Robust Model Predictive Control for Linear Systems with Interval Matrix Model Uncertainty

TL;DR

This paper introduces a robust MPC method for linear systems with interval matrix uncertainties, using set-theoretic over-approximations to reduce online computation while maintaining stability and feasibility.

Contribution

It develops a novel offline-computed uncertainty bound using matrix zonotopes, improving computational efficiency for systems with multiple uncertainties.

Findings

Matches the feasibility regions of state-of-the-art methods

Reduces online computational load significantly

Enables control of high-dimensional systems with multiple uncertainties

Abstract

This paper proposes a novel robust Model Predictive Control (MPC) scheme for linear discrete-time systems affected by model uncertainty described by interval matrices. The key feature of the proposed method is a bound on the uncertainty propagation along the prediction horizon which exploits a set-theoretic over-approximation of each term of the uncertain system impulse response. Such an approximation is based on matrix zonotopes and leverages the interval matrix structure of the uncertainty model. Its main advantage is that all the relevant bounds are computed offline, thus making the online computational load independent of the number of uncertain parameters. A variable-horizon MPC formulation is adopted to guarantee recursive feasibility and to ensure robust asymptotic stability of the closed-loop system. Numerical simulations demonstrate that the proposed approach is able to match the feasibility regions of the most effective state-of-the-art methods, while significantly reducing the computational burden, thereby enabling the treatment of nontrivial dimensional systems with multiple uncertain parameters.