Fully Distributed Robust Adaptive Nash Equilibrium Seeking of High-Order Uncertain Nonlinear Systems

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.