Neural Observer with Lyapunov Stability Guarantee for Uncertain Nonlinear Systems
Neural Observer with Lyapunov Stability Guarantee for Uncertain Nonlinear Systems
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DOI：
10.48550/arxiv.2208.13006
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发表时间：
2022-08
影响因子：
10.4
通讯作者：
Song Chen;Tehuan Chen;Chao Xu;Jian Chu
中科院分区：
文献类型：
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作者：
Song Chen;Tehuan Chen;Chao Xu;Jian Chu
在这篇文章中，我们提出了一种新的非线性观测器基于神经网络（NN），称为神经观测器，观测任务的线性时不变（LTI）系统和不确定的非线性系统。特别地，针对不确定系统设计的神经观测器受到自抗扰控制的启发，能够真实的实时测量不确定性。稳定性分析（例如，指数收敛速度），证明了观测问题只能用线性矩阵不等式（LMI）来解决.此外，它揭示了系统矩阵的可观性和可控性，以证明线性矩阵不等式的解的存在性。最后，在X-29 A飞机模型、非线性摆和四轮转向车辆三个仿真算例中验证了神经观测器的有效性。
In this article, we propose a novel nonlinear observer based on neural networks (NNs), called neural observers, for observation tasks of linear time-invariant (LTI) systems and uncertain nonlinear systems. In particular, the neural observer designed for uncertain systems is inspired by the active disturbance rejection control, which can measure the uncertainty in real time. The stability analysis (e.g., exponential convergence rate) of LTI and uncertain nonlinear systems (involving neural observers) are presented and guaranteed, where it is shown that the observation problems can be solved only using the linear matrix inequalities (LMIs). Also, it is revealed that the observability and controllability of the system matrices are required to demonstrate the existence of solutions for LMIs. Finally, the effectiveness of neural observers is verified in three simulation cases, including the X-29A aircraft model, the nonlinear pendulum, and the four-wheel steering vehicle.