Distributed RHC stabilization for discrete‐time large‐scale systems with imposed constraints

Abstract

SummaryThis paper is concerned with finite horizon distributed stabilization of linear discrete‐time large‐scale systems with imposed constraints. Firstly, by constructing the performance index with two terminal weighted matrices, the necessary and sufficient conditions for stabilizing the system are derived. It is shown that distributed receding horizon control (RHC) can stabilize the discrete time large system with constraints if and only if two novel Lyapunov inequalities on the terminal weighting matrix are satisfied. Secondly, the finite horizon optimal control problem is solved by using the maximum principle (necessary condition), and the Riccati equation satisfying the corresponding distributed control system is derived. Based on the Riccati equation, the explicit optimal distributed RHC controller is obtained. Finally, simulation examples are used to verify the feasibility of distributed RHC to stabilize the system.