Generic existence of solutions of nonconvex optimal control problems | Zendy

Alexander J. Zaslavski | Zendy

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Generic existence of solutions of nonconvex optimal control problems

Author(s) -

Alexander J. Zaslavski

Publication year - 2005

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/aaa.2005.375

Subject(s) - convexity , uniqueness , mathematics , class (philosophy) , optimal control , calculus (dental) , pure mathematics , mathematical optimization , mathematical analysis , computer science , artificial intelligence , medicine , dentistry , financial economics , economics

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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