Bounded-from-below solutions of the Hamilton-Jacobi equation for optimal control problems with exit times: vanishing lagrangians eikonal equations, and shape-from-shading

作     者：Malisoff, M 

作者机构：Louisiana State Univ Dept Math Baton Rouge LA 70803 USA 

出 版 物：《NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS》 (非线性微分方程与应用)

年 卷 期：2004年第11卷第1期

页      面：95-122页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

主　　题：optimal control dynamic programming viscosity solutions exit time problems 

摘      要：We study the Hamilton-Jacobi equation for undiscounted exit time control problems with general nonnegative Lagrangians using the dynamic programming approach. We prove theorems characterizing the value function as the unique bounded-from-below viscosity solution of the Hamilton-Jacobi equation that is null on the target. The result applies to problems with the property that all trajectories satisfying a certain integral condition must stay in a bounded set. We allow problems for which the Lagrangian is not uniformly bounded below by positive constants, in which the hypotheses of the known uniqueness results for Hamilton-Jacobi equations are not satisfied. We apply our theorems to eikonal equations from geometric optics, shape-from-shading equations from image processing, and variants of the Puller Problem.