ABSTRACT
This chapter considers only differential inclusions that admits a "smooth" control representation of the form. In the literature one can find several different and unfortunately non-equivalent formulations of Pontryagin Maximum Principle (PMP). Two of most significant are: Pontryagin's formulation for control systems and F. H. Clarke's formulation for differential inclusion. The chapter devotes to finding such representations or even a full class of such representations. The regularity of a system implies that the classic PMP may be read as: every optimal solution is P-extremal. Any two regular tame control systems with the same nondegenerate corresponding differential inclusion have the same extremals.
