Markov inequality rule for switching among time optimal controllers in a multiple vehicle intercept problem

In this paper, a Markov inequality based switching rule is proposed to switch among numerically computed, time optimal controllers in a multiple vehicle intercept problem. Each controller is optimal for the intercept of a single vehicle, i.e., for the segment of the complete time varying multiple vehicle target set. The switching rule guarantees that after every switch the time to the target set is shorter with a certain predefined probability. Furthermore, the rule guarantees that the target set is reached after a finite number of switches and the rule scales well with the number of vehicles, i.e., the segments covering the target set. The problem and results are illustrated by a numerical example.