Abstract
We propose a new technique for the identification of discrete-time hybrid systems in the Piece-Wise Affine (PWA) form. The identification cation algorithm proposed in [10] is first considered and then improved under various aspects. Measures of confidence on the samples are introduced and exploited in order to improve the performance of both the clustering algorithm used for classifying the data and the final linear regression procedure. Moreover, clustering is performed in a suitably defined space that allows also to reconstruct different submodels that share the same coefficients but are defined on different regions.
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References
A. Bemporad, G. Ferrari-Trecate, and M. Morari. Observability and controllability of piecewise affine and hybrid systems. IEEE Trans. on Automatic Control, 45(10):1864–1876, 2000.
A. Bemporad and M. Morari. Control of systems integrating logic, dynamics, and constraints. Automatica, 35(3):407–428, March 1999.
A. Bemporad and M. Morari. Verification of hybrid systems via mathematical programming. In F.W. Vaandrager and J.H. van Schuppen, editors, Hybrid Systems: Computation and Control, volume 1569 of Lecture Notes in Computer Science, pages 31–45. Springer Verlag, 1999.
A. Bemporad, J. Roll, and L. Ljung. Identification of hybrid systems via mixedinteger programming. Technical Report AUT00-28, Automatic Control Laboratory http://control.ethz.ch/, 2000.
H. Bischof, A. Leonardis, and A. Selb. MLD principle for robust vector quantisation. Pattern Analysis & Applications, 2:59–72, 1995.
C.M. Bishop. Neural networks for pattern recognition. Clarendon press, Oxford, 1995.
L. Breiman. Hinging hyperplanes for regression, classification, and function approximation. IEEE Trans. Inform. Theory, 39(3):999–1013, 1993.
R.O. Duda and P.E. Hart. Pattern Classification and Scene Analysis. Wiley, 1973.
G. Ferrari-Trecate, D. Mignone, and M. Morari. Moving Horizon Estimation for Piecewise Affine Systems. Proceedings of the American Control Conference, 2000.
G. Ferrari-Trecate, M. Muselli, D. Liberati, and M. Morari. Identification of piecewise affine and hybrid systems. Technical Report AUT00-21, http://control.ethz.ch, ETH Zürich, 2000.
B. Fritzke. Some competitive learning methods. Technical report, Institute for Neural Computation. Ruhr-Universit at Bochum., 1997. http://www.neuroinformatik.ruhr-uni-bochum.de/ini/VDM/research/gsn/Java%Paper/.
R.E. Groff, D.E. Koditschek, and P.P. Khargonekar. Piecewise linear homeomorphisms: The scalar case. Proc. Int. Joint Conf. on Neural Networks, 2000.
S. Haykin. Neural networks-a comprehensive foundation. Macmillan, Englewood Cliffs, 1994.
W.P.M.H. Heemels and B. De Schutter. On the equivalence of classes of hybrid systems: Mixed logical dynamical and complementarity systems. Technical Report 00 I/04, Dept. of Electrical Engineering, Technische Universiteit Eindhoven, June 2000.
P.J. Huber. Robust Statistics. Wiley, 1981.
T.A. Johansen and B.A. Foss. Identification of non-linear system structure and parameters using regime decomposition. Automatica, 31(2):321–326, 1995.
L. Ljung. System Identification-Theory For the User. Prentice Hall, Upper Saddle River, N.J., 1999. 2nd ed.
J. MacQueen. On convergence of K-means and partitions with minimum average variance. Ann. Math. Statist., 36:1084, 1965. Abstract.
D. Mignone, G. Ferrari-Trecate, and M. Morari. Stability and Stabilization of Piecewise Affine and Hybrid Systems: An LMI Approach. Conference on Decision and Control, 2000. 12–15 December, Sydney, Australia.
M. Muselli and D. Liberati. Training digital circuits with Hamming clustering. IEEE Trans. Circuits and Systems-Part I, 47(4):513–527, 2000.
K. Nakayama, A. Hirano, and A. Kanbe. A structure trainable neural network with embedded gating units and its learning algorithm. Proc. Int. Joint Conf. on Neural Networks, 2000.
A. Skeppstedt, L. Ljung, and M. Millnert. Construction of composite models from observed data. Int. J. Control, 55(1):141–152, 1992.
E.D. Sontag. Interconnected automata and linear systems: A theoretical framework in discrete-time. In R. Alur, T.A. Henzinger, and E.D. Sontag, editors, Hybrid Systems III-Verification and Control, number 1066 in Lecture Notes in Computer Science, pages 436–448. Springer-Verlag, 1996.
V. Vapnik. Statistical Learning Theory. John Wiley, NY, 1998.
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Ferrari-Trecate, G., Muselli, M., Liberati, D., Morari, M. (2001). A Clustering Technique for the Identification of Piecewise Affine systems. In: Di Benedetto, M.D., Sangiovanni-Vincentelli, A. (eds) Hybrid Systems: Computation and Control. HSCC 2001. Lecture Notes in Computer Science, vol 2034. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45351-2_20
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