Learning generalized Nash equilibria in multi-agent dynamical systems via extremum seeking control

Abstract

In this paper, we consider the problem of learning a generalized Nash equilibrium (GNE) in strongly monotone games. First, we propose a novel continuous-time solution algorithm that uses regular projections and first-order information. As second main contribution, we design a data-driven variant of the former algorithm where each agent estimates their individual pseudogradient via zero-order information, namely, measurements of their individual cost function values, as typical of extremum seeking control. Third, we generalize our setup and results for multi-agent systems with nonlinear dynamics. Finally, we apply our algorithms to connectivity control in robotic sensor networks and distributed wind farm optimization.

Sampled-Data Online Feedback Equilibrium Seeking: Stability and Tracking

“…In this example, modified from [28], we consider a collection of N = 4 robotic agents, each tasked with investigating a signal at…”

“…In the context of games with dynamical agents, two main control approaches have been considered, built on passivitybased [25], [26] and ES algorithms [27], [28], respectively. In [25], passivity is leveraged to design a distributed control law with convergence guarantees to a NE in games with single-integrator agents.…”

“…In [27], an ESbased controller is designed for NE seeking in games with nonlinear dynamical agents. The extension to games with coupling constraints is presented for the first time in [28]. In both cases, convergence is proven only in the disturbancefree case, and to an approximate solution of the game.…”