Distributed Control and Stabilization for Discrete-time Large Scale Systems With Imposed Constraints

TL;DR

This paper develops a method for distributed control and stabilization of large-scale discrete-time linear systems with constraints, using optimal control principles and Lyapunov functions to ensure stability.

Contribution

It introduces a novel approach combining the maximum principle and Lyapunov functions for constrained distributed control and stabilization.

Findings

Optimal distributed controllers derived using maximum principle.

Systems can be stabilized with the proposed controllers under constraints.

Method simplifies calculation of controllers for large-scale systems.

Abstract

This paper is concerned with the distributed control and stabilization problems for linear discrete-time large scale systems with imposed constraints. The main contributions of this paper are: Firstly, by using the maximum principle (necessary condition) for the finite horizon optimal control developed in this paper, the optimal distributed controller is thus derived, which can be easily calculated; Secondly, by defining the Lyapunov function with the optimal cost function, we show that the systems with imposed constraints can be stabilized by the optimal distributed controller for the infinite horizon case. The main techniques adopted in this paper are the maximum principle and the solution to the forward and backward difference equations (FBDE), which are the basis in solving distributed control and stabilization problems for linear systems with constraints.