@article{Wang2025, 
author = {Li Wang and Xiushan Jiang and Dongya Zhao and Bor-Sen Chen},
title = {Multiplayer Pareto optimal control with H∞ constraint for nonlinear stochastic system via online synchronous reinforcement learning},
year = {2025},
journal = {Journal of Automation and Intelligence},
volume = {4},
number = {3},
pages = {207-216},
keywords = {Pareto control, Nonlinear stochastic system, Hamilton–Jacobi equations, H∞ control, Reinforcement learning},
url = {https://www.sciopen.com/article/10.1016/j.jai.2025.05.004},
doi = {10.1016/j.jai.2025.05.004},
abstract = {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 H2/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.}
}