Minimization of a convex functional in a linear system of delay differential equations with fixed ends

摘要

A numerical method is proposed for solving the problem of moving a dynamic object described by a system of linear differential-difference equations to the origin with the minimization of a nonnegative convex functional. The method is proved to converge globally to an e{open}-optimal solution. The e{open}-optimal solution is understood as an extremal control u(t), t ∈ [0, T], that moves the system to the e{open}-neighborhood of the origin.