Robust Optimal Control Using Set-based Reachability Analysis

Providing formal guarantees for constraint satisfaction is a crucial problem in safety-critical applications. We address this problem by combining robust optimal control with set-based reachability analysis of nonlinear systems. Our algorithm is built on a recently proposed scheme for optimizing affine feedback policies by iterating between solving a perturbed nominal optimal control problem and synthesizing linear feedback controllers – however, constraint satisfaction is not guaranteed. To overcome this limitation, we leverage concepts from robust controller synthesis and set-based reachability analysis. Our experiments show only a modest decrease in performance compared to an approach without formal guarantees, while we outperform state-of-the-art approaches that guarantee constraint satisfaction.