Generic well-posedness of nonconvex optimal control problems Original Research Article

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.