Distributed Learning Model Predictive Control for Linear Systems

TL;DR

This paper introduces a distributed learning model predictive control scheme for linear systems with coupled dynamics, leveraging online optimization and iterative data to ensure stability, feasibility, and convergence to optimal control solutions.

Contribution

It proposes a novel distributed MPC approach that uses a control invariant terminal set and iterative learning to improve performance and guarantee stability in coupled linear systems.

Findings

Ensures recursive feasibility and asymptotic stability.

Achieves convergence to the global optimal control solution.

Demonstrates effectiveness through numerical experiments.

Abstract

This paper presents a distributed learning model predictive control (DLMPC) scheme for distributed linear time invariant systems with coupled dynamics and state constraints. The proposed solution method is based on an online distributed optimization scheme with nearest-neighbor communication. If the control task is iterative and data from previous feasible iterations are available, local data are exploited by the subsystems in order to construct the local terminal set and terminal cost, which guarantee recursive feasibility and asymptotic stability, as well as performance improvement over iterations. In case a first feasible trajectory is difficult to obtain, or the task is non-iterative, we further propose an algorithm that efficiently explores the state-space and generates the data required for the construction of the terminal cost and terminal constraint in the MPC problem in a safe and distributed way. In contrast to other distributed MPC schemes which use structured positive invariant sets, the proposed approach involves a control invariant set as the terminal set, on which we do not impose any distributed structure. The proposed iterative scheme converges to the global optimal solution of the underlying infinite horizon optimal control problem under mild conditions. Numerical experiments demonstrate the effectiveness of the proposed DLMPC scheme.