Distributed Nash Equilibrium Seeking for Aggregative Games With Nonlinear Dynamics Under External Disturbances

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

“…Remark Assumptions 2 and 3 have been commonly used when solving distributed Nash equilibrium seeking problems for noncooperative games 18,19,22‐24 . According to theorem 3 in Reference 43, Assumptions 2 and 3 guarantee that the considered game has a unique Nash equilibrium.…”

“…(1) This article formulates a noncooperative game for high-order nonlinear systems, and thereby the considered problem can cover the existing works associated with first-order systems, [16][17][18][19] second-order systems, 22,23 and multiintegrator systems 24 as special cases. Moreover, the focused players are subject to input saturation, input delay and external disturbances, which renders the existing seeking algorithms not applicable to the considered problem.…”

“…In Reference 18, robust Nash equilibrium seeking problems were considered with the consideration of unmodeled dynamics and external disturbances. Thereafter, aggregative games with first‐order uncertain perturbed nonlinear dynamics were addressed in Reference 19 by a synthesis of the internal model principle and the average consensus technique. One common feature in the above works is that the focused MASs are restricted to be of first‐order dynamics.…”

“…Compared with the existing works, the superior advantages of this work contribute to the following aspects. This article formulates a noncooperative game for high‐order nonlinear systems, and thereby the considered problem can cover the existing works associated with first‐order systems, 16‐19 second‐order systems, 22,23 and multiintegrator systems 24 as special cases. Moreover, the focused players are subject to input saturation, input delay and external disturbances, which renders the existing seeking algorithms not applicable to the considered problem. With the aid of the ESO, the unmeasured states and the external disturbances are successfully reconstructed, and thereby the proposed Nash equilibrium seeking algorithm cancels the assumption in References 22‐24 that full‐state measurements are available for feedback. Compared with the algorithms determined by the communication topology in References 16‐19,22‐24, the proposed seeking strategy drops this drawback by integrating the ADO.…”

“…Compared with the algorithms determined by the communication topology in References 16‐19,22‐24, the proposed seeking strategy drops this drawback by integrating the ADO. This contributes to broadening its applications in distributed systems.…”