ИСТИНА

We consider a class of optimal control problems related to target orbiting of autonomous objects group with carrier object use (satellites, UAVs etc.). To describe the corrsponding situation, we use system of ODEs that consists of two subsystems: the ``carrier'' subsystem and a number of ``payload'' ones. They are determined on the ``main'' and ``nested'' time segments ordered w.r.t. start times. Start time of each ``nested'' segment is in fact time of the corresponding payload ``decoupling''. Our aim is to formulate first-order necessary conditions of extended weak minimum (``extended'' means in fact that we consider variations of decoupling times also). To do this, we perfom the following scheme: first, introduce normalized time and replicate all constraints to reduce our OCP to classical form, then write necessary conditions, and finally, rewrite these conditions in original time. We also provide simple kinematic example of our conditions application (carrier moves along helix between two ``orbits'', payloads moves in passive way after decoupling and, in addition, provide problem statement related to group cooperation evasion)