Configuration-Constrained Tube MPC

TL;DR

This paper introduces a novel robust MPC approach using configuration-constrained polytopic tubes that optimize shape and control laws online, reducing conservativeness compared to existing methods.

Contribution

It presents a new class of configuration-constrained polytopic tubes and develops CCTMPC controllers that adapt tube shape via convex optimization, improving robustness and reducing conservativeness.

Findings

CCTMPC is less conservative than Rigid- and Homothetic- Tube MPC.

CCTMPC can outperform Elastic Tube MPC, Disturbance Affine Feedback MPC, and Fully Parameterized Tube MPC.

The approach enables online shape optimization of the control tube.

Abstract

This paper is about robust Model Predictive Control (MPC) for linear systems with additive and multiplicative uncertainty. A novel class of configuration-constrained polytopic robust forward invariant tubes is introduced, which admit a joint parameterization of their facets and vertices. They are the foundation for the development of novel Configuration-Constrained Tube MPC (CCTMPC) controllers that freely optimize the shape of their polytopic tube, subject to conic vertex configuration constraints, as well as associated vertex control laws by solving convex optimization problems online. It is shown that CCTMPC is -- under appropriate assumptions -- systematically less conservative than Rigid- and Homothetic- Tube MPC. Additionally, it is proven that there exist control systems for which CCTMPC is less conservative than Elastic Tube MPC, Disturbance Affine Feedback MPC, and Fully Parameterized Tube MPC.