A result is Control Theory. Define

Then in order for a control and a trajectory to be optimal, it is Necessary that there exist Nonzero absolutely continuous vector function corresponding to the functions and such that

- 1. The function
attains its maximum at the point almost everywhere in the interval
,

- 2. At the terminal time , the relations and are satisfied.

**References**

Iyanaga, S. and Kawada, Y. (Eds.). ``Pontrjagin's [sic] Maximum Principle.'' §88C in
*Encyclopedic Dictionary of Mathematics.* Cambridge, MA: MIT Press, p. 295-296, 1980.

© 1996-9

1999-05-26