The structure of the optimal tracking problem for distributed-parameter systems

The class of systems considered in this paper includes, among others, the classical self-adjoint Sturm-Liouville problems of partial differential equations. The control term is an additive inhomogeneous term in the system equations, and the control problem is that of minimizing the weighted sum of the system error and control. New results include the derivation of a sufficient condition for the optimal control and existence and uniqueness theorems for the solution of the associated two-point boundary-value problem. These results are illustrated by an example.