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Generic existence of Lipschitzian solutions of optimal control problems without convexity assumptions
Authors:Alexander J Zaslavski
Institution:Department of Mathematics, The Technion—Israel Institute of Technology, 32000 Haifa, Israel
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 this paper we consider a large class of optimal control problems which is identified with a complete metric space of integrands without convexity assumptions and show that for a generic integrand the corresponding optimal control problem possesses a unique solution and this solution is Lipschitzian.
Keywords:Banach space  Integrand  Generic result  Optimal control problem
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