Game-Theoretic Steady-State Control

We consider a set of autonomous agents with LTI dynamics subject to constant external disturbance. Each agent seeks to minimize a coupled cost function in steady-state subject to equality constraints. We propose a novel control methodology to solve the problem that captures much the past work done on Nash equilibrium seeking for dynamic agents. We show that using our methodology, the problem reduces to one of designing a set of decentralized stabilizing controllers. Example controller designs are provided for two cases.