Dynamic NE Seeking for Multi-Integrator Networked Agents with Disturbance Rejection
It addresses the problem of distributed Nash equilibrium seeking in multi-agent systems with integrator dynamics and disturbances, which is relevant for control and robotics applications.
This paper proposes Nash equilibrium seeking dynamics for multi-integrator agents under external disturbances, achieving convergence to the Nash equilibrium regardless of disturbances using gradient-play with internal-model-based disturbance rejection and consensus estimation.
In this paper, we consider game problems played by (multi)-integrator agents, subject to external disturbances. We propose Nash equilibrium seeking dynamics based on gradient-play, 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.