Robust explicit model predictive control for hybrid linear systems with parameter uncertainties

TL;DR

This paper introduces a robust explicit MPC approach for hybrid linear systems with parameter uncertainties, utilizing zonotope-based methods, order reduction, and a flexible policy algorithm to improve computational efficiency and robustness.

Contribution

It extends zonotope-based MPC to handle parametric uncertainties, proposes a zonotope order reduction technique, and develops a quasi-time-free policy for hybrid systems.

Findings

Validated on two experimental setups with varying parameters

Reduced computational complexity through zonotope order reduction

Achieved robust control performance despite uncertainties

Abstract

Explicit model-predictive control (MPC) is a widely used control design method that employs optimization tools to find control policies offline; commonly it is posed as a semi-definite program (SDP) or as a mixed-integer SDP in the case of hybrid systems. However, mixed-integer SDPs are computationally expensive, motivating alternative formulations, such as zonotope-based MPC (zonotopes are a special type of symmetric polytopes). In this paper, we propose a robust explicit MPC method applicable to hybrid systems. More precisely, we extend existing zonotope-based MPC methods to account for multiplicative parametric uncertainty. Additionally, we propose a convex zonotope order reduction method that takes advantage of the iterative structure of the zonotope propagation problem to promote diagonal blocks in the zonotope generators and lower the number of decision variables. Finally, we developed a quasi-time-free policy choice algorithm, allowing the system to start from any point on the trajectory and avoid chattering associated with discrete switching of linear control policies based on the current state's membership in state-space regions. Last but not least, we verify the validity of the proposed methods on two experimental setups, varying physical parameters between experiments.