Time adaptivity in model predictive control

TL;DR

This paper introduces a novel time-adaptive residual a-posteriori error control method for Model Predictive Control (MPC), optimizing the prediction and application horizons dynamically for systems governed by linear parabolic PDEs.

Contribution

It proposes a new adaptive error control approach that tailors the discretization and horizon lengths in MPC based on the optimality system, improving efficiency and robustness.

Findings

Demonstrates improved performance in numerical examples

Shows robustness of the adaptive MPC approach

Provides tailored discretization and horizon length control

Abstract

The core of the Model Predictive Control (MPC) method in every step of the algorithm consists in solving a time-dependent optimization problem on the prediction horizon of the MPC algorithm, and then to apply a portion of the optimal control over the application horizon to obtain the new state. To solve this problem efficiently, we propose a time-adaptive residual a-posteriori error control concept based on the optimality system of this optimal control problem. This approach not only delivers a tailored time discretization of the the prediction horizon, but also suggests a tailored length of the application horizon for the current MPC step. We apply this concept for systems governed by linear parabolic PDEs and present several numerical examples which demonstrate the performance and the robustness of our adaptive MPC control concept.