Pontryagin Maximum Principle

A result in 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, pp. 295-296, 1980.