Sampled-data reachability analysis using sensitivity and mixed-monotonicity

P.-J. Meyer, S. Coogan, M. Arcak
IEEE Control Systems Letters, 2018


This paper over-approximates the reachable sets of a continuous-time uncertain system using the sensitivity of its trajectories with respect to initial conditions and uncertain parameters. We first prove the equivalence between an existing over-approximation result based on the sign-stability of the sensitivity matrices and a discrete-time approach relying on a mixed-monotonicity property. We then present a new over- approximation result which scales at worst linearly with the state dimension and is applicable to any continuous-time system with bounded sensitivity. Finally, we provide a simulation- based approach to estimate these bounds through sampling and falsification. The results are illustrated with numerical examples on traffic networks and satellite orbits.