ON THE CONSTRUCTION OF SOLUTION TO NONREGULAR PROBLEMS OF OPTIMAL-CONTROL

In this paper a problem of asymptotical optimization under perturbed constraints is investigated. Conditions of partial stability and non-sensitivity with respect to certain kinds of perturbations are obtained. A correct extension in a special class of vector-valued finitely-additive measures is suggested; natural relations between exact, generalized and approximate solutions are stated; the relations are expressed in terms of closures of admisible sets and the sets of the optimal and "almost" optimal solutions. Applications to certain problems of optimal control are considered.