Model reduction of unstable systems using balanced truncation method and its application to shallow water equations

International Conference on Mathematics: Education, Theory and Application

数学;教育

Mustaqim, Kiki^1 ; Arif, Didik Khusnul^1 ; Apriliani, Erna^1 ; Adzkiya, Dieky^1

Department of Mathematics, Institut Teknologi Sepuluh Nopember, Surabaya, 60111, Indonesia^1

关键词: Balanced truncation method;    Dynamic behaviors;    Higher order modeling;    ITS applications;    Model reduction;    Original model;    Shallow water equations;    Unstable system;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/855/1/012029/pdf
DOI  :  10.1088/1742-6596/855/1/012029

学科分类：发展心理学和教育心理学

来源: IOP

【 摘 要 】

In this paper, we discuss the reduction of unstable systems. Suppose we have a large-scale unstable system. The reduction of such systems are done in order to obtain a simpler model that has a similar behavior with the original model. In reality, a higher order model is not preferred because the computation takes more time. Thus we need a method to reduce the order of a model that is known as model reduction. Model reduction of a system is the method of approximation of a system with a lower order but the dynamic behavior is equal or almost equal to the original model. In this paper, we discuss model reduction of unstable systems. Finally this method is applied to shallow water equation that describes the flow of water in rivers: we obtain a procedure for model reduction of unstable systems and the reduced model of shallow water equations.