Nonoccurrence of gap for infinite-dimensional control problems with nonconvex integrands

Abstract

In this article we establish nonoccurrence of gap for two classes of infinite-dimensional control systems with nonconvex integrands. For the first class of integrands we show the existence of a minimizing sequence of trajectory-control pairs with bounded controls while for the second class we establish that an infimum on the full admissible class is equal to the infimum on a set of trajectory-control pairs with controls which are bounded by the same constant.

Keywords:

• Banach space
• Hilbert space
• Integrand
• Lavrentiev phenomenon
• Optimal control problem

Keywords:

• 1991 Mathematics Subject Classifications: 49J27