Augmenting MPC Schemes With Active Learning: Intuitive Tuning and Guaranteed Performance

Abstract

A framework to augment an existing model predictive control (MPC) design/implementation with active learning is proposed. Active learning is achieved by employing a user-defined learning cost function (e.g., enforcing persistence of excitation or using exploration terms from reinforcement learning), with the aim to improve model knowledge and reduce uncertainty through model adaptation. The framework is applicable to a general class of nonlinear MPC design procedures and ensures desired performance bounds for the resulting closed-loop, which can be intuitively tuned compared to the initial MPC design. The performance bounds are obtained by coupling the active learning objective with performance bounds of the primary MPC, using tools from multi-objective MPC and average constraints from economic MPC. The overall framework can be easily implemented <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> and it is intuitive to tune. The resulting computational demand typically is comparable to the original MPC scheme. We demonstrate the practicality of the proposed framework using a numerical example involving a nonlinear uncertain model, and active learning. <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> An exemplary implementation can be found at: https://www.ist.unistuttgart.de/dokumente/public/Soloperto_20.m.