Generic existence of solutions of nonconvex optimal control problems.

*(English)*Zbl 1106.49007The 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, the author makes a survey of several of his articles, concerning generic existence and uniqueness results (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, as well as, an application of a certain variational principle to classes of optimal control problems with various topologies in the corresponding spaces of integrands. As a realization of this principle, generic existence results have been established for classes of optimal control problems in which the constraints maps and the cost functions are variable. The author presents some new extensions of his previous results.

Reviewer: Maxim Todorov (Puebla)

##### MSC:

49J22 | Optimal control problems with integral equations (existence) (MSC2000) |

49J53 | Set-valued and variational analysis |