Distributed Observer-based LQR Control for Discrete-time Multi-agent Systems

This paper investigates a set of uncoupled identical linear time-invariant multi-agent systems with a performance index coupling the behavior between the multi-agents. Based on the decomposition of the discrete algebraic Riccati equation of the centralized linear quadratic regulator control, an observer-based distributed controller design method is proposed. The design procedure is employed by applying the decomposition of the global discrete-time algebraic Riccati equations and estimation error systems. A stabilizing solution to the centralized linear quadratic regulator problem for the compact system is given firstly by compact Lyapunov function. The gain within a systematic solution is designed to make the closed-loop system asymptotically stable.