Learning-based Homothetic Tube MPC

TL;DR

This paper introduces an online learning approach for homothetic tube MPC that adaptively approximates unknown disturbance sets using real-time data, enhancing robustness and feasibility in constrained linear systems.

Contribution

It proposes a novel online learning algorithm for disturbance set approximation in homothetic tube MPC, with probabilistic guarantees and computationally efficient updates.

Findings

The algorithm effectively approximates true disturbance sets in simulations.

Probabilistic recursive feasibility is established for the learned MPC.

Numerical results show improved performance over existing MPC methods.

Abstract

In this paper, we study homothetic tube model predictive control (MPC) of discrete-time linear systems subject to bounded additive disturbance and mixed constraints on the state and input. Different from most existing work on robust MPC, we assume that the true disturbance set is unknown but a conservative surrogate is available a priori. Leveraging the real-time data, we develop an online learning algorithm to approximate the true disturbance set. This approximation and the corresponding constraints in the MPC optimisation are updated online using computationally convenient linear programs. We provide statistical gaps between the true and learned disturbance sets, based on which, probabilistic recursive feasibility of homothetic tube MPC problems is discussed. Numerical simulations are provided to demonstrate the efficacy of our proposed algorithm and compare with state-of-the-art MPC algorithms.