Dynamic NE Seeking for Multi-Integrator Networked Agents With Disturbance Rejection

Abstract

In this paper, we consider game problems played by (multi)-integrator agents, subject to external disturbances. We propose Nash equilibrium seeking dynamics based on gradientplay, augmented with a dynamic internal-model based component, which is a reduced-order observer of the disturbance. We consider single-, double-and extensions to multi-integrator agents, in a partial-information setting, where agents have only partial knowledge on the others' decisions over a network. The lack of global information is offset by each agent maintaining an estimate of the others' states, based on local communication with its neighbours. Each agent has an additional dynamic component that drives its estimates to the consensus subspace. In all cases, we show convergence to the Nash equilibrium irrespective of disturbances. Our proofs leverage input-to-state stability under strong monotonicity of the pseudo-gradient and Lipschitz continuity of the extended pseudo-gradient.

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

“…(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.…”

“…The authors of Reference 23 further investigated the Nash equilibrium seeking problem for aggregative games of Euler–Lagrange systems. In Reference 24, Nash equilibrium seeking algorithms were developed based on the gradient play technique for games played by multiintegrator agents subject to external disturbances. The works in References 22‐24 are applicable to address the game problems with second‐ or high‐order dynamics but still have the following limitations.…”

“…In Reference 24, Nash equilibrium seeking algorithms were developed based on the gradient play technique for games played by multiintegrator agents subject to external disturbances. The works in References 22‐24 are applicable to address the game problems with second‐ or high‐order dynamics but still have the following limitations. Nonlinear dynamics are not considered for the focused MASs. The developed seeking algorithms require full‐state measurements that are not available in many practical applications, especially for high‐order systems. The design of the seeking algorithms depends on the knowledge of the Laplacian matrix associated with the communication topology.…”

“…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.…”

“…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.…”