A graph theoretical approach toward a switched feedback controller for pursuit-evasion scenarios

This research introduces a novel method for constructing a switched feedback control system to be used for an autonomous agent. The state space is partitioned into sets of states where a specific control is applied. Each partition is represented by nodes of a digraph where the success of the control in traversing the partitions is represented by a connecting edge. Using the concept of capture sets in the field of differential games, it is shown that a set of states included in a particular partition is capable of reaching the target set if the eigenvalues of the adjacency matrix representing the digraph are all zero and none of the partitions are invariant. The advantage of this method is that it is possible to assign finite horizon controls to each partition that are easier to calculate than infinite horizon methods, but still maintain the infinite horizon guarantee of reaching the target. An example is given to illustrate the implementation of the proposed controller.