Dynamic Gradient Play for NE Seeking with Disturbance Rejection

Abstract

In this paper, we propose a control theoretic framework for game problems subject to external disturbances. We consider two cases: the classical setting with full information on the others' decisions, and the partial-decision information setting. The proposed agent dynamics has two components: a gradient-play component and a dynamic internal-model one, which is a reduced-order observer of the disturbance. In the case of partial-information, there is an additional component that drives agents to reach the consensus subspace, where all decision estimates are the same. In both cases, we prove that agents' dynamics converge to the Nash equilibrium, irrespective of the disturbance. Our proofs rely on input-to-state stability properties, under strong monotonicity of the pseudo-gradient and Lipschitz continuity of the extended pseudo-gradient.