On a Problem of Optimal Control for a Nonlinear Pseudohyperbolic Equation

• Main Author: T. K. Yuldashev
• Format: Article
• Language: English
• Published: Yaroslavl State University 2013-10-01
• Series: Modelirovanie i Analiz Informacionnyh Sistem
• Subjects: optimal control; generalized solvability; integral identity; approximate solution; functional minimization
• Online Access: https://www.mais-journal.ru/jour/article/view/175

In this article, it is considered some questions of approximation solving of an optimal control problem for nonlinear partial pseudohyperbolic differential equations of the fifth order with initial-boundary value conditions and general view of the optimality criterion. Using the method of separation of variables in the form of a Fourier series reduces the generalized solution of the initial-boundary value problem to a countable system of nonlinear integral equations. By the aid of the methods of successive approximations and integral inequalities it is studied the one-value solvability of a finite system of nonlinear integral equations for the fixed values of the control, which are bounded by the given positive constant. It is estimated the permissible error with respect to a state of a ”shorter” generalized solution of the initial-boundary value problem. Further, it is proved that the control sequence is a minimizing sequence for the considered problem.