保守性降低的非线性模型的线性变参数嵌入
Linear Parameter-Varying Embedding of Nonlinear Models with Reduced Conservativeness
摘要：
本文提出了一种将非线性系统的动力学描述嵌入到线性变参数（LPV）系统表示中的系统方法。最初，使用多元多项式回归来近似模型表示中的非线性函数。考虑到残差的近似作为潜在的调度参数，主成分分析（PCA）进行引入一组有限的辅助调度参数，在应付贸易？模型的准确性和复杂性之间的关系。以这种方式，LPV嵌入的非线性系统和调度变量的选择，共同执行，使得一个很好的交易o？LPV模型多项式地依赖于一些状态变量，并依赖于引入的辅助调度变量，这些变量共同构成了整个调度向量。该方法被施加到一个两自由度（2-DOF）的机器人机械手除了一个学术的例子，以揭示所提出的方法的有效性，并显示所提出的方法的优点与文献中的一些可用的结果相比。
英文摘要：
In this paper, a systematic approach is developed to embed the dynamical description of a nonlinear system into a linear parameter-varying (LPV) system representation. Initially, the nonlinear functions in the model representation are approximated using multivariate polynomial regression. Taking into account the residuals of the approximation as the potential scheduling parameters, a principle component analysis (PCA) is conducted to introduce a limited set of auxiliary scheduling parameters in coping with the trade-o? between model accuracy and complexity. In this way, LPV embedding of the nonlinear systems and scheduling variable selection are jointly performed such that a good trade-o? between complexity and conservativeness can be found. The developed LPV model depends polynomially on some of the state variables and affinely on the introduced auxiliary scheduling variables, which all together comprise the overall scheduling vector. The methodology is applied to a two-degree of freedom (2-DOf) robotic manipulator in addition to an academic example to reveal the effectiveness of the proposed method and to show the merits of the presented approach compared with some available results in the literature.
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