A control operator and some of its applications

The conventional function space algorithms for solving minimization of penalized cost functional for optimal control problem characterized by linear-system integral quadratic cost due to Di Pillo and others, though falling within the framework pertinent to the conjugate gradient method algorithm, is difficult to apply computationally. The difficulty arises principally because there exists in the algorithm a number of stringent requirements imposed on the minimization procedures to facilitate its convergence. Incidentally, such computations are very cumbersome to carry out numerically. To circumvent this major numerical draw back, we construct here a control operator associated with this class of problems and use our explicit knowledge of the operator to devise an extended conjugate gradient method algorithm for solving this family of problems. Furthermore, the establishment of some functional inequalities which are obtained using the knowledge of the control operator is discussed.