The method of extremal aiming, well-known in the theory of differential games, is applied to problems in which the level of dynamic disturbance is not stipulated in advance. Problems with linear dynamics, a fixed termination time and a geometric constraint on the effective control are considered. The aim of the control is to bring the system into a specified terminal set at the instant of termination. A feedback control method is proposed which ensures successful completion if the disturbance does not exceed a certain critical level. Here, "weak" disturbance is countered by a "weak" effective control. A guarantee theorem is formulated and proved. An illustrative example is considered.
Several misprints have been corrected in the paper.
pmm09eng.pdf (10 725 KB).
Ganebnyi S.A., Kumkov S.S., Patsko V.S.
Extremal aiming in problems with an unknown level of dynamic disturbance
// Journal of Applied Mathematics and Mechanics, vol. 73, 2009, pp. 411–420.
DOI: 10.1016/j.jappmathmech.2009.08.010