A singular solution to the problem of minimizing resource consumption
Vladimir Mikhailovich Aleksandrov
Sobolev Institute Mathematics of SB RAS, pr. Acad. Koptyug 4, 630090, Novosibirsk, Russia
Keywords: оптимальное управление, финитное управление, быстродействие, время перевода, расход ресурсов, момент включения управления, момент выключения, итерационный процесс, сопряженная система, фазовая траектория, optimal control, finite control, speed, transfer time, resource consumption, control start moment, control stop moment, iterative process, adjoint system, phase trajectory
Abstract
An iterative method of finding a singular solution to the problem of minimizing resource consumption has been developed. This method is based on the information about the finite control structure. A condition for existence of a singular solution is obtained. The limit value for transferring the time between the normal and the singular solutions is found. A relation between the variations of the control switching moments and the variations of the initial conditions of the adjoint system is determined. A system of linear algebraic equations relating the variations of the initial conditions of the adjoint system to the variations of the phase coordinates from a given final state of the system is obtained. The computational algorithm, the modeling results and the numerical calculations are presented.
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