A solution to the optimal pursuit problem for distributed parameter systems

摘要

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 “squares” of, the system error and control. New results include the derivation of a sufficient condition for the optimal control, existence, and uniqueness theorems for the solution of the associated “two-point boundary-value problem,” and an algorithm whose solutions converge to be optimal control. These results are illustrated by an example.