Non-zero sum differential game for stochastic Markovian jump systems with partially unknown transition probabilities

This paper focuses on the non-zero sum differential game problem for Markovian jump systems with partially unknown transition probabilities. Firstly, a suboptimal control problem is studied by the free-connection weighting matrix method, and then the non-zero sum differential game problem is investi...

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Bibliographic Details
Published in:Journal of the Franklin Institute 2021-10, Vol.358 (15), p.7528-7558
Main Authors: Zhang, Chengke, Li, Fangchao
Format: Article
Language:English
Subjects:
Cost function
Differential games
Equilibrium
Game theory
Linear matrix inequalities
Markov analysis
Mathematical analysis
Matrix
Stochastic models
Transition probabilities
Upper bounds
Zero sum games
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Summary:This paper focuses on the non-zero sum differential game problem for Markovian jump systems with partially unknown transition probabilities. Firstly, a suboptimal control problem is studied by the free-connection weighting matrix method, and then the non-zero sum differential game problem is investigated on this basis. Several sufficient conditions for the existence of ε-suboptimal control strategy and ε-suboptimal Nash equilibrium strategies are provided, and their explicit expressions are designed. Moreover, the precise form for the upper bound of the cost function is also given. To facilitate the calculation, all conditions are converted into the corresponding equivalent linear matrix inequalities or bilinear matrix inequalities form. Finally, two numerical examples are utilized to demonstrate the effectiveness of the main results.
ISSN:0016-0032
1879-2693
0016-0032
DOI:10.1016/j.jfranklin.2021.07.050