An optimal control for a hybrid hyperbolic dynamic system

Abstract

In this paper, we are concerned with a hybrid hyperbolic dynamic system formulated by partial differential equations with initial and boundary conditions. An optimal energy control of the system is investigated. First, the system is transformed to an abstract evolution system in an appropriate Hilbert space, and then semigroup generation of the system operator is discussed. Finally, an optimal energy control problem is proposed and it is shown that an optimal energy control can be obtained by a finite dimensional approximation.