Existence principle of an optimal control for a flexible beam with three turning axles

Abstract

A flexible robot beam with three turning axles is considered in this paper. An evolution equation corresponding to the beam system formulated by partial differential equations with initial and boundary conditions is established in an appropriate Hilbert space. Based on the results of spectral analysis and semigroup generation of the system operator studied previously, an optimal control of the robot beam system is invesigated. Finally, an existence principle of optimal control is proposed and proved.