Discontinuous control problems for non-convex dynamics and near viability for singularly perturbed control systems

被引：7

作者：

Goreac, Dan ^{[2
]}

Serea, Oana-Silvia ^{[1
]}

机构：

[1] Ecole Polytech, CMAP, F-91128 Palaiseau, France

[2] Univ Paris Est Marne la Vallee, LAMA, UMR8050, F-77454 Marne La Vallee, France

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2010年 / 73卷 / 08期

关键词：

Optimal control; Singular perturbations; Near viability; Hamilton-Jacobi-Bellman equations; VISCOSITY SOLUTIONS; DIFFERENTIAL-GAMES; SETS;

D O I：

10.1016/j.na.2010.06.050

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The aim of this paper is to study two classes of discontinuous control problems without any convexity assumption on the dynamics. In the first part we characterize the value function for the Mayer problem and the supremum cost problem using viscosity tools and the notion of epsilon-viability (near viability). These value functions are given with respect to discontinuous cost functionals. In the second part we obtain results describing the epsilon-viability (near viability) of singularly perturbed control systems. (C) 2010 Elsevier Ltd. All rights reserved.

引用

页码：2699 / 2713

页数：15

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