Dynamic Nash Equilibrium Seeking for Higher-Order Integrators in Networks

In this paper we consider a set of heterogeneous agents modelled as higher-order integrators, playing a game over a network. In such networked scenarios, agents have to make decisions compatible with seeking a Nash equilibrium, while using partial-networked information, and possibly rejecting disturbances. We propose dynamic agent decision-making based on gradient-play with an additional stabilizing component for the higher-order dynamics. In the partial-information setting, each agent makes its decision based on a dynamic estimate of the others' states, updated by local communication with its neighbours, which offsets the lack of global information. When external disturbances are present, the agent decision dynamics is augmented with an internal-model component, in the form of a reduced-order observer for the disturbance. We show convergence of agents' dynamics 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 extended pseudo-gradient. Applications to mobile robots in sensor networks are provided.