Safe Bayesian Optimization for Complex Control Systems via Additive Gaussian Processes

Controller tuning and optimization have long been recognized as fundamental challenges in robotics and mechatronic systems. Traditional controller design techniques are usually model-based, and their closed-loop performance depends on the fidelity of the mathematical model. Subsequent tuning of the controller parameters is frequently carried out via empirical rules, which may still suffer from model inaccuracies. In control applications with complex dynamics, obtaining a precise model is often challenging, leading us towards a data-driven approach. While various researchers have explored the optimization of a single controller, it remains a challenge to obtain the optimal controller parameters safely and efficiently when multiple controllers are involved. In this letter, a method called <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SAFECTRLBO</small> is proposed to optimize multiple controllers simultaneously while ensuring safety. The exploration process in existing safe Bayesian optimization is simplified to reduce computational effort without sacrificing expansion capability. Additionally, additive Gaussian kernels are employed to enhance the efficiency of Gaussian process updates for unknown functions. Hardware experiments on a permanent magnet synchronous motor (PMSM) demonstrate that, compared to baseline safe Bayesian optimization algorithms, <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SAFECTRLBO</small> attains the best overall performance while ensuring safety.