Distributed adaptive Nash equilibrium seeking and disturbance rejection for noncooperative games of high‐order nonlinear systems with input saturation and input delay

• Published in: International journal of robust and nonlinear control Vol. 31; no. 7; pp. 2827 - 2846
• Main Authors: Ai, Xiaolin, Wang, Long
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 10.05.2021
• Subjects: Adaptive algorithms; Equilibrium; external disturbances; Game theory; Games; input delay; input saturation; Multiagent systems; Nash equilibrium; Nonlinear systems; Saturation; Sliding mode control; State observers
• ISSN: 1049-8923; 1099-1239
• DOI: 10.1002/rnc.5418

This article aims to investigate Nash equilibrium seeking problems for noncooperative games played by high‐order nonlinear multiagent systems subject to input saturation, input delay, and external disturbances. Based on the gradient play technique, an adaptive Nash equilibrium seeking algorithm is designed in a distributed fashion via backstepping, where a fixed‐time sliding mode observer is used to tackle the problem of “explosion of terms.” In the proposed algorithm, an extended‐state observer and an adaptive distributed observer are included for state/disturbance estimates and information sharing, respectively. Detailed convergence results are presented by leveraging Lyapunov stability theory. Finally, the effectiveness of the proposed approach is numerically verified through simulation results.