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Robust tracking and model following control with zero tracking error for uncertain dynamical systems. (English) Zbl 0999.93062
Summary: The problem of robust tracking and model following for a class of linear dynamical systems with time-varying uncertain parameters and disturbances is considered. A class of continuous (nonlinear) state feedback controllers is proposed for robust tracking of dynamical signals. The proposed robust tracking controllers can guarantee that the tracking error decreases asymptotically to zero in the presence of uncertain parameters and disturbances. A procedure for designing such a zero tracking state feedback controller is also introduced. Finally, a numerical example is given to demonstrate the validity of the results.

MSC:
93D15 Stabilization of systems by feedback
93B52 Feedback control
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[1] Corless, M. J., Leitman, G., and Ryan, E. P., Tracking in the Presence of Bounded Uncertainties, Proceedings of the 4th International Conference on Control Theory, Cambridge University, Cambridge, England, 1984.
[2] Corless, M. J., Goodall, D. P., Leitmann, G., and Ryan, E. P., Model-Following Controls for a Class of Uncertain Dynamical Systems, Proceedings of the 7th IFAC Symposium on Identification and System Parameter Estimation, York University, York, England, 1985.
[3] Hopp, T. H., and Schmitendorf, W. E., Design of a Linear Controller for Robust Tracking and Model Following, ASME Journal of Dynamic Systems, Measurement, and Control, Vol. 112, pp. 552–558, 1990. · Zbl 0747.93022
[4] Sugie, T., and Osuka, K., Robust Model-Following Control with Prescribed Accuracy for Uncertain Nonlinear Systems, International Journal of Control, Vol. 58, pp. 991–1009, 1993. · Zbl 0787.93034
[5] Barmish, B. R., Corless, M. J., and Leitmann, G., A New Class of Stabilizing Controllers for Uncertain Dynamical Systems, SIAM Journal on Control and Optimization, Vol. 21, pp. 246–255, 1983. · Zbl 0503.93049
[6] Wu, H. S., and Mizukami, K., Exponential Stability of a Class of Nonlinear Dynamical Systems with Uncertainties, Systems and Control Letters, Vol. 21, pp. 307–313, 1993. · Zbl 0793.93098
[7] Corless, M. J., and Leitmann, G., Continuous State FeedbackGuaranteeing Uniform Ultimate Boundedness for Uncertain Dynamic Systems, IEEE Transactions on Automatic Control, Vol. 26, pp. 1139–1144, 1981. · Zbl 0473.93056
[8] Qu, Z., Global Stabilization of Nonlinear Systems with a Class of Unmatched Uncertainties, Systems and Control Letters, Vol. 18, pp. 301–307, 1992. · Zbl 0759.93060
[9] Barmish, B. R., and Leitmann, G., On Ultimate Boundedness Control of Uncertain Systems in the Absence of Matching Conditions, IEEE Transactions on Automatic Control, Vol. 27, pp. 153–158, 1982. · Zbl 0469.93043
[10] Chen, H. Y., On the Robustness of Mismatched Uncertain Dynamical Systems, ASME Journal of Dynamic Systems, Measurement, and Control, Vol. 109, pp. 29–35, 1987. · Zbl 0637.93020
[11] Chen, H. Y., and Leitmann, G., Robustness of Uncertain Systems in the Absence of Matching Conditions, International Journal of Control, Vol. 45, pp. 1527–1535, 1987. · Zbl 0623.93023
[12] Cheres, E., Gutman, S., and Palmor, Z., Stabilization of Uncertain Dynamic Systems Including State Delay, IEEE Transactions on Automatic Control, Vol. 34, pp. 1199–1203, 1989. · Zbl 0693.93059
[13] Gutman, S., Uncertain Dynamical Systems: A Lyapunov Min–Max Approach, IEEE Transactions on Automatic Control, Vol. 24, pp. 437–443, 1979. · Zbl 0416.93076
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