Safe Bayesian Optimization for Complex Control Systems via Additive Gaussian Processes

Automatic controller tuning is attractive for robotics and mechatronic systems whose dynamics are difficult to model accurately, but direct black-box optimization can be unsafe because each query is executed on the physical plant. Existing safe Bayesian optimization (BO) methods provide high-probability safety guarantees, yet their practical use in multi-loop control is limited by two coupled difficulties: the controller parameter space is often moderately high-dimensional, and hardware evaluations are too expensive to allow hundreds or thousands of exploratory trials. This paper proposes \textsc{SafeCtrlBO}, a safe BO method for simultaneously tuning multiple coupled controllers. The method uses additive Gaussian-process kernels to encode low-order structure across controller gains and reduce the sample complexity associated with dense full-dimensional kernels. It also replaces the expensive potential-expander computation used in \textsc{SafeOpt}-style exploration with a boundary-based expansion rule that preserves the intended safe-set expansion behavior under explicit geometric conditions and is validated empirically. Experiments on synthetic benchmarks and on a permanent magnet synchronous motor (PMSM) speed-control platform show that \textsc{SafeCtrlBO} reaches high-performing controller parameters with fewer hardware evaluations than representative safe BO baselines, while maintaining the prescribed high-probability safety criterion and avoiding violations of the hard signal-safety constraint in the hardware study. The code implementation is publicly available at https://github.com/hxwangnus/SafeCtrlBO.