Sussmann, Hector (Rutgers Univ.)

Chattering Variations, Finitely Additive Measures, and the Nonsmooth Maximum Principle with State Space Constraints

Scheduled for presentation during the Mini-Symposium "Recent Developments in Optimal Control: Theory and Applications" (MoP11), Monday, July 24, 2006, 15:45−16:10, Room 104a

17th International Symposium on Mathematical Theory of Networks and Systems, July 24-28, 2006, Kyoto, Japan

This information is tentative and subject to change. Compiled on May 9, 2025

Abstract

Since the work of Milyutin and his collaborators in the 1970s, it has been clear that the correct formulation of the Pontryagin maximum principle with state space constraints involves finitely additive vector-valued measures of finite total variation. We prove a version of the maximum principle for data with very weak regularity properties, using the classical method of packets of needle variations (PNVs), as in Pontryagin's book, but coupling it with a nonclassical theory of multivalued differentials, the so-called "generalized differential quotients." The key technical point of our argument is the use of a different type of PNVs, that we call "chattering PNVs".