Reachability analysis of hybrid control systems using reduced-order models

Complexity of reachability computations for continuous and hybrid dynamic systems typically grows exponentially with respect to the dimension of the continuous state space. Consequently, reduced-order models usually need to be constructed to make reachability analysis tractable. Use of reduced-order models makes reachability-based verification unsound, however. This paper presents a method for incorporating bounds on errors due to model reduction into reachability analysis for a class of hybrid control systems so that the computed sets are guaranteed to be conservative (i.e., over-) approximations of the reachable sets for the original system. We also present an efficient method for computing error bounds due to model reduction for finite-time horizons that are less conservative than error bounds from the model-reduction literature. The effectiveness of the approach is illustrated with an example.