ON OPTIMALITY OF SINGULAR CONTROLS IN AN OPTIMAL CONTROL PROBLEM.

In this paper, a Moskalenko type optimal control problem is considered. We consider the optimal control problem of minimizing the terminal type functional (Equation presented) under constraints (Equation presented) Here, f(t,x,z,u) (g(x,y,v)) is an n-dimensional vector function which is continuous on the set of variables, together with partial derivatives with respect to z (y) up to second order, t 0 ,t 1 , x 0 ,x 1 (t 0 < t 1 ,x 0 <x 1 ) are given, φ(y) (G(x,z)) is a given twice continuously differentiable with respect to y (z) scalar function, U (V) is a given nonempty bounded set, and u(t,x) is an r-dimensional control vector function piecewise continuous with respect to t and continuous with respect to x, v(x) is a q-dimensional piecewise continuous vector of control actions. The necessary optimality conditions for singular controls in the sense of the Pontryagin maximum principle have been obtained. © 2018 Tomsk State University. All rights reserved.