Abstract and Applied Analysis
Volume 2005 (2005), Issue 4, Pages 375-421
doi:10.1155/AAA.2005.375
Generic existence of solutions of nonconvex optimal control problems
Department of Mathematics, Technion – Israel Institute of Technology, Haifa 32000, Israel
Received 8 December 2003
Copyright © 2005 Alexander J. Zaslavski. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
The Tonelli existence theorem in the calculus of variations and its subsequent modifications
were established for integrands f which satisfy convexity and growth conditions. In 1996, the author
obtained a generic existence and uniqueness result (with respect to variations of the integrand of the integral functional)
without the convexity condition for a class of optimal control problems satisfying the Cesari growth condition. In this paper, we
survey this result and its recent extensions, and establish several new results in this direction.