Sampled-data reachability analysis using sensitivity and mixed-monotonicity
For control and verification engineers, this provides a scalable reachability analysis method for continuous-time systems, though the approach is incremental.
This paper over-approximates reachable sets for continuous-time uncertain systems using trajectory sensitivity, proving equivalence between sign-stability and mixed-monotonicity approaches, and presenting a new method that scales linearly with state dimension. Numerical examples on traffic networks and satellite orbits demonstrate the approach.
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.