A Multi-Fidelity Bayesian Approach to Safe Controller Design

Safely controlling unknown dynamical systems is one of the biggest challenges in the field of control. Oftentimes, an approximate model of a system's dynamics exists which provides beneficial information for the selection of controls. However, differences between the approximate and true systems present challenges as well as safety concerns. We propose an algorithm called SAFE-SLOPE to safely evaluate points from a Gaussian process model of a function when its Lipschitz constant is unknown. We establish theoretical guarantees for the performance of SAFE-SLOPE and quantify how multi-fidelity modeling improves the algorithm's performance. Finally, we demonstrate how SAFE-SLOPE achieves lower cumulative regret than a naive sampling method by applying it to find the control gains of a linear time-invariant system.Comment: 9 pages, 3 figures, extended version of the paper accepted for publication in L-CSS and the 2023 CDC. V3 contains alignments to the accepted version and minor typo corrections. V2 contains additional motivations in Sec. I, a description of Thm. 3.1, the omitted main point of Thm. 3.3, and an additional section with possible extensions. Missing definitions and typos have also been correcte