Optimization for nonlinear hyperbolic equations without the uniqueness theorem for a solution of the boundary-value problem

S. Ya. Serovaĭskiĭ

Al-Farabi Kazakh National University

Abstract: We consider the optimal control problem for a system governed by a nonlinear hyperbolic equation without any constraints on the parameter of nonlinearity. No uniqueness theorem is established for a solution to this problem. The control-state mapping of this system is not Gateaux differentiable. We study an approximate solution of the optimal control problem by means of the penalty method.

Keywords: optimal control, hyperbolic equation, penalty method, approximate solution.

UDC: 517.977

Received: 26.01.2007

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2009, 53:1, 64–70

Bibliographic databases:

• 
•