Guaranteed Reachability for Systems with Unknown Dynamics.

Abstract

The problem of computing the reachable set for a given system is a quintessential question in nonlinear control theory. Motivated by prior work on safety-critical online planning, this paper considers an environment where the only available information about system dynamics is that of dynamics at a single point. Limited to such knowledge, we study the problem of describing the set of all states that are guaranteed to be reachable regardless of the unknown true dynamics. We show that such a set can be underapproximated by a reachable set of a related known system whose dynamics at every state depend on the velocity vectors that are available in all control systems consistent with the assumed knowledge. Complementing the theory, we discuss a simple model of an aircraft in distress to verify that such an underapproximation is meaningful in practice.