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首页> 外文期刊>IEEE Transactions on Automatic Control >Control-Sharing and Merging Control Lyapunov Functions
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Control-Sharing and Merging Control Lyapunov Functions

机译：控制共享和合并控制Lyapunov函数

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摘要

Given two control Lyapunov functions (CLFs), a “merging” is a new CLF whose gradient is a positive combination of the gradients of the two parents CLFs. The merging function is an important trade-off since this new function may, for instance, approximate one of the two parents functions close to the origin, while being close to the other far away. For nonlinear control-affine systems, some equivalence properties are shown between the control-sharing property, i.e., the existence of a single control law which makes simultaneously negative the Lyapunov derivatives of the two given CLFs, and the existence of merging CLFs. It is shown that, even for linear time-invariant systems, the control-sharing property does not always hold, with the remarkable exception of planar systems. The class of linear differential inclusions is also discussed and similar equivalence results are presented. For this class of systems, linear matrix inequalities conditions are provided to guarantee the control-sharing property. Finally, a constructive procedure, based on the recently considered “R-functions,” is defined to merge two smooth positively homogeneous CLFs.
机译：给定两个控制Lyapunov函数（CLF），“合并”是一个新的CLF，其梯度是两个父CLF的梯度的正组合。合并功能是一个重要的权衡，因为此新功能可能（例如）近似两个接近原始值的父函数之一，而另一个靠近另一个原函数。对于非线性控制仿射系统，在控制共享特性之间显示了一些等价特性，即，存在一个使两个给定CLF的Lyapunov导数同时为负的单一控制定律和合并CLF的存在。结果表明，即使对于线性时不变系统，控制共享属性也并不总是成立，平面系统例外。还讨论了线性微分包含物的类别，并给出了相似的等效结果。对于此类系统，提供了线性矩阵不等式条件以保证控制共享特性。最后，基于最近考虑的“ R函数”，定义了一个构造性过程来合并两个平滑的正齐次CLF。

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