A Stabilizing Controller for Jump Linear Gaussian Systems with Noisy State Observations

Pan, Guolin; Bar‐Shalom, Yaakov

doi:10.1016/s0947-3580(96)70047-x

Cited by 9 publications

(5 citation statements)

References 22 publications

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“…A lot of achievements have been made in jump linear quadratic (JLQ) control theory since the pioneering work on JLQ control [4]. For some representative work on this general topic, to name a few, we refer reader to References [5][6][7][8][9][10][11][12][13]. In the counterpart of H 1 control for systems with Markovian jump parameters, the results for both continuous-time and discrete-time systems have been obtained by de Souza and Fragoso [14].…”

Section: Introductionmentioning

confidence: 99%

Robust disturbance attenuation for discrete‐time active fault tolerant control systems with uncertainties

Shi

Boukas

Nguang

et al. 2003

Optim Control Appl Methods

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SUMMARYThe problems of stochastic stability and stochastic disturbance attenuation for a class of linear discretetime systems are considered in this paper. The system under study is a state space model possessing two Markovian jump parameters: one is failure process and another is failure detection and isolation scheme. A controller is designed to guarantee the stochastic stability and a disturbance attenuation level. Robustness problems for the above system with norm-bounded parameter uncertainties are also investigated. It is shown that the uncertain system can be robustly stochastically stabilized and have a robust disturbance attenuation level for all admissible perturbations if a set of coupled Riccati inequalities has solutions. A numerical example is given to show the potential of the proposed technique.

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Section: Introductionmentioning

confidence: 99%

Robust disturbance attenuation for discrete‐time active fault tolerant control systems with uncertainties

Shi

Boukas

Nguang

et al. 2003

Optim Control Appl Methods

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“…A lot of achievements have been made in jumping linear quadratic control theory; see [6-8, 10, 16-19], and [14,[25][26][27][28][29][30][31]. In [25], the problem of jumping linear quadratic control of a class of linear systems with discrete Markov processes which are not directly observable has been examined.…”

mentioning

confidence: 99%

“…In [25], the problem of jumping linear quadratic control of a class of linear systems with discrete Markov processes which are not directly observable has been examined. Discrete-time linear quadratic optimal control problems for infinite Markov jump parameter systems have been studied in [26]. Using averaging and aggregation techniques, in [27] the control design for large scale jump linear systems where the process admits strong and weak interactions has been studied.…”

mentioning

confidence: 99%

“…The issue of robust stability analysis and synthesis of Markovian jumping linear continuous-time systems has been investigated by [10] and [31]. Though linear Markovian jump systems have been extensively studied [14,[25][26][27][28][29][30][31], to the best of our knowledge, the filter design for nonlinear Markovian jump dynamical systems remains an open research area. Recently, there has been some attempt in this area; see [1] and [9].…”

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confidence: 99%

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ℋ ∞ Filter for Uncertain Markovian Jump Nonlinear Systems: An LMI Approach

Nguang

Assawinchaichote

Shi

2007

Circuits Syst Signal Process

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The paper addresses the problem of designing a robust filter for a class of uncertain Markovian jump nonlinear systems described by a Takagi-Sugeno fuzzy model with Markovian jumps. LMI-based sufficient conditions for the existence of a robust filter that guarantees the L 2 -gain from an exogenous input to an estimation error to be less than a prescribed value are derived. A tunnel diode circuit is used to illustrate the effectiveness of the proposed design techniques.

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“…Finally, we would like to emphasize that a number of important results were recently obtained in the theory of linear jump control systems (see [24], [45], [49], and [67], and the references therein). Most of these results were derived via an analysis of differential or algebraic Riccati-type equations which is possible only for systems with special "linear-quadratic" structure and unconstrained controls.…”

Section: Discussionmentioning

confidence: 94%

Control of singularly perturbed hybrid stochastic systems

Filar

Gaitsgory

Haurie

Proceedings of 35th IEEE Conference on Decision and Control

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Abstract-In this paper, we study a class of optimal stochastic control problems involving two different time scales. The fast mode of the system is represented by deterministic state equations whereas the slow mode of the system corresponds to a jump disturbance process. Under a fundamental "ergodicity" property for a class of "infinitesimal control systems" associated with the fast mode, we show that there exists a limit problem which provides a good approximation to the optimal control of the perturbed system. Both the finite-and infinite-discounted horizon cases are considered. We show how an approximate optimal control law can be constructed from the solution of the limit control problem. In the particular case where the infinitesimal control systems possess the so-called turnpike property, i.e., are characterized by the existence of global attractors, the limit control problem can be given an interpretation related to a decomposition approach.

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A Stabilizing Controller for Jump Linear Gaussian Systems with Noisy State Observations

Cited by 9 publications

References 22 publications

Robust disturbance attenuation for discrete‐time active fault tolerant control systems with uncertainties

Robust disturbance attenuation for discrete‐time active fault tolerant control systems with uncertainties

ℋ ∞ Filter for Uncertain Markovian Jump Nonlinear Systems: An LMI Approach

Control of singularly perturbed hybrid stochastic systems

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