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Simultaneous state and input estimation of hybrid systems with unknown inputs. (English) Zbl 1137.93333

Summary: This paper addresses the problem of the simultaneous state and input estimation for hybrid systems when subject to input disturbances. The proposed algorithm is based on the Moving Horizon Estimation (MHE) method and uses mixed logical dynamical systems as equivalent representations of piecewise affine systems. So far the MHE method has been successfully applied for the state estimation of linear, hybrid, and nonlinear systems. The proposed extension of the MHE algorithm enables the estimation of unknown inputs, or disturbances, acting on the hybrid system. The new algorithm is shown to improve the convergence characteristics of the MHE method by reducing the delay of convergent estimates, while assuring convergence for every possible sequence of input disturbances. To ensure convergence the system is required to be incrementally input observable, which is an extension to the classical incremental observability property.

MSC:

93B40 Computational methods in systems theory (MSC2010)
93C55 Discrete-time control/observation systems
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[1] Alessandri, A., & Coletta, P. (2001). Switching observers for continuous-time and discrete-time linear systems. Proceedings of American control conference; Alessandri, A., & Coletta, P. (2001). Switching observers for continuous-time and discrete-time linear systems. Proceedings of American control conference
[2] Alessandri, A., & Coletta, P. (2003). Design of observers for switched discrete-time linear systems. Proceedings of American control conference; Alessandri, A., & Coletta, P. (2003). Design of observers for switched discrete-time linear systems. Proceedings of American control conference
[3] Antsaklis, P., A brief introduction to the theory and applications of hybrid systems, Proceedings of IEEE, Special Issue on Hybrid Systems: Theory and Applications, 88, 7, 879-886 (2000)
[4] Balluchi, A., Benvenuti, L., Benedetto, M. D. D., & Sangiovanni-Vincentelli, A. L. (2001). Hybrid control of force transients for multi-point injection engines. International Journal of Robust and Nonlinear Control, 11, 515-539.; Balluchi, A., Benvenuti, L., Benedetto, M. D. D., & Sangiovanni-Vincentelli, A. L. (2001). Hybrid control of force transients for multi-point injection engines. International Journal of Robust and Nonlinear Control, 11, 515-539. · Zbl 1123.93312
[5] Bemporad, A.; Ferrari-Trecate, G.; Morari, M., Observability and controllability of piecewise affine and hybrid systems, IEEE Transactions on Automatic Control, 45, 10, 1864-1876 (2000) · Zbl 0990.93010
[6] Bemporad, A., Mignone, D., & Morari, M. (1999). Moving horizon estimation for hybrid systems and fault detection. Proceedings of American control conference; Bemporad, A., Mignone, D., & Morari, M. (1999). Moving horizon estimation for hybrid systems and fault detection. Proceedings of American control conference
[7] Bemporad, A.; Morari, M., Control of systems integrating logic, dynamics, and constraints, Automatica, 35, 3, 407-427 (1999) · Zbl 1049.93514
[8] Bemporad, A., & Morari, M. (1999b). Verification of hybrid systems via mathematical programming. Hybrid SystemsComputation and Control; Bemporad, A., & Morari, M. (1999b). Verification of hybrid systems via mathematical programming. Hybrid SystemsComputation and Control · Zbl 0954.93019
[9] Bhattacharyya, S. P., Observers design for linear systems with unknown inputs, IEEE Transactions on Automatic Control, 23, 3, 483-484 (1978) · Zbl 0377.93025
[10] Böker, G.; Lunze, J., Stability and performance of switching kalman filters, International Journal of Control, 75, 16/17, 1269-1281 (2002) · Zbl 1052.93055
[11] Corless, M.; Tu, J., State and input estimation for a class of uncertain systems, Automatica, 34, 6, 757-764 (1998) · Zbl 0932.93008
[12] Darouach, M.; Zasadzinski, M.; Xu, S. J., Full-order observers for linear systems with unknown inputs, IEEE Transactions on Automatic Control, 39, 3, 606-609 (1994) · Zbl 0813.93015
[13] Ferrari-Trecate, G.; Mignone, D.; Morari, M., Moving horizon estimation for hybrid systems, IEEE Transactions on Automatic Control, 47, 10, 1663-1676 (2002) · Zbl 1364.93768
[14] Fletcher, R., & Leyffer, S. (1995). Numerical experience with lower bounds for miqp branch-and-bound; Fletcher, R., & Leyffer, S. (1995). Numerical experience with lower bounds for miqp branch-and-bound · Zbl 0912.90225
[15] Ha, Q. P.; Trinh, H., State and input simultaneous estimation for a class of nonlinear systems, Automatica, 40, 10, 1779-1785 (2004) · Zbl 1088.93004
[16] Heemels, W.; Schumacher, J.; Weiland, S., Linear complementarity systems, SIAM Journal on Applied Mathematics, 60, 4, 1234-1269 (2000) · Zbl 0954.34007
[17] Heemels, W.; Schutter, B. D.; Bemporad, A., Equivalence of hybrid dynamical models, Automatica, 37, 7, 1085-1091 (2001) · Zbl 0990.93056
[18] Hirschorn, R., Invertibility of multivariable nonlinear control systems, IEEE Transactions on Automatic Control, 24, 6, 855-865 (1979) · Zbl 0427.93020
[19] Hou, M.; Muller, P. C., Design of observers for linear systems with unknown inputs, IEEE Transactions on Automatic Control, 37, 6, 871-875 (1992) · Zbl 0775.93021
[20] Hou, M.; Muller, P. C., Fault detection and isolation observers, International Journal of Control, 60, 5, 827-846 (1994) · Zbl 0825.93085
[21] Hou, M.; Patton, R. J., Input observability and input reconstruction, Automatica, 34, 6, 789-794 (1998) · Zbl 0959.93006
[22] Juloski, A., Heemels, W., & Weiland, S. (2002). Observer design for a class of piecewise affine systems. Proceedings of the 41th IEEE conference on decision and control; Juloski, A., Heemels, W., & Weiland, S. (2002). Observer design for a class of piecewise affine systems. Proceedings of the 41th IEEE conference on decision and control
[23] Juloski, A. L., Heemeles, W. P. M. H., Boers, Y., & Verschure, F. (2003). Two approaches to state estimation for a class of piecewise affine systems (pp. 143-148), Maui, HA, USA.; Juloski, A. L., Heemeles, W. P. M. H., Boers, Y., & Verschure, F. (2003). Two approaches to state estimation for a class of piecewise affine systems (pp. 143-148), Maui, HA, USA.
[24] Keerthi, S. S.; Gilbert, E. G., Optimal infinite-horizon feedback control laws for a general class of constrained discrete-time systems: Stability and moving horizon approximations, Journal of Optimal Theory and Applications, 57, 265-293 (1988) · Zbl 0622.93044
[25] Kurek, J. E., The state vector reconstruction for linear systems with unknown inputs, IEEE Transactions on Automatic Control, 28, 12, 1120-1122 (1983) · Zbl 0538.93005
[26] Mendel, J. M., White-noise estimators for seismic data processing in oil exploration, IEEE Transactions on Automatic Control, 22, 5, 694-706 (1977) · Zbl 0362.93026
[27] Miller, R. J.; Mukundan, R., On designing reduced order observers for linear time-invariant systems subject to unknown inputs, International Journal of Control, 35, 2, 183-188 (1982) · Zbl 0473.93027
[28] Patton, R. J. (1997). Fault-tolerant control systems: The 1997 situation. IFAC symposium on fault detection supervision and safety for technical processes; Patton, R. J. (1997). Fault-tolerant control systems: The 1997 situation. IFAC symposium on fault detection supervision and safety for technical processes
[29] Rao, C. V.; Rawlings, J. B.; Lee, J. H., Constrained linear state estimation: A moving horizon approach, Automatica, 37, 10, 1619-1628 (2001) · Zbl 0998.93039
[30] Rao, C.; Rawlings, J.; Mayne, D., Constrained state estimation for nonlinear discrete-time systems: Stability and moving horizon approximations, IEEE Transactions on Automatic Control, 48, 2, 246-258 (2003) · Zbl 1364.93781
[31] Schutter, B. D.; van den Boom, T., Model predictive control for max-plus-linear discrete event systems, Automatica, 37, 7, 1049-1056 (2001) · Zbl 0991.93042
[32] Silverman, L. M., Inversion of multivariable linear systems, IEEE Transactions on Automatic Control, 17, 3, 270-276 (1969)
[33] Sontag, E., Nonlinear regulation: The piecewise linear approach, IEEE Transactions on Automatic Control, 26, 2, 346-358 (1981) · Zbl 0474.93039
[34] Torrisi, F., Bemporad, A., & Mignone, D. (2000). HYSDEL—a language for describing hybrid systems\( \langle\) http://control.ethz.ch/hybrid/hysdel \(\rangle \); Torrisi, F., Bemporad, A., & Mignone, D. (2000). HYSDEL—a language for describing hybrid systems\( \langle\) http://control.ethz.ch/hybrid/hysdel \(\rangle \)
[35] Viswanadham, N.; Srichander, R., Fault detection using unknown-input observers, Control Theory and Advanced Technology, 3, 2, 91-101 (1987)
[36] Wang, S. H.; Davison, E. J.; Dorato, P., Observing the states of systems with unmeasurable disturbances, IEEE Transactions on Automatic Control, 20, 5, 716-717 (1975) · Zbl 0318.93048
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