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Front. Inform. Technol. Electron. Eng.  2012, Vol. 13 Issue (11): 850-858    DOI: 10.1631/jzus.C1200096
    
Uniform modeling of parameter dependent nonlinear systems
Najmeh Eghbal, Naser Pariz, Ali Karimpour
Department of Electrical Engineering, Ferdowsi University of Mashhad, P. O. Box 91775-1111, Iran
Uniform modeling of parameter dependent nonlinear systems
Najmeh Eghbal, Naser Pariz, Ali Karimpour
Department of Electrical Engineering, Ferdowsi University of Mashhad, P. O. Box 91775-1111, Iran
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摘要： 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 ‘multiplied simplices’. 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： Parameter dependent nonlinear systems;  Approximation method;  Parameter dependent piecewise affine systems;  Modeling    
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 ‘multiplied simplices’. 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.
Key words: Parameter dependent nonlinear systems    Approximation method    Parameter dependent piecewise affine systems    Modeling
收稿日期: 2012-04-03 出版日期: 2012-11-02
CLC:  TP273  
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Najmeh Eghbal
Naser Pariz
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Najmeh Eghbal, Naser Pariz, Ali Karimpour. Uniform modeling of parameter dependent nonlinear systems. Front. Inform. Technol. Electron. Eng., 2012, 13(11): 850-858.

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http://www.zjujournals.com/xueshu/fitee/CN/10.1631/jzus.C1200096    或    http://www.zjujournals.com/xueshu/fitee/CN/Y2012/V13/I11/850

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