Optimal control of stochastic singular affine systems with Markovian jumps

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...

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Bibliographic Details
Published inJournal of inequalities and applications Vol. 2022; no. 1; pp. 1 - 17
Main Authors Wang, Xin, Wang, Lisha, Liu, Yuxiang
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 23.05.2022
Springer Nature B.V
SpringerOpen
Subjects
Analysis
Applications of Mathematics
Control theory
Differential equations
Differential games
Leader-follower differential game
Markov jump systems
Mathematical analysis
Mathematics
Mathematics and Statistics
Noise
Optimal control
Riccati equation
Singular affine systems
91A23
93E03
60J27
Singular affine systems
34H05
Markov jump systems
Leader-follower differential game
34A09
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Summary: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 Itô’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.
ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-022-02804-1