Distributed Solving of Linear Quadratic Optimal Controller with Terminal State Constraint
Wenjing Yang, Zhaorong Zhang, Juanjuan Xu
TL;DR
This paper develops a distributed solution to the continuous-time LQ control problem with terminal state constraints in networks of agents with partial information. The core approach interleaves distributed Riccati updates, a backward differential equation driven by an optimal Lagrange multiplier, and distributed state updates to compute the optimal controller, with theoretical guarantees of convergence. The framework is extended to optimal consensus control for heterogeneous multi-agent systems, enabling each agent to approximate a centralized solution using only local communications. Numerical examples demonstrate that the distributed controller achieves or surpasses the performance of standard consensus methods, validating both feasibility and practical benefits for networked control applications.
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.