Generic well-posedness of optimal control problems without convexity assumptions

The Tonelli existence theorem in the calculus of variations and its subsequ ent modi cations were established for integrands f which satisfy convexity and growth conditions. In A. J. Zaslavski [Nonlinear Anal., to appear], a g eneric existence and uniqueness result ( with respect to variations of the integrand of the integral functional) without the convexity condition was e stablished for a class of optimal control problems satisfying the Cesari gr owth condition. In this paper we extend the generic existence and uniquenes s result in A. J. Zaslavski [ Nonlinear Anal., to appear], to a class of op timal control problems in which constraint maps are also subject to variati ons. The main result of the paper is obtained as a realization of a variati onal principle extending the variational principle introduced in A. D. Ioff e and A. J. Zaslavski [SIAM J. Control Optim., 38 ( 2000), pp. 566-581].