Open Access
21 June 2005 Generic existence of solutions of nonconvex optimal control problems
Alexander J. Zaslavski
Abstr. Appl. Anal. 2005(4): 375-421 (21 June 2005). DOI: 10.1155/AAA.2005.375


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.


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Alexander J. Zaslavski. "Generic existence of solutions of nonconvex optimal control problems." Abstr. Appl. Anal. 2005 (4) 375 - 421, 21 June 2005.


Published: 21 June 2005
First available in Project Euclid: 25 July 2005

zbMATH: 1106.49007
MathSciNet: MR2202487
Digital Object Identifier: 10.1155/AAA.2005.375

Rights: Copyright © 2005 Hindawi

Vol.2005 • No. 4 • 21 June 2005
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