Conditions for Feedback Linearization of Network Systems
Conditions for Feedback Linearization of Network Systems
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DOI：
10.1109/lcsys.2020.2981339
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发表时间：
2020-07-01
影响因子：
3
通讯作者：
Pasqualetti, Fabio
中科院分区：
文献类型：
--
作者：
Menara, Tommaso;Baggio, Giacomo;Pasqualetti, Fabio
反馈线性化允许通过坐标变换和反馈定律将非线性系统局部变换为等效线性系统。大规模非线性网络系统的反馈线性化通常很困难，因为随着网络规模变大，现有条件变得更难以检查。在这封信中，我们提供了新颖的条件来测试非线性网络是否可反馈线性化。具体来说，给定一些注入到一组网络节点的专用控制输入，我们得出一个易于检查的代数条件，可以在某些所需工作点评估的网络动态的雅可比矩阵上进行测试。此外，我们的要求足以满足（局部）可控性，从而为大规模非线性网络的可控性提供了可测试的条件。最后，我们通过在耦合振荡器网络中强制形成所需的同步模式来验证我们的发现。
Feedback linearization allows for the local transformation of a nonlinear system to an equivalent linear one by means of a coordinate transformation and a feedback law. Feedback linearization of large-scale nonlinear network systems is typically difficult, since existing conditions become harder to check as the network size becomes larger. In this letter, we provide novel conditions to test whether a nonlinear network is feedback-linearizable. Specifically, given some dedicated control inputs injected to a set of network nodes, we derive an easy-to-check algebraic condition that can be tested on the Jacobian matrix of the network dynamics evaluated at some desired working point. Furthermore, our requirements are sufficient for (local) controllability, and thus provide a testable condition for controllability of large-scale nonlinear networks. Finally, we validate our findings by enforcing the formation of desired synchronization patterns in networks of coupled oscillators.