MAXIMUM PRINCIPLE FOR THE OPTIMAL-CONTROL OF A HYPERBOLIC EQUATION INONE SPACE DIMENSION .2. APPLICATION

The optimal open-loop control of a beam subject to initial disturbance s is studied by means of a maximum principle developed for hyperbolic partial differential equations in one space dimension. The cost functi onal representing the dynamic response of the beam is taken as quadrat ic in the displacement and its space and time derivatives. The objecti ve of the control is to minimize a performance index consisting of the cost functional and a penalty term involving the control function. Ap plication of the maximum principle leads to boundary-value problems fo r hyperbolic partial differential equations subject to initial and ter minal conditions. The explicit solution of this system is obtained yie lding the expressions for the state and optimal control functions. The behavior of the controlled and uncontrolled beam is studied numerical ly, and the effectiveness of the proposed control is illustrated.