Uniform modeling of parameter dependent nonlinear systems

Najmeh EGHBAL; Naser PARIZ; Ali KARIMPOUR

doi:10.1631/jzus.C1200096

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Uniform modeling of parameter dependent nonlinear systems

Computer & Automation | Updated：2022-12-09

- Uniform modeling of parameter dependent nonlinear systems
- Uniform modeling of parameter dependent nonlinear systems
- Frontiers of Information Technology & Electronic Engineering Vol. 13, Issue 11, Pages: 850-858(2012)
- Affiliations：
  
  Department of Electrical Engineering, Ferdowsi University of Mashhad, P. O. Box 91775-1111, Iran
- Author bio：
  
  [ "Najmeh EGHBAL, E-mail: najmeh.eghbal@gmail.com" ]
- Funds：
- DOI：10.1631/jzus.C1200096
  CLC： TP273
- Received：03 April 2012，
  
  Revised：2012-10-12，
  
  Published：2012-11
- Accepted：
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Najmeh EGHBAL, Naser PARIZ, Ali KARIMPOUR. Uniform modeling of parameter dependent nonlinear systems[J]. Frontiers of Information Technology & Electronic Engineering, 2012, 13(11): 850-858.
DOI：

Najmeh EGHBAL, Naser PARIZ, Ali KARIMPOUR. Uniform modeling of parameter dependent nonlinear systems[J]. Frontiers of Information Technology & Electronic Engineering, 2012, 13(11): 850-858. DOI： 10.1631/jzus.C1200096.

摘要

Abstract

This paper addresses the problem of approximating parameter dependent nonlinear systems in a unified framework. This modeling has been presented for the first time in the form of parameter dependent piecewise affine systems. In this model

the matrices and vectors defining piecewise affine systems are affine functions of parameters. Modeling of the system is done based on distinct spaces of state and parameter

and the operating regions are partitioned into the sections that we call nmultiplied simpliceso. It is proven that this method of partitioning leads to less complexity of the approximated model compared with the few existing methods for modeling of parameter dependent nonlinear systems. It is also proven that the approximation is continuous for continuous functions and can be arbitrarily close to the original one. Next

the approximation error is calculated for a special class of parameter dependent nonlinear systems. For this class of systems

by solving an optimization problem

the operating regions can be partitioned into the minimum number of hyper-rectangles such that the modeling error does not exceed a specified value. This modeling method can be the first step towards analyzing the parameter dependent nonlinear systems with a uniform method.

关键词

Keywords

references

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