Performance-Driven Constrained Optimal Auto-Tuner for MPC

Abstract

A key challenge in tuning Model Predictive Control (<sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">MPC</small>) cost function parameters is to ensure that the system performance stays consistently above a certain threshold. To address this challenge, we propose a novel method, <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">COAt-MPC</small>, Constrained Optimal Auto-Tuner for <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">MPC</small>. With every tuning iteration, <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">COAt-MPC</small> gathers performance data and learns by updating its posterior belief. It explores the tuning parameters' domain towards optimistic parameters in a goal-directed fashion, which is key to its sample efficiency. We theoretically analyze <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">COAt-MPC</small>, showing that it satisfies performance constraints with arbitrarily high probability at all times and provably converges to the optimum performance within finite time. Through comprehensive simulations and comparative analyses with a hardware platform, we demonstrate the effectiveness of <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">COAt-MPC</small> in comparison to classical Bayesian Optimization (BO) and other state-of-the-art methods. When applied to autonomous racing, our approach outperforms baselines in terms of constraint violations and cumulative regret over time.