Two steps piecewise affine identification of nonlinear systems

• Autorzy: Stevek J. , Szucs A. , Kvasnica M. , Fikar M. , Kozak S.
• Języki publikacji: PL

Abstrakty

EN

Given a set of input-output measurements, the paper proposes a method for approximation of a nonlinear system by a piecewise affine model (PWA). First step of the two-stage procedure is identification from input-output data, in order to obtain an appropriate nonlinear function in analytic form. The analytic expression of the model can be represented either by a static nonlinear function or by a dynamic system and can be obtained using a basis function expansion modeling approach. Subsequently we employ nonlinear programming to derive optimal PWA approximation of the identified model such that the approximation error is minimized. Moreover, we show that approximation of multivariate systems can be transformed into a series of one-dimensional approximations, which can be solved efficiently using standard optimization techniques.

Słowa kluczowe

EN

piecewise affine systems; piecewise linear; approximation; nonlinear systems; orthogonal polynomials; basis function expansion

• Wydawca: Polish Academy of Sciences, Committee of Automatic Control and Robotics
• Czasopismo: Archives of Control Sciences
• Rocznik: 2012
• Tom: Vol. 22, no. 4
• Strony: 371--388
• Opis fizyczny: Bibliogr. 22 poz., rys., tab., wzory

Twórcy

autor

Stevek J.

autor

Szucs A.

autor

Kvasnica M.

autor

Fikar M.

autor

Kozak S.

• Slovak University of Technology, Slovak Republic

Bibliografia

• [1] C. S. Adjiman, I. P. Androulakis, C. D. Maranas and C. A. Floudas: A global optimization method, αBB for process design. Computers & Chemical Engineering, 20(96), (1996), 419-424.
• [2] A. Bemporad and M. Morari: Control of systems integrating logic, dynamics, and constraints. Automatica, 35(3), (1999), 407-427.
• [3] M. S. Branicky: Studies in Hybrid Systems: Modeling, Analysis, and Control. PhD thesis, Massachusetts Institute of Technology, 1995.
• [4] B. Chachuat, A. B. Singer and P. I. Barton: Global methods for dynamic optimization and mixed-integer dynamic optimization. Industrial & EngineeringChemistry Research, 45(25), (2006), 8373-8392.
• [5] G. Ferrari-Trecate: Hybrid Identification Toolbox (HIT), 2005.
• [6] J. H. Friedman: Multivariate adaptive regression splines. Annals of Statistics, 19(1), (1991), 1-67.
• [7] P. Julian, A. Desages and O. Agamennoni: High-level canonical piecewise linear representation using a simplicial partition. IEEE Trans. on Circuits andSystems I: Fundamental Theory and Applications, 46(4), (1999), 463-480.
• [8] M. Kvasnica, M. Fikar and A. Szucs: Automatic derivation of optimal piecewise affine approximations of nonlinear systems. In: Proc. of the 18th IFAC WorldCongress, (2011), 8675-8680.
• [9] L. Ljung: Approaches to identification of nonlinear systems. In: Proc. of the 29thChinese Control Conf. CCC 2010, (2010), 1-5.
• [10] A. Magnani and S. P. Boyd: Convex piecewise-linear fitting. Optimization andEngineering, 10(1), (2008), 1-17.
• [11] K. S. Narendra: Neural networks for control theory and practice. Proc. of theIEEE, 84(10), (1996), 1385-1406.
• [12] J. C. Patra and A. C. Kot: Nonlinear dynamic system identification using Chebyshev functional link artificial neural networks. IEEE Trans. on Systems Man andCybernetics. Part B, 32(4), (2002), 505-511.
• [13] J. Roll, A. Bemporad and L. Ljung: Identification of piecewise affine systems via mixed-integer programming. Automatica, 40(1), (2004), 37-50.
• [14] M. F. Sevat: Glasmost: A mosfet model of high numerical quality. In: Int. Symp. on Circuits and Systems, (1988), 2597-2600.
• [15] E. D. Sontag: Nonlinear regulation: The piecewise linear approach. IEEE Trans.on Automatic Control, 26(2), (1981), 346-358.
• [16] F. D. Torrisi and A. Bemporad: Hysdel - A tool for generating computational hybrid models for analysis and synthesis problems. IEEE Trans. on ControlSystems Technology, 12(2), (2004), 235-249.
• [17] V. Totik: Orthogonal polynomials. J. of Computational and Applied Mathematics, 0427 (2005), 84-86.
• [18] H. P. Williams: Model Building in Mathematical Programming. Third edition. Volume 4 of A Wiley - Interscience Publication. John Wiley & Sons, 1999.
• [19] C. Zhu, D. Shukla and F. W. Paul: Orthogonal functions for systems identification and control. In C.T. Leondes (Ed.) Control and Dynamic Systems. Academic Press, London, 1997, 1-73.