An approximation scheme for the minimum time function
An approximation scheme for the minimum time function
复制标题
最小时间函数的近似方案
DOI：
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发表时间：
1990
期刊：
影响因子：
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通讯作者：
M. Falcone
中科院分区：
文献类型：
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作者：
M. Bardi;M. Falcone
本文对具有紧目标的非线性最小时间问题提出了一种近似格式。该计划是来自离散动态规划原理和主要的收敛结果，通过应用有关的技术不连续粘性解的Hamilton-Jacobi方程。在一般能控性假设下，证明了该方法在连续和离散系统上的收敛性。给出了系统和目标能控的一个显式充分条件。当目标光滑时，该条件是最小时间函数Lipschitz连续的充分必要条件。一个点形目标的情况下的扩展。
This paper presents an approximation scheme for the nonlinear minimum time problem with compact target. The scheme is derived from a discrete dynamic programming principle and the main convergence result is obtained by applying techniques related to discontinuous viscosity solutions for Hamilton–Jacobi equations. The convergence is proved under general controllability assumptions on both the continuous-time and the discrete-time systems. An explicit sufficient condition on the system and the target ensuring the desired controllability is given. This condition is shown to be necessary and sufficient for the Lipschitz continuity of the minimum time function if the target is smooth. An extension to the case of a point-shaped target is given.