Determination of functional parameters in boundary conditions of linear hyperbolic systems by optimal control methods

Abstract

Abstract An inverse problem of a functional parameter determination is considered for a hybrid system of population dynamics. Dynamics of several interacting populations is described by a system of first-order linear hyperbolic equations. The boundary conditions for this system are determined from the initial problem for ordinary differential equations. The problem is interpreted as an optimal control problem. A non-classic optimality condition of variational maximum principle type is proved. The original problem in distributed parameter systems is reduced to the optimal control problem for ordinary differential equations.