Geodesic
On a Problem of Optimal Control for a Nonlinear Pseudohyperbolic Equation
Modelirovanie i analiz informacionnyh sistem, Tome 20 (2013) no. 5, pp. 78-89

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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.
Keywords: optimal control, generalized solvability, integral identity, approximate solution, functional minimization. 
@article{MAIS_2013_20_5_a4,
     author = {T. K. Yuldashev},
     title = {On a {Problem} of {Optimal} {Control} for a {Nonlinear} {Pseudohyperbolic} {Equation}},
     journal = {Modelirovanie i analiz informacionnyh sistem},
     pages = {78--89},
     publisher = {mathdoc},
     volume = {20},
     number = {5},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MAIS_2013_20_5_a4/}
}
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T. K. Yuldashev. On a Problem of Optimal Control for a Nonlinear Pseudohyperbolic Equation. Modelirovanie i analiz informacionnyh sistem, Tome 20 (2013) no. 5, pp. 78-89. http://geodesic.mathdoc.fr/item/MAIS_2013_20_5_a4/