半线性热方程的反馈零能控性

刘宏超;岳红云

系统科学与数学 ›› 2009, Vol. 29 ›› Issue (4) : 555-561.

PDF(304 KB)
PDF(304 KB)
系统科学与数学 ›› 2009, Vol. 29 ›› Issue (4) : 555-561. DOI: 10.12341/jssms08393
论文

半线性热方程的反馈零能控性

    刘宏超, 岳红云
作者信息 +

Feedback Null Controllability of the Semilinear Heat Equation

    LIU Hongchao, YUE Hongyun

Author information +
文章历史 +

摘要

考虑具有Lipschitz非线性项,半线性热方程的最优控制问题.我们将运用观测不等式,证明值函数φ作为相应Hamilton-Jacobi方程的唯一粘性正解是局部Lipschitz连续的.最后,运用动态规划方法,得到系统最优的反馈控制.

Abstract

The quadratic control problem is considered for the semilinear heat equation with Lipschitz nonlinearity and associated cost function. It is proved that the value
function is locally Lipschitz using by the observability inequality and then can be characterized as the unique positive viscosity solution of the corresponding Hamilton-Jacobi equation. Consequently the optimal feedback law is obtained.

关键词

最优控制 / 零能控性 / 反馈控制 / 值函数 / Hamilton-Jacobi方程.

Key words

Null controllability / feedback law / value function / Hamilton-Jacobi equation.

引用本文

导出引用
刘宏超 , 岳红云. 半线性热方程的反馈零能控性. 系统科学与数学, 2009, 29(4): 555-561. https://doi.org/10.12341/jssms08393
LIU Hongchao , YUE Hongyun . Feedback Null Controllability of the Semilinear Heat Equation. Journal of Systems Science and Mathematical Sciences, 2009, 29(4): 555-561 https://doi.org/10.12341/jssms08393
中图分类号: 49J20   
PDF(304 KB)

160

Accesses

0

Citation

Detail

段落导航
相关文章

/