AN APPROACH OF DETERMINISTIC CONTROL-PROBLEMS WITH UNBOUNDED DATA

被引：28

作者：

BARLES, G

机构：

[1] CEREMADE, Université de Paris-Dauphine, Place du Maréchal-De-Lattre-de-Tassigny, Cedex 16, Paris

来源：

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE | 1990年 / 7卷 / 04期

关键词：

Bellman Equations; comparison results; contraintes sur le gradient; Contrôle déterministe non borné; Deterministic unbounded control problems; gradient-constraints; Hamilton-Jacobi Equations; résultats de comparaison; équations de Bellman; équations de Hamilton-Jacobi;

D O I：

10.1016/S0294-1449(16)30290-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove that the value function of a deterministic unbounded control problem is a viscosity solution and the maximum viscosity subsolution of a family of Bellman Equations; in particular, the one given by the hamiltonian, generally discontinuous, associated formally to the problem by analogy with the bounded case. In some cases, we show that this equation is equivalent to a first-order Hamilton-Jacobi Equation with gradient constraints for which we give several existence and uniqueness results. Finally, we indicate other applications of these results to first-order H. J. Equations, to some cheap control problems and to uniqueness results in the nonconvex Calculus of Variations. © 2016 L'Association Publications de l'Institut Henri Poincaré

引用

页码：235 / 258

页数：24