Dynamic Nash Equilibrium Seeking for a Class of Nonlinear Uncertain Multi-agent Systems

We consider seeking a Nash equilibrium (NE) of a monotone game, played by dynamic agents which are modeled as a class of lower-triangular nonlinear uncertain dynamics with external disturbances. We establish a general framework that converts the problem into a distributed robust stabilization problem of an appropriately augmented system. To be specific, we construct a virtual single-integrator multi-agent system, as a reference signal generator, to compute an NE in a fully distributed manner. By introducing internal models to tackle the disturbances, as well as embedding the virtual system, we derive an augmented system. Following that, we show that the outputs of all agents reach an NE of the game if the augmented system can be stabilized by a control law. Finally, resorting to a backstepping procedure, we design a distributed state-feedback controller to stabilize the augmented system semi-globally.