The problem of the estimation of the discrete state of a switching system is studied. The knowledge of the switching law is essential for this kind of system as it simplifies their manipulation for control purposes. This paper investigates the use of a model-based diagnosis method for the determination of the active mode at each time point based on the system input/output data. The issue of the parametric identification of the switching law is also addressed.
A. Bemporad and M. Morari, “Control of systems integrating logic, dynamics, and constraints,” Automatica, vol. 35, no. 3, pp. 407–427, 1999.
View at: Publisher Site | Google ScholarW. P. M. H. Heemels, B. De Schutter, and A. Bemporad, “Equivalence of hybrid dynamical models,” Automatica, vol. 37, no. 7, pp. 1085–1091, 2001.
View at: Publisher Site | Google ScholarG. Ferrari-Trecate, M. Muselli, D. Liberati, and M. Morari, “A clustering technique for the identification of piecewise affine systems,” Automatica, vol. 39, no. 2, pp. 205–217, 2003.
View at: Publisher Site | Google ScholarA. Juloski, M. Heemels, G. Ferrari-Trecate, R. Vidal, S. Paoletti, and H. Niessen, “Comparison of four procedures for identification of hybrid systems,” in Hybrid Systems: Computation and Control, vol. 3141 of Lecture Notes in Computer Science, pp. 354–369, Springer, Zurich, Switzerland, 2005.
View at: Google ScholarJ. Ragot, G. Mourot, and D. Maquin, “Parameter estimation of switching piecewise linear systems,” in Proceedings of the 42nd IEEE Conference on Decision and Control (CDC '03), vol. 6, pp. 5783–5788, Maui, Hawaii, USA.
View at: Google ScholarJ. Roll, A. Bemporad, and L. Ljung, “Identification of piecewise affine systems via mixed-integer programming,” Automatica, vol. 40, no. 1, pp. 37–50, 2004.
View at: Publisher Site | Google ScholarM. S. Branicky, V. S. Borkar, and S. K. Mitter, “A unified framework for hybrid control: model and optimal control theory,” IEEE Transactions on Automatic Control, vol. 43, no. 1, pp. 31–45, 1998.
View at: Publisher Site | Google ScholarM. Johansson and A. Rantzer, “Computation of piecewise quadratic Lyapunov functions for hybrid systems,” IEEE Transactions on Automatic Control, vol. 43, no. 4, pp. 555–559, 1998.
View at: Publisher Site | Google ScholarG. A. Ackerson and K. S. Fu, “On state estimation in switching environnements,” IEEE Transactions on Automatic Control, vol. 15, no. 1, pp. 10–17, 1970.
View at: Publisher Site | Google ScholarA. Balluchi, L. Benvenuti, M. D. Di Benedetto, and A. L. Sangiovanni-Vincentelli, “Design of observers for hybrid systems,” in Proceedings of the 5th International Workshop on Hybrid Systems: Computation and Control (HSCC '02), vol. 2289, pp. 76–89, Stanford, Calif, USA.
View at: Google ScholarV. Cocquempot, M. Staroswiecki, and T. El Mezyani, “Switching time estimation and fault detection for hybrid systems using structured parity residuals,” in Proceedings of the 15th IFAC Symposium on Fault Detection, Supervison and Safety of Technical Processes (SAFEPROCESS '03), pp. 681–686, Washington, DC, USA, June 2003.
View at: Google ScholarE. A. Domlan, Diagnostic des systèmes à changement de régime de fonctionnement, Ph.D. thesis, Institut National Polytechnique de Lorraine, Nancy, France, 2006.
E. A. Domlan, D. Maquin, and J. Ragot, “Diagnostic des systèmes à commutation, approche par la méthode de l'espace de parité,” in Proceedings of the Conférence Internationale Francophone d'Automatique (CIFA '04), Douz, Tunisie, Novembre 2004.
View at: Google ScholarM. Babaali and M. Egerstedt, “Observability of switched linear systems,” in Hybrid Systems: Computation and Control, R. Alur and G. J. Pappas, Eds., Lecture Notes in Computer Science, pp. 48–63, Springer, Berlin, Germany, 2004.
View at: Google ScholarM. Babaali and M. Egerstedt, “Asymptotic observers for discrete-time switched linear systems,” in Proceedings of the 16th IFAC World Congress, vol. 16, Prague, Czech Republic, July 2005.
View at: Google ScholarR. Vidal, A. Chiuso, and S. Soatto, “Observability and identifiabilty of jump linear systems,” in Proceedings of the 41st IEEE Conference on Decision and Control (CDC '02), vol. 4, pp. 3614–3619, Las Vegas, Nev, USA, December 2002.
View at: Publisher Site | Google ScholarR. J. Patton, “Robustness in model-based fault diagnosis: the 1995 situation,” Annual Reviews in Control, vol. 21, pp. 103–123, 1997.
View at: Publisher Site | Google ScholarA. Bemporad, G. Ferrari-Trecate, and M. Morari, “Observability and controllability of piecewise affine and hybrid systems,” IEEE Transactions on Automatic Control, vol. 45, no. 10, pp. 1864–1876, 2000.
View at: Publisher Site | Google ScholarM. Babaali and M. Egerstedt, “Pathwise observability and controllability are decidable,” in Proceedings of the 42nd IEEE Conference on Decision and Control (CDC '03), vol. 6, pp. 5771–5776, Maui, Hawaii, USA.
View at: Publisher Site | Google ScholarJ. Gertler, “Fault detection and isolation using parity relations,” Control Engineering Practice, vol. 5, no. 5, pp. 653–661, 1997.
View at: Publisher Site | Google ScholarI. Hwang, H. Balakrishnan, and C. Tomlin, “Observability criteria and estimator design for stochastic linear hybrid systems,” in Proceedings of the IEE European Control Conference, Cambridge, UK, September 2003.
View at: Google ScholarO. Adrot, Diagnostic à base de modèles incertains utilisant l'analyse par intervalle: l'approche bornante, Ph.D. thesis, Institut National Polytechnique de Lorraine, Nancy, France, 2000.
M. Basseville and I. V. Nikiforov, Detection of Abrupt Changes: Theory and Application, Information and System Science, Prentice Hall, Englewood Cliffs, NJ, USA, 1993.
K. P. Bennett and O. L. Mangasarian, “Multicategory discrimination via linear programming,” Optimization Methods and Software, vol. 3, no. 1–3, pp. 27–39, 1994.
View at: Publisher Site | Google ScholarE. J. Bredensteiner and K. P. Bennett, “Multicategory classification by support vector machines,” Computational Optimization and Applications, vol. 12, no. 1–3, pp. 53–79, 1999.
View at: Publisher Site | Google ScholarJ. F. Bonnans, J. C. Gilbert, C. Lemarchal, and C. A. Sagastizbal, Numerical Optimization: Theoretical and Practical Aspects, Springer, New York, NY, USA, 2003.