Guaranteed avoidance strategies

We consider a dynamical system under the control of two agents, one of whom desires to keep the system's state out of a given set regardless of the other agent's actions. The guaranteed avoidance conditions of Ref. 1 are generalized to admit piecewiseC1 test functions; this generalization permits application to a wider class of problems. The results are illustrated by application to a version of the homicidal chauffeur game.