To the Necessary Conditions of Optimality of the First and Second Order in the Problem of Optimal Control of the Rosser Type Equations Discrete Systemstems

Abstract

This article considers an optimal process control problem described by a system of nonlinear Rosser-type difference equations. The process is controlled using a boundary condition. This boundary condition is a solution to an analog of the Cauchy problem for a nonlinear Volterra-type difference equation. The control domain is assumed to be bound and open. By introducing a special variation of the control function, the first and second variations (in the classical sense) of the performance functional are calculated. Taking advantage of the arbitrariness of the admissible variation of the control function, a first-order necessary optimality condition is proven in the form of an analog of the Euler equation from the calculus of variations. Considering the non-negativity of the second variation of the functional along the optimal control, a general second-order necessary optimality condition is proved. From this, a few necessary optimality conditions are derived that are explicit, i.e., expressed in terms of the parameters of the optimal control problem under consideration.