A note on avoidance control

Earlier work has dealt with controls which guarantee that every trajectory of a given dynamical system remains outside (avoids) a prescribed set (anti‐target) for all time. In the present treatment, we permit the intersection of the anti‐target but consider two cases of avoidance: the anti‐target must be avoided during a prescribed time interval (finite‐time avoidance), or the anti‐target must be avoided for all time after some calculable or prescribed time interval (ultimate avoidance). Sufficient conditions are presented for these two kinds of avoidance. The use of these conditions is illustrated by two examples.