OPTIMAL TRAJECTORIES IN THE PROBLEM OF TARGETS BYPASS // BSU Bulletin. Mathematics, Informatics. - 2017. №2. . - С. 46-53.

OPTIMAL TRAJECTORIES IN THE PROBLEM OF TARGETS BYPASS

Работа выполнена при частичной финансовой поддержке Российского фонда фундаментальных исследований (проект № 15-07-00925a).

DOI: 10.18101/2304-5728-2017-2-46-53 UDK: 517.977

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 expres- sion for point-to-point control and for optimal trajectories with the corresponding multi-point mixed boundary conditions. The point-to-point control and the corre- sponding 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 paramet- ric specification of the fixed passes rates.

problem of targets bypass; unmanned vehicle; dynamic system; linearquadratic problem; optimal trajectory; point-to-point control; mixed boundary conditions.