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Iterative-learning procedures for nonlinear-model-order reduction in discrete time
IMA Journal of Mathematical Control and Information ( IF 1.5 ) Pub Date : 2019-12-11 , DOI: 10.1093/imamci/dnz028
Salim Ibrir 1
Affiliation  

Efficient numerical procedures are developed for model-order reduction of a class of discrete-time nonlinear systems. Based on the solution of a set of linear-matrix inequalities, the Petrov–Galerkin projection concept is utilized to set up the structure of the reduced-order nonlinear model that preserves the input-to-state stability while ensuring an acceptable approximation error. The first numerical algorithm is based on the construction of a constant optimal projection matrix and a constant Lyapunov matrix to form the reduced-order dynamics. The second proposed algorithm aims to incorporate the output of the original system to correct the instantaneous value of the truncation matrix and maintain an acceptable approximation error even with low-order systems. An extension to uncertain systems is provided. The usefulness and the efficacy of the developed procedures are approved by the consideration of two numerical examples treating a nonlinear low-order system and a high-dimensional system, issued from the discretization of the damped heat-transfer partial-differential equation.

中文翻译:

离散时间非线性模型降阶的迭代学习程序

为减少一类离散时间非线性系统的模型阶数,开发了有效的数值程序。根据一组线性矩阵不等式的解决方案,利用彼得罗夫-加勒金投影概念建立了降阶非线性模型的结构,该模型保留了输入至状态的稳定性,同时确保了可接受的近似误差。第一个数值算法是基于恒定的最优投影矩阵和恒定的Lyapunov矩阵的构造,以形成降阶动力学。提出的第二种算法旨在合并原始系统的输出,以校正截断矩阵的瞬时值并即使在低阶系统中也保持可接受的近似误差。提供了不确定系统的扩展。
更新日期:2019-12-11
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