On optimal terminal control

This paper is concerned with the behavior, near the terminal time, of a fixed time fixed endpoint linear optimal control problem. The optimal control is represented in feedback form by a time-varying gain matrix operating on the present state of the system. The gain matrix is shown to have a pole at the final time. Furthermore, the limiting behavior of the gain matrix is shown to be independent of most of the parameters of the system and to depend solely on the orders of the matrices involved. Thus, the terminal behavior for this entire class of systems is identical to the behavior of a single limiting system.