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

计算机与自动化 | Updated：2022-12-09

- Uniform modeling of parameter dependent nonlinear systems
- Uniform modeling of parameter dependent nonlinear systems
- 信息与电子工程前沿（英文） 2012年13卷第11期页码：850-858
- 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
  中图分类号： TP273
- 收稿：2012-04-03，
  
  修回：2012-10-12，
  
  纸质出版：2012-11
- Accepted：
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Uniform modeling of parameter dependent nonlinear systems[J]. 信息与电子工程前沿（英文）, 2012,13(11):850-858.

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.
Uniform modeling of parameter dependent nonlinear systems[J]. 信息与电子工程前沿（英文）, 2012,13(11):850-858. DOI： 10.1631/jzus.C1200096.

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

A. Bemporad . . Efficient conversion of mixed logical dynamical systems into an equivalent piecewise affine form . . IEEE Trans. Autom. Control , , 2004 . . 49 ( ( 5 ): ): 832 - - 838 . . DOI: 10.1109/TAC.2004.828315 http://doi.org/10.1109/TAC.2004.828315 . .

M. Bergami , , , F. Bizzarri , , , A. Carlevaro , , , M. Storace . . Structurally stable PWL approximation of nonlinear dynamical systems admitting limit cycles: an example . . IEICE Trans. Fund. Electron. Commun. Comput. Sci. , , 2006 . . 89 ( ( 10 ): ): 2759 - - 2766 . . DOI: 10.1093/ietfec/e89-a.10.2759 http://doi.org/10.1093/ietfec/e89-a.10.2759 . .

S. Boyd , , , L.E. Ghaoui , , , E. Feron , , , V. Balakrishnan . . Linear Matrix Inequalities in Systems and Control Theory . . Philadelphia, PA , , 1994 . . .

L. Breiman . . Hinging hyper-planes for regression, classification, and function approximation . . IEEE Trans. Inf. Theory , , 1993 . . 39 ( ( 3 ): ): 999 - - 1013 . . DOI: 10.1109/18.256506 http://doi.org/10.1109/18.256506 . .

M. Chien , , , E. Kuh . . Solving nonlinear resistive networks using piecewise-linear analysis and simplicial subdivision . . IEEE Trans. Circ. Syst. , , 1977 . . 24 ( ( 6 ): ): 305 - - 317 . . DOI: 10.1109/TCS.1977.1084349 http://doi.org/10.1109/TCS.1977.1084349 . .

O. de Feo , , , G. Maggio , , , M. Kennedy . . The Colpitts oscillator: families of periodic solutions and their bifurcations . . Int. J. Bifurc. Chaos , , 2000 . . 10 ( ( 5 ): ): 935 - - 958 . . DOI: 10.1142/S0218127400000670 http://doi.org/10.1142/S0218127400000670 . .

M. di Federico , , , P. Julin , , , T. Poggi , , , M. Storace . . Integrated circuit implementation of multi-dimensional piecewise-linear functions . . Dig. Signal Process. , , 2010 . . 20 ( ( 6 ): ): 1723 - - 1732 . . DOI: 10.1016/j.dsp.2010.02.007 http://doi.org/10.1016/j.dsp.2010.02.007 . .

Y. Gao , , , Z.H. Chen . . Robust H ∞ control for constrained discrete-time piecewise affine systems with time-varying parametric uncertainties . . IET Control Theory Appl. , , 2009 . . 3 ( ( 8 ): ): 1132 - - 1144 . . DOI: 10.1049/iet-cta.2008.0182 http://doi.org/10.1049/iet-cta.2008.0182 . .

W.P.M.H. Heemels , , , B. de Schutter , , , A. Bemporad . . Equivalence of hybrid dynamical models . . Automatica , , 2001 . . 37 ( ( 7 ): ): 1085 - - 1091 . . DOI: 10.1016/S0005-1098(01)00059-0 http://doi.org/10.1016/S0005-1098(01)00059-0 . .

P. Julian , , , A. Desages , , , O. Agamennoni . . High-level canonical piecewise linear representation using a simplicial partition . . IEEE Trans. Circ. Syst. I , , 1999 . . 46 ( ( 4 ): ): 463 - - 480 . . DOI: 10.1109/81.754847 http://doi.org/10.1109/81.754847 . .

P. Julian , , , A. Desages , , , B. D'Amico . . Orthonormal high level canonical PWL functions with applications to model reduction . . IEEE Trans. Circ. Syst. I , , 2000 . . 47 ( ( 5 ): ): 702 - - 712 . . DOI: 10.1109/81.847875 http://doi.org/10.1109/81.847875 . .

H. Lin , , , P. Antsaklis . . Robust Regulation of Polytopic Uncertain Linear Hybrid Systems with Networked Control System Applications . . In : Liu D., Antsaklis P.J., (Eds.), Stability and Control of Dynamical Systems with Applications: a Tribute to Anthony N. Michel. Birkhauser, Boston , , 2003a . . p.83 - - 108 . . . .

H. Lin , , , P. Antsaklis . . Robust Invariant Control Synthesis for Discrete Time Polytopic Uncertain Linear Hybrid Systems . . American Control Conf. , , 2003b . . p.5221 - - 5226 . . . .

J.N. Lin , , , R. Unbehauen . . Canonical piecewise-linear approximations . . IEEE Trans. Circ. Syst. I , , 1992 . . 39 ( ( 8 ): ): 697 - - 699 . . DOI: 10.1109/81.168933 http://doi.org/10.1109/81.168933 . .

G. Maggio , , , O. de Feo , , , M. Kennedy . . Nonlinear analysis of the Colpitts oscillator and applications to design . . IEEE Trans. Circ. Syst. I , , 1999 . . 46 ( ( 9 ): ): 1118 - - 1130 . . DOI: 10.1109/81.788813 http://doi.org/10.1109/81.788813 . .

T. Poggi . . Circuit Implementation of Piecewise-Affine Functions and Applications . . PhD Thesis, University of Genoa, Italy , , 2010 . . .

M. Storace , , , F. Bizzarri . . Towards accurate PWL approximations of parameter-dependent nonlinear dynamical systems with equilibria and limit cycles . . IEEE Trans. Circ. Syst. I , , 2007 . . 54 ( ( 3 ): ): 620 - - 631 . . DOI: 10.1109/TCSI.2006.887623 http://doi.org/10.1109/TCSI.2006.887623 . .

M. Storace , , , O. de Feo . . PWL approximation of nonlinear dynamical systems . . Part I: structural stability. J. Phys. , , 2005a . . 22 208 - - 221 . . . .

M. Storace , , , O. de Feo . . Piecewise-linear approximation of nonlinear dynamical systems . . IEEE Trans. Circ. Syst. I , , 2005b . . 51 ( ( 4 ): ): 830 - - 842 . . DOI: 10.1109/TCSI.2004.823664 http://doi.org/10.1109/TCSI.2004.823664 . .

M. Storace , , , P. Julin , , , M. Parodi . . Synthesis of nonlinear multiport resistors: a PWL approach . . IEEE Trans. Circ. Syst. I , , 2002 . . 49 ( ( 8 ): ): 1138 - - 1149 . . DOI: 10.1109/TCSI.2002.801253 http://doi.org/10.1109/TCSI.2002.801253 . .

M. Storace , , , L. Repetto , , , M. Parodi . . A method for the approximate synthesis of cellular nonlinear networks . . Part 1: circuit definition. Int. J. Circ. Theor. Appl. , , 2003 . . 31 ( ( 3 ): ): 277 - - 297 . . DOI: 10.1002/cta.232 http://doi.org/10.1002/cta.232 . .

J.M. Tarela , , , M.V. Martinez . . Region configurations for realizability of lattice piecewise-linear models . . Math. Comput. Model. , , 1993 . . 30 ( ( 11-12 ): ): 17 - - 27 . . DOI: 10.1016/S0895-7177(99)00195-8 http://doi.org/10.1016/S0895-7177(99)00195-8 . .

J. Thomas , , , S. Olaru , , , J. Buisson , , , D. Dumur . . Attainability and Set Analysis for Uncertain PWA Systems with Parameter Variations and Bounded Disturbance . . 21st Chinese Control and Decision Conf. , , 2009 . . p.4238 - - 4244 . . . .

A. Ulbig , , , S. Olaru , , , D. Dumur , , , P. Boucher . . Explicit nonlinear predictive control for a magnetic levitation system . . Asian J. Control , , 2010 . . 12 ( ( 3 ): ): 434 - - 442 . . DOI: 10.1002/asjc.191 http://doi.org/10.1002/asjc.191 . .

G. Zhai , , , H. Lin , , , P.J. Antsaklis . . Quadratic stabilizability of switched linear systems with polytopic uncertainties . . Int. J. Control , , 2003 . . 76 ( ( 7 ): ): 747 - - 753 . . DOI: 10.1080/0020717031000114968 http://doi.org/10.1080/0020717031000114968 . .

L. Zhang , , , C. Wang , , , L. Chen . . Stability and stabilization of a class of multimode linear discrete-time systems with polytopic uncertainties . . IEEE Trans. Ind. Electron. , , 2009 . . 56 ( ( 9 ): ): 3684 - - 3692 . . DOI: 10.1109/TIE.2009.2026375 http://doi.org/10.1109/TIE.2009.2026375 . .

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