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

TL;DR

This paper introduces a robust distributed model predictive control framework for linear systems with disturbances, ensuring stability and constraint satisfaction through adaptive terminal sets and constraint tightening, demonstrated via simulations.

Contribution

It presents a novel robust DMPC formulation with separable costs and adaptive terminal sets, along with a synthesis method for practical implementation.

Findings

Closed-loop system is recursively feasible and input-to-state stable.

Constraint satisfaction is guaranteed despite disturbances.

Simulation confirms effectiveness of the proposed approach.

Abstract

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 interagent coupling like vehicle platooning, 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.