Set-based MPC for discrete-time LTI systems with maximal domain of attraction and minimal predictive control horizon

TL;DR

This paper introduces a set-based model predictive control approach for discrete-time LTI systems that maximizes the domain of attraction with minimal control horizon, ensuring stability and feasibility.

Contribution

It proposes a novel single-optimization MPC formulation that achieves the largest domain of attraction with minimal predictive horizon for tracking control.

Findings

Maximal domain of attraction achieved in simulations.

Asymptotic stability of closed-loop system proved.

Recursive feasibility maintained under setpoint changes.

Abstract

This paper presents a novel set-based model predictive control for tracking, which provides the largest domain of attraction, even with the minimal predictive/control horizon. The formulation - which consists of a single optimization problem - shows a dual behavior: one operating inside the maximal controllable set to the feasible equilibrium set, and the other operating at the N-controllable set to the same equilibrium set. Based on some finite-time convergence results, asymptotic stability of the resulting closed-loop is proved, while recursive feasibility is ensured for any change of the setpoint. The properties and advantages of the proposal have been tested on simulation models.