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Stochastic adaptive linear quadratic nonzero-sum differential games

Author

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  • Tian, Xiu-Qin
  • Liu, Shu-Jun
  • Yang, Xue

Abstract

This paper focuses on solving stochastic linear quadratic nonzero-sum differential games with completely unknown system matrices and long-time average costs. Firstly, for the case that the system matrices are known, we design a model-based value iteration (VI) algorithm and a model-based robust VI algorithm to solve the coupled algebraic Riccati equations (AREs), which are directly related to the construction of the feedback Nash equilibrium solution. Then, we present a model-free VI algorithm, based on which feedback control strategies for players are designed using only the data of states and inputs, without requiring the prior knowledge of the system matrices. Moreover, we show that the designed feedback control strategies make the closed-loop game system stable and reach the Nash equilibrium. Finally, a numerical simulation is given to demonstrate the effectiveness of the proposed method.

Suggested Citation

  • Tian, Xiu-Qin & Liu, Shu-Jun & Yang, Xue, 2024. "Stochastic adaptive linear quadratic nonzero-sum differential games," Applied Mathematics and Computation, Elsevier, vol. 477(C).
    • Handle: RePEc:eee:apmaco:v:477:y:2024:i:c:s0096300324002649
    DOI: 10.1016/j.amc.2024.128803
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    References listed on IDEAS

    as
    1. Sun, Zhongshi & Jia, Guangyan, 2023. "Reinforcement learning for exploratory linear-quadratic two-person zero-sum stochastic differential games," Applied Mathematics and Computation, Elsevier, vol. 442(C).
    2. Liu, Xikui & Ge, Yingying & Li, Yan, 2019. "Stackelberg games for model-free continuous-time stochastic systems based on adaptive dynamic programming," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.
    3. Xin, Xilin & Tu, Yidong & Stojanovic, Vladimir & Wang, Hai & Shi, Kaibo & He, Shuping & Pan, Tianhong, 2022. "Online reinforcement learning multiplayer non-zero sum games of continuous-time Markov jump linear systems," Applied Mathematics and Computation, Elsevier, vol. 412(C).
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