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Generic well-posedness of nonconvex optimal control problems
Institution:1. CEFET/RJ, Departamento de Ensino Superior, DEPBG CEP: 20271-110, Rio de Janeiro, RJ, Brazil;2. UNICAMP – IMECC, Departamento de Matemática Aplicada, Caixa Postal 6065, CEP: 13081-970, Campinas, SP, Brazil;3. Departamento de Matemáticas, Facultad de Ciencias, UNAM 04510, México DF, Mexico;1. Department of Mathematics, Tianjin Polytechnic University, Tianjin 300160, China;2. Department of Mathematics Education and the RINS, Gyeongsang National University, Chinju 660-701, Republic of Korea;3. Department of Information Management, Cheng Shiu University, Kaohsiung 833, Taiwan;1. Department of Mathematics, Tianjin Polytechnic University, Tianjin 300160, China;2. Department of Mathematics and the RINS, Gyeongsang National University, Jinju 660-701, Republic of Korea;3. Department of Information Management, Cheng Shiu University, Kaohsiung 833, Taiwan;1. School of Mathematical Sciences, South China Normal University, Guangzhou 510631, Guangdong, PR China;2. Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Department of Mathematics, Xiangtan University, Xiangtan 411105, Hunan, PR China;1. Laboratorio di Tecnologia Medica, Istituto Ortopedico Rizzoli, Bologna, Italy;2. Dipartimento di Elettronica, Informatica e Sistemistica, Università di Bologna, Italy;3. Department of Anatomy, Université Libre de Bruxelles, Belgium;4. Movement Analysis Laboratory, Istituto Ortopedico Rizzoli, Bologna, Italy
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 our previous work a generic existence and uniqueness result (with respect to variations of the integrand of the integral functional) without the convexity condition was established for a class of optimal control problems satisfying the Cesari growth condition. In this paper we extend this generic existence and uniqueness result to a class of optimal control problems in which the right-hand side of differential equations is also subject to variations.
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