Distributed Solving of Linear Quadratic Optimal Controller with Terminal State Constraint

Abstract

This paper is concerned with the linear quadratic (LQ) optimal control of continuous-time system with terminal state constraint. In particular, multiple agents exist in the system which can only access partial information of the matrix parameters. This makes the classical solving method based on Riccati equation with global information suffering. The main contribution is to present a distributed algorithm to derive the optimal controller which is consisting of the distributed iterations for the Riccati equation, a backward differential equation driven by the optimal Lagrange multiplier and the optimal state. Furthermore, the proposed distributed iteration method is extended to solve the consensus control problem for heterogeneous multi-agent systems, achieving the globally optimal performance of the system. The effectiveness of the proposed algorithm is verified by two numerical examples, where the performance index under the proposed distributed controller is smaller than that under the commonly used consensus control.