Distributed Model Predictive Control for Linear Systems with Adaptive Terminal Sets

TL;DR

This paper introduces a unified distributed model predictive control framework for linear systems that adaptively synthesizes terminal sets and controllers, improving stability and performance by considering the current system state.

Contribution

It presents a novel integrated approach for synthesizing terminal controllers and invariant sets respecting system structure, unlike previous methods that decouple these processes.

Findings

Enhanced stability through adaptive terminal sets

Improved control performance on benchmark problems

Unified synthesis approach outperforms existing methods

Abstract

In this paper, we propose a distributed model predictive control (DMPC) scheme for linear time-invariant constrained systems which admit a separable structure. To exploit the merits of distributed computation algorithms, the stabilizing terminal controller, value function and invariant terminal set of the DMPC optimization problem need to respect the loosely coupled structure of the system. Although existing methods in the literature address this task, they typically decouple the synthesis of terminal controllers and value functions from the one of terminal sets. In addition, these approaches do not explicitly consider the effect of the current state of the system in the synthesis process. These limitations can lead the resulting DMPC scheme to poor performance since it may admit small or even empty terminal sets. Unlike other approaches, this paper presents a unified framework to encapsulate the synthesis of both the stabilizing terminal controller and invariant terminal set into the DMPC formulation. Conditions for Lyapunov stability and invariance are imposed in the synthesis problem in a way that allows the value function and invariant terminal set to admit the desired distributed structure. We illustrate the effectiveness of the proposed method on several examples including a benchmark spring-mass-damper problem.