Distributed linear–quadratic regulator control for discrete‐time multi‐agent systems

Abstract

This study will investigate the distributed linear quadratic (LQ) control problem for discrete identical uncoupled multi-agent systems with a global performance index coupling the behaviour of the multiple agents. An existence condition to the optimal distributed LQ controller is given first. In general, such condition can be checked by solving a discrete algebraic Riccati equation through a numerical method. When the condition fails to hold, a suboptimal distributed controller design method is proposed for a class of LQ performance. The solution can be obtained by solving two local algebraic Riccati equations whose dimension is the same as a single agent. The stability condition is given in terms of the spectrum of a matrix representing the desired sparsity pattern of the distributed controller. Comparing to the centralised control, the computation and communication complexity is much lesser. Finally, the suboptimality is parameterised, and can be measured by solving a Lyapunov equation.