This paper extends Pontryagin's maximum principle to differential inclusions and nonsmooth criterion functions, relying on a checkable "surjectivity property" of a "linearized set-valued system" around the optimal trajectory. As an example, Pontryagin's principle is obtained for optimal control problems with constraints on both the initial and the final states. 

The research described here was undertaken within the framework of the Dynamics of Macrosystems Feasibility Study in the System and Decision Sciences Program.