Exponential stabilization of linear systems with feedback optimization and its application to microgrids control

Abstract

This paper proposes a feedback-optimization-based control method for linear time-invariant systems, which is aimed to exponentially stabilize the system and, meanwhile, drive the system output to an approximate solution of an optimization problem with convex set constraints and affine inequality constraints. To ensure the exponential stability of the closed-loop system, the original optimization problem is first reformulated into a counterpart that has only convex set constraints. It is shown that the optimal solution of the new optimization problem is an approximate optimal solution of the original problem. Then, based on this new optimization problem, the projected primal–dual gradient dynamics algorithm is used to design the controller. By using the singular perturbation method, sufficient conditions are provided to ensure the exponential stability of the closed-loop system. The proposed method is also applied to microgrid control.