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

[21]

Yong J., 1999, Stochastic Controls: Hamiltonian Systems and HJB Equations, DOI [DOI 10.1007/978-1-4612-1466-3, 10.1007/978-1-4612-1466-3]

[22] On nearly optimal controls of hybrid LQG problems [J].

Zhang, Q ;

Yin, GG .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1999, 44 (12) :2271-2282

[23] Stability analysis and optimal control of stochastic singular systems [J].

Zhang, Qingling ;

Xing, Shuangyun .

OPTIMIZATION LETTERS, 2014, 8 (06) :1905-1920

[24] Linear quadratic Pareto optimal control problem of stochastic singular systems [J].

Zhang, Weihai ;

Lin, Yaning ;

Xue, Lingrong .

JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS, 2017, 354 (02) :1220-1238

← 1 2 3 →