Distributed Extremum Seeking Control of networked large-scale systems under constraints

We consider the distributed optimization problem of networked large-scale systems under specified constraints. In particular, we aim to optimize the steady-state performance of the system by making it (in a distributed manner) working at the optimal operation point. To solve the problem, a primal-dual method is employed to seek the optimal setpoint in conjunction with Extremum Seeking Control (ESC) which is utilized as a tool for efficient gradient estimation without knowing the specific form of the cost functions as well as the constraints of the system. The proposed overall scheme is termed as Distributed Extremum Seeking Control (D-ESC) as it is designed based on the ESC scheme and implemented in a distributed way. It will be shown, by resorting to singular perturbation and averaging theory as well as duality theory, that the overall networked large-scale system equipped with D-ESC is Semi-globally Practically Asymptotically Stable (SPAS) and thus will eventually converge to the neighborhood of the Pareto-optimal solution of the primal problem.