Control problems for a class of set valued evolutions (Q1928764)

The authors study a particular class of control problems which represents a model that describes the controlled motion of a flock of animals. Necessary and sufficient conditions for the existence of a confining strategy for this problem are provided. Similar results are obtained in order to ensure that the steering problem admits a solution. Also, the situation is studied when stabilization is obtained by a control function which rotates with constant speed. In this case, it is proved that the reachable set converges in a strong sense to a periodic set-valued map.