LINEARIZED REQUIRED OPTIMALITY CONDITIONS IN ONE SMOOTH GURSA-DARBU SYSTEM MANAGEMENT PROBLEM

Abstract

In class measurable (in Lebesgue sense) and bounded control vector functions, we consider one non-smooth optimal control problem of the Goursat – Darboux system with a multipoint quality functional, which is a generalization terminal type functional. Applying one modified version of the increment method, and assuming that the right side of the equation and the functional qualities in a vector state have derivatives in any direction, the necessary optimality condition in derivative terms in the direction flax general is proved. The case of a quasidifferentiable quality functional is considered. In particular, the minimax problem is studied. Under the assumption that the control region is convex, taking into account the properties of non-differentiable functions, the necessary optimality condition is established, which is an analog of the linearized integral principle of maximin, which is constructive in nature and generalizes the point wise linearized (differential) maximum principle.