Guerra, Manuel (ISEG/Tech. Univ. of Lisbon), Sarychev, Andrey (Univ. di Firenze)

Regularizations of Optimal Control Problems for Control-Affine Systems

Scheduled for presentation during the Mini-Symposium "Recent Developments in Optimal Control: Theory and Applications" (MoP11), Monday, July 24, 2006, 17:25−17:50, 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 April 23, 2024

Abstract

An open problem has been suggested by Yu. Orlov for a recently published volume "Unsolved Problems in Mathematical Systems and Control Theory", V.D. Blondel & A. Megretski (eds), Princeton Univ. Press, 2004. The problem regards possible approaches to regularization of control-affine optimal control problems which may admit 'cheap (generalized) controls' as minimizers. We show that Orlov's conjecture admits, in general, a positive answer, independently of commutativity assumptions for the controlled fields and other issues typically involved in the study of generalized controls.

We propose an index to measure the "singular behavior" of minimizing sequences for control-affine optimal control problems. It is shown that, in the particular case of singular linear-quadratic problems, this index is tightly related to the "order of singularity" of the problem. A partial result for the commutative nonlinear case is presented.