Closed-Loop Nash Equilibrium in the Class of Piecewise Constant Strategies in a Linear State Feedback Form for Stochastic LQ Games

In this paper, we examine a sampled-data Nash equilibrium strategy for a stochastic linear quadratic (LQ) differential game, in which admissible strategies are assumed to be constant on the interval between consecutive measurements. Our solution first involves transforming the problem into a linear...

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Bibliographic Details
Published in:Mathematics (Basel) 2021-11, Vol.9 (21), p.2713
Main Authors: Drăgan, Vasile, Ivanov, Ivan Ganchev, Popa, Ioan-Lucian, Bagdasar, Ovidiu
Format: Article
Language:English
Subjects:
Algorithms
Differential games
Dynamical systems
Equilibrium
equilibrium strategies
Game theory
Games
Mathematics
nash equilibria
Noise
Numerical analysis
optimal trajectories
Random variables
sampled-data controls
State feedback
stochastic LQ differential games
Stochastic systems
Strategy
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Summary:In this paper, we examine a sampled-data Nash equilibrium strategy for a stochastic linear quadratic (LQ) differential game, in which admissible strategies are assumed to be constant on the interval between consecutive measurements. Our solution first involves transforming the problem into a linear stochastic system with finite jumps. This allows us to obtain necessary and sufficient conditions assuring the existence of a sampled-data Nash equilibrium strategy, extending earlier results to a general context with more than two players. Furthermore, we provide a numerical algorithm for calculating the feedback matrices of the Nash equilibrium strategies. Finally, we illustrate the effectiveness of the proposed algorithm by two numerical examples. As both situations highlight a stabilization effect, this confirms the efficiency of our approach.
ISSN:2227-7390
2227-7390
DOI:10.3390/math9212713