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.
Key words:
optimal control, finite control, speed, transfer time, resource consumption, control start moment, control stop moment, iterative process, adjoint system, phase trajectory.
Citation:
V. M. Aleksandrov, “A singular solution to the problem of minimizing resource consumption”, Sib. Zh. Vychisl. Mat., 19:1 (2016), 5–18; Num. Anal. Appl., 9:1 (2016), 1–11