Higher Order Methods for Differential Inclusions
This work addresses the need for rigorous reachability analysis in control and verification, extending prior methods to handle all possible inputs with provable error bounds.
The paper develops a high-order numerical method for rigorously over-approximating reachable sets of differential inclusions, providing explicit error bounds based on Lipschitz constants and derivative bounds, with uniform error control over finite time intervals.
We present a numerical method for rigorous over-approximation of a reachable set of differential inclusions. The method gives high-order error bounds for single step approximations and a uniform bound on the error over the finite time interval. We provide formulas for the local error based on Lipschitz constants and bounds on higher-order derivatives. The method is based on a Fliess-like expansion, and extends previous results by providing error estimates which are valid for all possible inputs.