Explicit Distributed and Localized Model Predictive Control via System Level Synthesis

TL;DR

This paper introduces an explicit distributed and localized model predictive control method based on System Level Synthesis, significantly reducing computational complexity for large-scale systems by providing explicit solutions and local information exchange.

Contribution

It presents a novel explicit solution for distributed MPC using SLS, enabling efficient control of large-scale systems with local information exchange and reduced computational overhead.

Findings

Explicit solutions are divided into three regions per state and input.

Locality constraints lead to smaller subproblems, reducing computation.

Numerical simulations show significant runtime improvements over online solvers.

Abstract

An explicit Model Predictive Control algorithm for large-scale structured linear systems is presented. We base our results on Distributed and Localized Model Predictive Control (DLMPC), a closed-loop model predictive control scheme based on the System Level Synthesis (SLS) framework wherein only local state and model information needs to be exchanged between subsystems for the computation and implementation of control actions. We provide an explicit solution for each of the subproblems resulting from the distributed MPC scheme. We show that given the separability of the problem, the explicit solution is only divided into three regions per state and input instantiation, making the point location problem very efficient. Moreover, given the locality constraints, the subproblems are of much smaller dimension than the full problem, which significantly reduces the computational overhead of explicit solutions. We conclude with numerical simulations to demonstrate the computational advantages of our method, in which we show a large improvement in runtime per MPC iteration as compared with the results of computing the optimization with a solver online.