Nonlinear MIMO observable normal forms with output injection and output diffeomorphism

IF 3.5 2区 数学 Q1 MATHEMATICS, APPLIED Applied Mathematics and Computation Pub Date : 2024-11-12 DOI:10.1016/j.amc.2024.129174
Jie Liu , Driss Boutat , Da-Yan Liu , Xue-Feng Zhang
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Abstract

This research note establishes a specific framework for transforming nonlinear multi-input and multi-output diffeomorphism systems into extended observable normal forms without using differential geometry techniques. For this purpose, the nonlinear MIMO systems whose nonlinear terms do not need to be Lipschitz, are proposed. First, a change of coordinates is designed to eliminate the square items and coupled items for each nonlinear dynamical subsystem. Second, coupled auxiliary dynamics are constructed to transform the nonlinear multi-input and multi-output diffeomorphism systems into extended observable normal forms such that the finite-time and robust step-by-step sliding mode observer can be applied. Then, the state variables for the considered nonlinear dynamical systems are estimated by using the inverse of the transformations. Finally, the validity of the proposed design methods is verified by two numerical examples.
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具有输出注入和输出差分的非线性多输入多输出可观测正则表达式
本研究论文建立了一个特定框架,无需使用微分几何技术,即可将非线性多输入和多输出差分系统转化为扩展的可观测正则表达式。为此,本文提出了非线性 MIMO 系统,其非线性项无需为 Lipschitz。首先,设计了一种坐标变化,以消除每个非线性动力学子系统的平方项和耦合项。其次,构建耦合辅助动力学,将非线性多输入和多输出差分系统转化为扩展的可观测正态形式,从而应用有限时间和鲁棒逐步滑模观测器。然后,利用逆变换估计所考虑的非线性动力系统的状态变量。最后,通过两个数值示例验证了所提设计方法的有效性。
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来源期刊
CiteScore
7.90
自引率
10.00%
发文量
755
审稿时长
36 days
期刊介绍: Applied Mathematics and Computation addresses work at the interface between applied mathematics, numerical computation, and applications of systems – oriented ideas to the physical, biological, social, and behavioral sciences, and emphasizes papers of a computational nature focusing on new algorithms, their analysis and numerical results. In addition to presenting research papers, Applied Mathematics and Computation publishes review articles and single–topics issues.
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