Optimal control of stochastic singular affine systems with Markovian jumps

被引：0

作者：

Wang, Xin ^{[1
]}

Wang, Lisha ^{[1
]}

Liu, Yuxiang ^{[1
]}

机构：

[1] Qingdao Univ Technol, Sch Sci, Qingdao 266000, Shandong, Peoples R China

来源：

JOURNAL OF INEQUALITIES AND APPLICATIONS | 2022年 / 2022卷 / 01期

关键词：

Singular affine systems; Markov jump systems; Leader-follower differential game; LINEAR-QUADRATIC CONTROL; ASYMPTOTIC STABILITY; RICCATI-EQUATIONS;

D O I：

10.1186/s13660-022-02804-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider an optimal control problem for a class of stochastic singular affine systems with Markovian jumps. We establish the existence and uniqueness of the solution to stochastic singular affine systems with Markovian jumps for the first time. Via square completion technique and the generalized Ito's formula, we derive new kinds of generalized differential Riccati equations (GDREs) and generalized backward differential equations (GBDEs), which give sufficient conditions for the well-posedness of the optimal control problem, and present an explicit representation of optimal control. Also, we discuss the solvability of the GDREs in two cases. As an application, we present a leader-follower differential game to demonstrate the practicability of our results.

引用

页数：17

共 24 条

[11]

Mariton M, 1990, Jump Linear Systems in Automatic Control

[12] LMI optimization for nonstandard Riccati equations arising in stochastic control [J].

Rami, MA ;

ElGhaoui, L .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1996, 41 (11) :1666-1671

[13] Indefinite stochastic linear quadratic control and generalized differential Riccati equation [J].

Rami, MA ;

Moore, JB ;

Zhou, XY .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2001, 40 (04) :1296-1311

[14] Linear matrix inequalities, Riccati equations, and indefinite stochastic linear quadratic controls [J].

Rami, MA ;

Zhou, XY .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2000, 45 (06) :1131-1143

[15] OPEN-LOOP AND CLOSED-LOOP SOLVABILITIES FOR STOCHASTIC LINEAR QUADRATIC OPTIMAL CONTROL PROBLEMS [J].

Sun, Jingrui ;

Li, Xun ;

Yong, Jiongmin .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2016, 54 (05) :2274-2308

[16] Qualitative Analyses of Differential Systems with Time-Varying Delays via Lyapunov-Krasovskii Approach [J].

Tunc, Cemil ;

Tunc, Osman ;

Wang, Yuanheng ;

Yao, Jen-Chih .

MATHEMATICS, 2021, 9 (11)

[17] On the asymptotic stability of solutions of stochastic differential delay equations of second order [J].

Tunc, Osman ;

Tunc, Cemil .

JOURNAL OF TAIBAH UNIVERSITY FOR SCIENCE, 2019, 13 (01) :875-882

[18]

Wang X., OPTIMAL CONTROL STOC

[19] A DESCRIPTOR-SYSTEM APPROACH TO SINGULAR PERTURBATION OF LINEAR REGULATORS [J].

WANG, YY ;

SHI, SJ ;

ZHANG, ZJ .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1988, 33 (04) :370-373

[20]

Wiener Norbert, 1948, CYBERNETICS CONTROL

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