SC-BO: Stability-certified Bayesian optimization for fixed-order LTI controllers

Improving closed-loop control performance from data is challenging when stability must be guaranteed throughout the optimization process. Bayesian optimization provides a sample-efficient framework for this setting by selecting informative evaluations of the closed-loop system. Safe Bayesian Optimization (SafeBO) methods extend this framework by incorporating safety constraints during learning, but they do not directly provide formal certificates of closed-loop robust stability. This limits their use in applications where controllers must satisfy explicit stability-margin requirements. In this paper, we introduce Stability-Certified Bayesian Optimization (SC-BO), a framework for fixed-order Linear Time-Invariant (LTI) controllers that enforces robust stability within the optimization loop through disk-margin certification. The method alternates between two steps: (i) a Bayesian optimization step that proposes candidate controller parameters to improve closed-loop performance, and (ii) a robust-stability enforcement step, in which the proposed controller is certified against a prescribed disk-margin condition and, when necessary, projected onto the certified set by solving a convex semidefinite program. Numerical results on a high-fidelity quadrotor simulator show that SC-BO improves closed-loop performance while ensuring that all evaluated controllers satisfy the prescribed robust-stability requirement. The comparison with representative SafeBO baselines highlights the role of the certification/projection layer: in the considered application, SC-BO maintains competitive performance while preventing stability violations by construction.