On Resilience Against Cyber-Physical Uncertainties in Distributed Nash Equilibrium Seeking Strategies for Heterogeneous Games

Abstract

This paper designs distributed Nash equilibrium seeking strategies for heterogeneous dynamic cyber-physical systems. In particular, we are concerned with parametric uncertainties in the control channel of the players. Moreover, the weights on communication links can be compromised by time-varying uncertainties, which can result from possibly malicious attacks, faults and disturbances. To deal with the unavailability of measurement of optimization errors, an output observer is constructed, based on which adaptive laws are designed to compen-sate for physical uncertainties. With adaptive laws, a new distributed Nash equilibrium seeking strategy is designed by further integrating consensus protocols and gradient search algorithms. Moreover, to further accommodate compromised communication weights resulting from cyber-uncertainties, the coupling strengths of the consensus module are designed to be adaptive. As a byproduct, the coupling strengths are independent of any global information. With theoretical investigations, it is proven that the proposed strategies are resilient to these uncertainties and play-ers' actions are convergent to the Nash equilibrium. Simulation examples are given to numerically validate the effectiveness of the proposed strategies.