Robust tracking MPC for perturbed nonlinear systems -- Extended version

TL;DR

This paper introduces a robust nonlinear model predictive control method capable of handling bounded perturbations and tracking piece-wise constant setpoints, ensuring feasibility and convergence in uncertain environments.

Contribution

It extends nonlinear MPC for tracking to systems with bounded, non-additive perturbations, incorporating conservative constraints and stability guarantees.

Findings

Guarantees convergence to setpoints or optimal reachable steady states.

Ensures robust feasibility under bounded uncertainties.

Provides stability and convergence proofs for the proposed controller.

Abstract

This paper presents a novel robust predictive controller for constrained nonlinear systems that is able to track piece-wise constant setpoint signals. The tracking model predictive controller presented in this paper extends the nonlinear MPC for tracking to the more complex case of nonlinear systems subject to bounded and not necessarily additive perturbations. The optimal control problem that is solved at each step penalizes the deviation of the predicted nominal system trajectory from an artificial reference, which is added as a decision variable, as well as the distance between the artificial reference and the setpoint. Robust feasibility is ensured by imposing conservative constraints that take into account the effect of uncertainties and convergence to a neighborhood of any feasible setpoint is guaranteed by means of an appropriate terminal cost and an extended stabilizing terminal constraint. In the case of unreachable setpoints, convergence to a neighborhood of the optimal reachable steady output is also proved.