Reachability Analysis Using Spectrum of Koopman Operator

This letter proposes using the Koopman operator for reachability analysis of an autonomous dynamical system. In particular, we demonstrate the application of spectral analysis of the Koopman operator involving eigenfunctions and eigenvalues in the approximate computation of forward and backward reachable sets for an autonomous dynamical system. The formal guarantees for the approximate reachable sets are provided using the Hausdorff distance between sets that measure how far the approximate reachable set is from the true reachable set. A computational framework based on convex optimization is provided to compute the Koopman spectrum and the approximate reachable set. Finally, we present simulation results to demonstrate the application of the developed framework.