Distributed Attack-Resilient Nash Equilibrium Seeking for Networked Games: An Event-Triggered Extended State Observer Approach

For the non-cooperative game in networked systems with individuals having the second-order dynamics, a new resilient distributed Nash Equilibrium (NE) seeking algorithm with only strategies on event-triggered time instants is proposed when considering attacks target the actuators and sensors. Malicious attacks are assumed to inject some unknown false data into each agent’s control inputs and also manipulate the exchanging information between agents. In order to alleviate the negative impacts of attacks on the agents’ strategies, an event-triggered extended state observer (ET-ESO) with dynamic event-triggered condition is proposed. The designed ET-ESO aims to approximate both agents’ strategies and attack signals by regarding the attack signals as extended states. The estimation can be made with arbitrary accuracy directly related to the ESO parameter. The Zeno behavior is also proved to be excluded related to the ETESO. The attack-resilient NE seeking algorithm with distributed manner is then proposed based on such ET-ESO, and agents’ strategies would converge to an arbitrary small bound around the NE despite unknown injected cyber attack signals. Lastly, a numerical example is given to illustrate the effectiveness of the obtained results.