Optimal trajectories in the problem of targets bypass

Optimal bypass of the given spatial targets at fixed times with the same speed of passes of these targets is formulated as a linear-quadratic optimal control problem. Such dynamic problems often arise when controlling the movement of mechanical systems, aircraft (in particular, unmanned vehicles), robotic manipulators, and so on. We have justified the procedure for constructing an explicit analytical expression for point-to-point control and for optimal trajectories with the corresponding multi-point mixed boundary conditions. The point-to-point control and the corresponding sets of optimal trajectories in this class of bypass problems of the given targets at fixed times with the same speed of passes are simply constructed using the described procedure. In the article we give an example illustrating the optimal trajectories construction in one bypass target problem on the plane with a parametric specification of the fixed passes rates.