant systems. A computation procedure is presented using a QR decomposition of the transition matrix for the state equation. A numerical example is given to illustrate this procedure.

关键词： continuous time systems linear systems matrix decomposition poles and zeros stability time-varying systems QR decomposition blocked transmission computation procedure continuous-time linear systems exponential input linear time-varying state equation lin Poles and zeros Pole equations of state Zero Packet transmission continuous time systems linear time-varying system matrix decomposition time-varying systems linear system S matrix

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Model-Free Solution for Inverse linear-Quadratic Nonzero-Sum Differential Games

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IEEE CONTROL systems LETTERS 2024年 8卷 2445-2450页

作者： Martirosyan, Emin Cao, Ming Univ Groningen Fac Sci & Engn ENTEG Groningen Netherlands

This letter addresses the inverse problem for linear-Quadratic (LQ) nonzero-sum N-player differential games, where the goal is to learn cost function parameters such that the given tuple of feedback laws, which is known to stabilize a linear system, is a Nash equilibrium (NE) for the synthesized game. We show a model-free algorithm that can accomplish this task using the given feedback laws and the system matrices. The algorithm makes extensive use of gradient descent optimization that allow to find the solution to the inverse problem without solving the forward problem. To further illustrate possible solution characterization, we show how to generate an infinite number of equivalent games without repeatedly running the complete algorithm. Simulation results demonstrate the effectiveness of the proposed algorithms.

关键词： Games Cost function Inverse problems Differential games Symmetric matrices Nash equilibrium linear systems Heuristic algorithms System dynamics Matrix converters Inverse differential game inverse optimal control continuous-time linear systems

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continuous-time linear Parallel Control

Continuous-Time Linear Parallel Control

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Chinese Automation Congress (CAC)

作者： Wei, Qinglai Li, Hongyang Wang, Fei-Yue Chinese Acad Sci Inst Automat State Key Lab Management & Control Complex Syst Beijing Peoples R China

ISBN: (纸本)9781728176871

This paper presents a continuous-time linear parallel control by modeling the derivative of system control with respect to time. The framework and properties of continuous-time linear parallel control are first presented. Then, considering the controllability, the pole assignment theorems will be analyzed. Finally, two examples show the correctness of continuous-time linear parallel control.

关键词： Parallel controller parallel systems parallel systems theory continuous-time linear systems

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