Open AccessDistributed linear–quadratic regulator control for discrete‐time multi‐agent systems
Author(s) -
Wang Wei,
Zhang Fangfang,
Han Chunyan
Publication year - 2017
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2016.1641
Subject(s) - algebraic riccati equation , linear quadratic regulator , riccati equation , control theory (sociology) , mathematics , linear quadratic gaussian control , controller (irrigation) , discrete time and continuous time , computation , optimal control , quadratic equation , dimension (graph theory) , algebraic number , lyapunov equation , matrix (chemical analysis) , linear system , lyapunov function , mathematical optimization , computer science , control (management) , nonlinear system , algorithm , differential equation , mathematical analysis , materials science , artificial intelligence , composite material , biology , geometry , quantum mechanics , agronomy , statistics , physics , pure mathematics
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.