Error variance-constrained ℋ<sub>∞</sub>filtering for a class of nonlinear stochastic systems with degraded measurements: the finite horizon case

Ma, Lifeng; Bo, Yuming; Zhou, Yuchen; Guo, Zhi

doi:10.1080/00207721.2011.577249

Cited by 12 publications

(9 citation statements)

References 20 publications

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“…We concentrate our attention on the finite horizon indefinite stochastic LQ control with terminal inequality constraint. Such constraints are often seen in ∞ filtering problems [23,24]. The existence of optimal linear state feedback control in terms of KKT theorem will be shown.…”

Section: Introductionmentioning

confidence: 94%

Stochastic Linear Quadratic Optimal Control with Indefinite Control Weights and Constraint for Discrete-Time Systems

Liu

2015

Mathematical Problems in Engineering

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The Karush-Kuhn-Tucker (KKT) theorem is used to study stochastic linear quadratic optimal control with terminal constraint for discrete-time systems, allowing the control weighting matrices in the cost to be indefinite. A generalized difference Riccati equation is derived, which is different from those without constraint case. It is proved that the well-posedness and the attainability of stochastic linear quadratic optimal control problem are equivalent. Moreover, an optimal control can be denoted by the solution of the generalized difference Riccati equation.

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Section: Introductionmentioning

confidence: 94%

Stochastic Linear Quadratic Optimal Control with Indefinite Control Weights and Constraint for Discrete-Time Systems

Liu

2015

Mathematical Problems in Engineering

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“…It should be emphasized that, for nonlinearities, there are many different constraints conditions for certain aim, such as Lipschitz conditions, among which the kind of stochastic nonlinearities described by statistical means has drawn particular research focus since it covers several wellstudied nonlinearities in stochastic systems; see [29,[32][33][34][35] and the references therein. Several techniques for analysis and synthesis of this type of nonlinear systems have been exploited, including linear matrix inequality approach [32], Riccati equation method [33], recursive matrix inequality approach [34], gradient method [35], sliding mode control scheme [36], and the game theory approach [29].…”

Section: Nonlinear Systemsmentioning

confidence: 99%

Variance-Constrained Multiobjective Control and Filtering for Nonlinear Stochastic Systems: A Survey

Wang

Dong

et al. 2013

Abstract and Applied Analysis

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The multiobjective control and filtering problems for nonlinear stochastic systems with variance constraints are surveyed. First, the concepts of nonlinear stochastic systems are recalled along with the introduction of some recent advances. Then, the covariance control theory, which serves as a practical method for multi-objective control design as well as a foundation for linear system theory, is reviewed comprehensively. The multiple design requirements frequently applied in engineering practice for the use of evaluating system performances are introduced, including robustness, reliability, and dissipativity. Several design techniques suitable for the multi-objective variance-constrained control and filtering problems for nonlinear stochastic systems are discussed. In particular, as a special case for the multi-objective design problems, the mixedH2/H∞control and filtering problems are reviewed in great detail. Subsequently, some latest results on the variance-constrained multi-objective control and filtering problems for the nonlinear stochastic systems are summarized. Finally, conclusions are drawn, and several possible future research directions are pointed out.

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“…In this paper, we focus our attention on the finite horizon indefinite stochastic linear quadratic control with Markovian jumps and terminal inequality constraint. There are homologous constraints in H ∞ filtering problems [1,2]. The summary of this paper is arranged as follows.…”

Section: Introductionmentioning

confidence: 99%

Stochastic Linear Quadratic Optimal Control for Discrete-time Systems with Inequality Constraint and Markovian Jumps

Wang¹,

Zhang²,

Miao³

2015

Proceedings of the 2015 4th International Conference on Computer, Mechatronics, Control and Electronic Engineering

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This paper primarily discusses the linear quadratic optimal control problem for discrete-time stochastic systems with indefinite control weights and constraint and Markovian jumps. We use the Karush-Kuhn-tucker (KKT) theorem basically in this paper. It is testified that the well-posedness and the attainability are equivalent about the stochastic linear quadratic optimal control problem with Markovian jumps. Furthermore, the solution of the generalized difference Riccati equation (GDRE) can indicate an optimal control.

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Error variance-constrained ℋ_∞filtering for a class of nonlinear stochastic systems with degraded measurements: the finite horizon case

Cited by 12 publications

References 20 publications

Stochastic Linear Quadratic Optimal Control with Indefinite Control Weights and Constraint for Discrete-Time Systems

Stochastic Linear Quadratic Optimal Control with Indefinite Control Weights and Constraint for Discrete-Time Systems

Variance-Constrained Multiobjective Control and Filtering for Nonlinear Stochastic Systems: A Survey

Stochastic Linear Quadratic Optimal Control for Discrete-time Systems with Inequality Constraint and Markovian Jumps

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Error variance-constrained ℋ∞filtering for a class of nonlinear stochastic systems with degraded measurements: the finite horizon case

Cited by 12 publications

References 20 publications

Stochastic Linear Quadratic Optimal Control with Indefinite Control Weights and Constraint for Discrete-Time Systems

Stochastic Linear Quadratic Optimal Control with Indefinite Control Weights and Constraint for Discrete-Time Systems

Variance-Constrained Multiobjective Control and Filtering for Nonlinear Stochastic Systems: A Survey

Stochastic Linear Quadratic Optimal Control for Discrete-time Systems with Inequality Constraint and Markovian Jumps

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Error variance-constrained ℋ_∞filtering for a class of nonlinear stochastic systems with degraded measurements: the finite horizon case