This paper investigates a multiplayer Pareto game for affine nonlinear stochastic systems disturbed by both external and the internal multiplicative noises.The Pareto cooperative optimal strategies with the H_(∞) con...This paper investigates a multiplayer Pareto game for affine nonlinear stochastic systems disturbed by both external and the internal multiplicative noises.The Pareto cooperative optimal strategies with the H_(∞) constraint are resolved by integrating H_(2)/H_(∞) theory with Pareto game theory.First,a nonlinear stochastic bounded real lemma(SBRL)is derived,explicitly accounting for non-zero initial conditions.Through the analysis of four cross-coupled Hamilton-Jacobi equations(HJEs),we establish necessary and sufficient conditions for the existence of Pareto optimal strategies with the H_(∞) constraint.Secondly,to address the complexity of solving these nonlinear partial differential HJEs,we propose a neural network(NN)framework with synchronous tuning rules for the actor,critic,and disturbance components,based on a reinforcement learning(RL)approach.The designed tuning rules ensure convergence of the actor-critic-disturbance components to the desired values,enabling the realization of robust Pareto control strategies.The convergence of the proposed algorithm is rigorously analyzed using a constructed Lyapunov function for the NN weight errors.Finally,a numerical simulation example is provided to demonstrate the effectiveness of the proposed methods and main results.展开更多
基金supported by the National Natural Science Foundation of China(12426609,62203220,62373229)the Taishan Scholar Project Foundation of Shandong Province(tsqnz20230619,tsqn202408110)+2 种基金the Fundamental Research Foundation of the Central Universities(23Cx06024A)the Natural Science Foundation of Shandong Province(ZR2024QF096)the Outstanding Youth Innovation Team in Shandong Higher Education Institutions(2023KJ061).
文摘This paper investigates a multiplayer Pareto game for affine nonlinear stochastic systems disturbed by both external and the internal multiplicative noises.The Pareto cooperative optimal strategies with the H_(∞) constraint are resolved by integrating H_(2)/H_(∞) theory with Pareto game theory.First,a nonlinear stochastic bounded real lemma(SBRL)is derived,explicitly accounting for non-zero initial conditions.Through the analysis of four cross-coupled Hamilton-Jacobi equations(HJEs),we establish necessary and sufficient conditions for the existence of Pareto optimal strategies with the H_(∞) constraint.Secondly,to address the complexity of solving these nonlinear partial differential HJEs,we propose a neural network(NN)framework with synchronous tuning rules for the actor,critic,and disturbance components,based on a reinforcement learning(RL)approach.The designed tuning rules ensure convergence of the actor-critic-disturbance components to the desired values,enabling the realization of robust Pareto control strategies.The convergence of the proposed algorithm is rigorously analyzed using a constructed Lyapunov function for the NN weight errors.Finally,a numerical simulation example is provided to demonstrate the effectiveness of the proposed methods and main results.
基金Supported by the National Natural Science Foundation of China under Grant Nos.60473037,60483081,40275034,60204001,60133010(国家自然科学基金)the China Postdoctoral Science Foundation under Grant No.2003034505(中国博士后科学基金)the open research program of the Geological Processes and Mineral Resources(GPMR),China University of Geosciences under Grant No.GPMR200618(中国地质大学地质过程与矿产资源国家重点实验室开放课题)
