Control Lyapunov Functions and Zubov's Method
Control Lyapunov Functions and Zubov's Method
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DOI：
10.1137/06065129x
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发表时间：
2008
期刊：
影响因子：
--
通讯作者：
F. Camilli;L. Grüne;Fabian R. Wirth
中科院分区：
文献类型：
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作者：
F. Camilli;L. Grüne;Fabian R. Wirth
对于有限维非线性控制系统，研究了渐近零能控性与控制李雅普诺夫函数之间的关系。结果表明，控制李雅普诺夫函数（CLF）可以构造在域的渐近零可控性作为粘性解的一阶PDE，推广Zubov方程。解也作为最优控制问题的值函数给出，由此可得到若干正则性结果。
For finite-dimensional nonlinear control systems we study the relation between asymptotic null-controllability and control Lyapunov functions. It is shown that control Lyapunov functions (CLFs) may be constructed on the domain of asymptotic null-controllability as viscosity solutions of a first order PDE that generalizes Zubov's equation. The solution is also given as the value function of an optimal control problem from which several regularity results may be obtained.