Robust distributed model predictive control of linear systems: Analysis and synthesis

• Published in: Automatica (Oxford) Vol. 137; p. 110141
• Main Authors: Wang, Ye, Manzie, Chris
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.03.2022
• Subjects: Distributed model predictive control; Robust adaptive terminal sets; Robust constraint tightening; Set-membership approach; Distributed model predictive control; Robust adaptive terminal sets; Robust constraint tightening; Set-membership approach
• ISSN: 0005-1098; 1873-2836
• DOI: 10.1016/j.automatica.2021.110141

To provide robustness of distributed model predictive control (DMPC), this work proposes a robust DMPC formulation for discrete-time linear systems subject to unknown-but-bounded disturbances. Taking advantage of the structure of certain classes of distributed systems seen in applications with inter-agent coupling, a novel robust DMPC is formulated. The proposed approach is characterised by separable terminal costs and locally robust terminal sets, with the latter sets adaptively estimated in the online optimisation problem. A constraint tightening approach based on a set-membership approach is used to guarantee constraint satisfaction for coupled subsystems in the presence of disturbances. Under this formulation, the closed-loop system is shown to be recursively feasible and input-to-state stable. To aid in the deployment of the proposed robust DMPC, a possible synthesis method and design conditions for practical implementation are presented. Finally, simulation results with a mass–spring–damper system are provided to demonstrate the proposed robust DMPC.