Fully Distributed Robust Adaptive Nash Equilibrium Seeking of High-Order Uncertain Nonlinear Systems
针对高阶非线性多智能体系统，提出了一种完全分布式的鲁棒自适应纳什均衡搜索策略，通过引入辅助系统和反步控制器，使所有智能体的动作指数收敛到纳什均衡，并进一步设计了基于输出反馈的自适应策略。
This article investigates fully distributed robust adaptive Nash equilibrium (NE) seeking strategies in noncooperative games. Different from existing NE seeking results, this article considers high-order nonlinear multiagent systems (MASs) with mismatched uncertainties and disturbances. To deal with the challenges brought by the high-order structure, a new auxiliary system is first introduced based on the gradient play rule to generate a reference trajectory, which converges to the NE exponentially without requiring any global graph information. Then, a backstepping-based robust adaptive controller is developed for each agent to exponentially track the reference trajectory. By resorting to the Lyapunov stability theory, the developed robust seeking strategies drive all agents’ actions to the NE exponentially. Moreover, considering the circumstance that only the information of the agent’s action is available for control law design, an adaptive output-feedback NE seeking strategy is further developed by constructing <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i>-filters to estimate the immeasurable states. Finally, the effectiveness of the two proposed NE seeking algorithms are verified by different simulation examples.