The Hamiltonian Formalism for Problems of Group Control Under Obstacles*

This paper suggests a unified method of solving target team control problems using methods of the Hamiltonian formalism. Considered is the problem of steering a team of m members towards a given target set while avoiding external obstacles. The team members must avoid collisions of their respective safety zones while remaining close to each other within a virtual ellipsoidal container or a chain of such containers. The container trajectory is therefore constructed firstly then used as an external state constraint for the team. Solvability conditions for such target team control problem are formulated with routes for calculating respective control strategies indicated.