Optimal control for discrete-time singular stochastic systems with input delay

Fan, Wenhui; Liang, Jinling; Wang, Feng

doi:10.1002/oca.2237

Cited by 10 publications

(2 citation statements)

References 32 publications

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“…As such, for the case in the absence of Markovian jumping parameters, some meaningful results have been addressed for stability of the SSS in [18]. It should be pointed out that, complicated features of the SSS may result in many difficulties for the stability analysis and numerical treatment of such systems [19], particularly when there is a need for their control [20, 21].…”

Section: Introductionmentioning

confidence: 99%

Observer‐based adaptive control of uncertain stochastic singular systems via integral sliding mode technique

Liu

Zhao

Gao

2017

IET Control Theory & Applications

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Section: Introductionmentioning

confidence: 99%

Observer‐based adaptive control of uncertain stochastic singular systems via integral sliding mode technique

Liu

Zhao

Gao

2017

IET Control Theory & Applications

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“…Generally, uncertain terms involved in stochastic systems are classified mainly into two types, namely, the state‐independent one known as the addictive noise and the state‐dependent one referred to as the multiplicative noise. For multiplicative noise, Wang and Wang discussed the finite horizon LQ optimal control problem for discrete descriptor systems with input delay by means of incremental analysis method and auxiliary functions. In view of descriptor systems with addictive noise, for square descriptor systems case, Dai firstly transformed the discrete‐time stochastic descriptor systems into the normal form via state augmentation, and then solved by utilizing standard results for nonsingular systems.…”

Section: Introductionmentioning

confidence: 99%

Singular Linear Quadratic Optimal Control Problem for Stochastic Nonregular Descriptor Systems

Wang

Liu

2017

Asian Journal of Control

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This paper is concerned with the singular linear quadratic (SLQ) optimal control problem for stochastic nonregular descriptor systems with time‐delay. By means of some reasonable assumptions and a series of equivalent transformations, the problem is finally transformed into a positive linear quadratic (LQ) problem for standard stochastic systems. Then dynamic programming principle is used to establish the solvability of the original problem, and the desired explicit presentation of the optimal controller is given in terms of matrix iterative form. The results due to Feng et al. are generalized and improved. As an application, a numerical example is presented to demonstrate the efficiency of the proposed approach.

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Optimal linear quadratic Gaussian control for discrete time‐varying system with simultaneous input delay and state/control‐dependent noises

Zhang

Liang

et al. 2020

Optim Control Appl Methods

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This article focuses on the problem of linear quadratic Gaussian (LQG) control for discrete time-varying system with input delay and state/control-dependent noises. When the state variables can be exactly observed, first, we obtain the maximum principle by applying the method of variation. Second, a nonhomogeneous relationship between the state and the costate is developed in virtue of the obtained maximum principle and the mathematical induction. It is noted that the nonhomogeneous relationship is the solution to the forward and backward stochastic difference equations (FBSDEs). Finally, based on the solution to the FBSDEs, a necessary and sufficient condition for the optimal LQG control is derived in terms of coupled Riccati equations. Moreover, the analytical expression of the optimal controller is presented. The derived results are applied in networked control systems with packet dropout. Numerical examples are shown to illustrate the effectiveness of the proposed algorithm. K E Y W O R D SLQG control, discrete time-varying system, input delay, state/control-dependent noises INTRODUCTIONThe optimal linear quadratic Gaussian (LQG) control problem has received considerable attentions. 1-4 Generally, the standard LQG model contains the additive Gaussian white noises that are not state/control dependent. 5,6 With the rapid development of networked control systems (NCSs), the optimal control has been applied in various fields, such as vehicle industry, building automation surveillance, and Internet-based teleoperation, 7-11 which makes the control system models be more complicated. Obviously, the standard LQG model has no longer been applicable to the practical applications. Hence, we focus on the study of the LQG control systems with both state/control-dependent noises and input delay. It is generally known that the packet dropout occurred in NCSs can be described by the state/control-dependent noises. On one hand, many references have been investigated for LQG control with state/control-dependent noises. [12][13][14][15][16][17][18] Joshi 12 presented a suboptimal controller by using the "enforced separation principle." For NCSs with any arbitrary packet-drop pattern, Gupta et al 13 investigated the optimal LQG control by decomposing the problem into a standard LQR state-feedback controller, along with an optimal encoder-decoder design. Sinopoli et al 14 modeled the arrival of both observations and control packets as stochastic Bernoulli processes to describe the packet dropout. Liang and Xu 15 studied 882

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Optimal control for discrete-time singular stochastic systems with input delay

Cited by 10 publications

References 32 publications

Observer‐based adaptive control of uncertain stochastic singular systems via integral sliding mode technique

Observer‐based adaptive control of uncertain stochastic singular systems via integral sliding mode technique

Singular Linear Quadratic Optimal Control Problem for Stochastic Nonregular Descriptor Systems

Optimal linear quadratic Gaussian control for discrete time‐varying system with simultaneous input delay and state/control‐dependent noises

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