Set-Point Tracking MPC with Avoidance Features

TL;DR

This paper introduces a novel set-point tracking MPC method that incorporates avoidance features through artificial variables, ensuring recursive feasibility and stability even with multiple regions to avoid, demonstrated via numerical examples.

Contribution

It presents a new MPC framework that integrates avoidance features using artificial variables, maintaining feasibility and stability in dynamic environments.

Findings

Recursive feasibility is guaranteed under bounded avoidance costs.

The closed-loop system is input-to-state stable.

Numerical examples validate the effectiveness of the proposed approach.

Abstract

This work proposes a finite-horizon optimal control strategy to solve the tracking problem while providing avoidance features to the closed-loop system. Inspired by the set-point tracking model predictive control (MPC) framework, the central idea of including artificial variables into the optimal control problem is considered. This approach allows us to add avoidance features into the set-point tracking MPC strategy without losing the properties of an enlarged domain of attraction and feasibility insurances in the face of any changing reference. Besides, the artificial variables are considered together with an avoidance cost functional to establish the basis of the strategy, maintaining the recursive feasibility property in the presence of a previously unknown number of regions to be avoided. It is shown that the closed-loop system is recursively feasible and input-to-state-stable under the mild assumption that the avoidance cost is uniformly bounded over time. Finally, two numerical examples illustrate the controller behavior.