Approximate Solution of an Optimal Control Dot Mobile Problem for a Nonlinear Hyperbolic Equation

Abstract

In this article, we consider the approximate solution of an optimal control dot mobile problem for a system of nonlinear partial hyperbolic and ordinary differential equations with initial and boundary value conditions and a nonlinear optimality criterion. The use of the Fourier method of variables separation reduces the generalized solution of the initial-boundary value problem to the countable system of nonlinear integral equations (CSNIE). To ease the computational procedures, it is considered the corresponding shorter (truncated) system of nonlinear integral equations (SSNIE) instead of CSNIE. By the methods of successive approximations and integral inequalities, it is studied the one-value solvability of SSNIE for the fixed values of the control. It is estimated a permissible error with respect to the shorter generalized solution of the initial-boundary value problem. It is approximately calculated the nonlinear functional of quality under the known optimal operating influences.

Keywords

• hyperbolic equation
• initial and boundary value conditions
• dot mobile optimal control
• generalized solvability
• functional minimization
• approximate solution