Generic existence of Lipschitzian solutions of optimal control problems without convexity assumptions

[摘要] 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. (c) 2007 Elsevier Inc. All rights reserved.

[发布日期] 2007-11-15

[关键词] Banach space;integrand;generic result;optimal control problem