Infinite horizon linear quadratic optimal control for discrete‐time stochastic systems

Huang, Yili; Zhang, Weihai; Zhang, Huanshui

doi:10.1002/asjc.61

Cited by 81 publications

(56 citation statements)

References 9 publications

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“…Furthermore, stochastic indefinite LQ problems with jumps in infinite time horizon and finite time horizon were, respectively, studied in 13, 14 . Discrete-time case was also studied in [15][16][17] . Among these, a central issue is solving corresponding SARE.…”

Section: Introductionmentioning

confidence: 99%

Discrete‐Time Indefinite Stochastic LQ Control via SDP and LMI Methods

Zhou

Zhang

2012

Journal of Applied Mathematics

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This paper studies a discrete-time stochastic LQ problem over an infinite time horizon with state-and control-dependent noises, whereas the weighting matrices in the cost function are allowed to be indefinite. We mainly use semidefinite programming SDP and its duality to treat corresponding problems. Several relations among stability, SDP complementary duality, the existence of the solution to stochastic algebraic Riccati equation SARE , and the optimality of LQ problem are established. We can test mean square stabilizability and solve SARE via SDP by LMIs method.

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Section: Introductionmentioning

confidence: 99%

Discrete‐Time Indefinite Stochastic LQ Control via SDP and LMI Methods

Zhou

Zhang

2012

Journal of Applied Mathematics

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“…P > In the same way, (25) has a close relation with the stability of system (18). See [18] and [20].…”

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confidence: 62%

“…Then by Lemma 3 in [18], ( ) A BK C DK + , + is stable. It is well known that a real symmetric solution P ∈ S n of GARE is called a feedback stabilizing solution [6], if (29) is asymptotically mean square stable with K defined in Lemma 3, i.e., ( )…”

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confidence: 97%

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Critical stability and stabilization of discrete-time stochastic systems and its applications

Sun

Zhang

2011

Int. J. Control Autom. Syst.

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In this paper, critical stability and critical stabilization for discrete stochastic systems with both state and control dependent noise are discussed via the spectrum technique. The Popov-BelevitchHautus (PBH) criterion for exact observability in a discrete version is presented. As applications, some interesting results on a class of generalized Lyapunov equations (GLE), unremovable spectra and discrete generalized algebraic Riccati equation (GARE) are obtained. Finally, the problem of assigning the spectra of discrete stochastic systems in a specified disk is considered and some numerical examples are given to demonstrate our results.

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“…This problem has been extensively treated on literature from the classical control, or model-based approach [6,8,21], unlike on the learning paradigm. Work on [11] uses neural networks for reducing calculus efforts on providing optimal control for the stochastic LQR, while other works focus on relaxing assumptions on the ARE under different scenarios, but still requiring knowledge of the system dynamics [5,22].…”

Section: Introductionmentioning

confidence: 99%

Stabilizing Dynamic State Feedback Controller Synthesis: A Reinforcement Learning Approach

Solís

Olivares

Allende

2016

SIC

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State feedback controllers are appealing due to their structural simplicity. Nevertheless, when stabilizing a given plant, dynamics of this type of controllers could lead the static feedback gain to take higher values than desired. On the other hand, a dynamic state feedback controller is capable of achieving the same or even better performance by introducing additional parameters into the model to be designed. In this document, the Linear Quadratic Tracking problem will be tackled using a (linear) dynamic state feedback controller, whose parameters will be chosen by means of applying reinforcement learning techniques, which have been proved to be especially useful when the model of the plant to be controlled is unknown or inaccurate.

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Infinite horizon linear quadratic optimal control for discrete‐time stochastic systems

Cited by 81 publications

References 9 publications

Discrete‐Time Indefinite Stochastic LQ Control via SDP and LMI Methods

Discrete‐Time Indefinite Stochastic LQ Control via SDP and LMI Methods

Critical stability and stabilization of discrete-time stochastic systems and its applications

Stabilizing Dynamic State Feedback Controller Synthesis: A Reinforcement Learning Approach

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