Asymptotic solution of the optimal control problem for standard systems with delay

Abstract

The authors consider the construction of an asymptotic solution of the terminal optimal control problem using the averaging method. The optimal process is described by the equation z = eZ (t, z, z(t-l, e, u), u), z/t=[-1,0] = {var_phi}(t), where the delay is constant and of unit magnitude, z {element_of} G is an n-dimensional vector, G {contained_in} R{sup n}, e > 0 is a small parameter, t {element_of} T {triple_bond} [0, e{sup -1}], Z {var_phi} are n-dimensional vector functions, Z is strictly convex in u for any (t, z) {element_of} T X G, u {element_of} U is the r-dimensional control vector, U is a compact set.