Systems and Control Theory for Game Equilibrium Seeking

Distributed game theory and optimal control provide the foundation for the analysis and design of multi-agent systems. A central challenge in this area is game equilibrium seeking, which this talk presents from a systems and control perspective. First, variational analysis, operator theory, and systems theory are employed to model and analyze equilibrium-seeking algorithms as dynamical systems, thereby leading to a unified framework for their convergence. Dynamic games for constrained systems are considered next. Leveraging optimal control theory, equilibrium control policies are devised in feedback form associated with lifted optimal value functions, thus enabling receding-horizon model-predictive control in dynamic games. The talk concludes with an outlook on data-driven game equilibrium seeking for systems with partially known objective functions, dynamics, and constraints.