Existence of local solutions in constrained dynamic systems

Abstract

The control systems with mixed constraints are considered in this article. The sufficient conditions for local solvability of this type of control systems are studied. For the function that defines mixed constraints two types of assumptions are presented. When the function is smooth, the assumption of its 2-regularity in the control variable is considered. For the case when the function is not smooth it is assumed that it has covering properties with respect to the control variable.

Keywords:

• control systems
• mixed constraints
• local solvability
• 2-regularity
• covering mappings

AMS Subject Classifications::

• 34H05
• 47J07

Acknowledgement

The investigation is supported by RFBR grant (project No 09-01-00619) and by the grant of the President of the Russian Federation (MK-119.2009.1).