Optimal control methods in solving inverse problems of mathematical physics for first-order hyperbolic systems

摘要

The paper deals with using optimal control methods for solving inverse problems of mathematical physics. In many cases this problem can be considered as an optimal control problem in which unknown control functions are smooth elements of initial or boundary conditions, coefficients of differential operators or right-hand sides of differential equations. A non-classic optimality condition and numerical algorithm for smooth boundary controls in semi-linear first-order hyperbolic systems are presented. The special feature of the general optimization problem for boundary conditions is non-validity of the classic optimality condition of Pontryagin's type. The suggested approach is based on special variations of admissible continuously differentiable controls. These variations can be applied for controls satisfying either restrictions of inclusion type or integral restrictions.