A path planning approach to compute the smallest robust forward invariant sets

Robustness of nonlinear systems can be analyzed by computing robust forward invariant sets (RFIS). The smallest RFIS provides the least conservative estimate of system performance under perturbations. However, computation of the smallest RFIS through brute force search can be a difficult task. We develop a novel algorithm to find the smallest RFIS for two-dimensional systems subjected to bounded additive perturbations. The algorithm leverages path planning algorithms to produce an approximation of the boundary of the smallest RFIS. The algorithm is mathematically justified, and simulation results are provided showing that the proposed algorithm can be used to find an RFIS that is very close to the smallest RFIS. The amount of computation is effectively reduced. Hence the algorithm may be generalized to higher dimensional systems with generic perturbations.