Optimal control of distributed systems with derivative dependent cost functionals

The optimal regulator of Distributed Parameter Systems with its cost functional involving time derivatives of distributed control vectors or state spatial and time derivative terms as well as the usual terms containing the control and state vectors has been analyzed by introducing augmented variables. A very significant result in modern control theory is that, for a linear, finite-dimensional, dynamical systems, the state feedback law derived from a quadratic performance index function minimization problem is linear. Generalization of the above result to a infinite-dimensional, distributed parameter dynamical systems with quadratic cost functional involving derivative terms is made possible from stability considerations. The state feedback law, realized by a linear distributed parameter dynamical system, has operator representations.