A system level approach to generalised feedback Nash equilibrium seeking in partially-observed games

Abstract: This work proposes an algorithm for seeking generalised feedback Nash equilibria (GFNE) in noncooperative dynamic games. The focus is on cyber-physical systems with dynamics which are linear, stochastic, potentially unstable, and partially observed. We employ System Level Synthesis (SLS) to reformulate the problem as the search for an equilibrium profile of closed-loop responses to noise, which can then be used to reconstruct a stabilising output-feedback policy. Under this setup, we leverage monotone operator theory to design a GFNE-seeking algorithm capable to enforce closed-loop stability, operational constraints, and communication constraints onto the control policies. This algorithm is amenable to numerical implementation and we provide conditions for its convergence. We demonstrate our approach in a simulated experiment on the noncooperative stabilisation of a decentralised power-grid.