Abstract
This paper considers the adaptive tracking problem for a class of first-order systems with binary-valued observations generated via fixed thresholds. A recursive projection algorithm is proposed for parameter estimation based on the statistical properties of the system noise. Then, an adaptive control law is designed via the certainty equivalence principle. By use of the conditional expectations of the innovation and output prediction with respect to the estimates, the closed-loop system is shown to be stable and asymptotically optimal. Meanwhile, the parameter estimate is proved to be both almost surely and mean square convergent, and the convergence rate of the estimation error is also obtained. A numerical example is given to demonstrate the efficiency of the adaptive control law.
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References
J. C. Agüero, G. C. Goodwin, and J. I. Yuz, System identification using quantized data, Proceedings of the 46th IEEE Conference on Decision and Control, New Orleans, USA, 2007.
M. Casini, A. Garulli, and A. Vicino, Time complexity and input design in worst-case identification using binary sensors, Proceedings of the 46th IEEE Conference on Decision and Control, New Orleans, USA, 2007.
B. I. Godoya, G. C. Goodwin, J. C. Agüero, D. Marelli, and T. Wigrenb, On identification of FIR systems having quantized output data, Automatica, 2011, 47: 1905–1915.
J. Guo, J. F. Zhang, and Y. L. Zhao, Adaptive tracking control of a class of first-order systems with binary-valued observations and time-varying thresholds, IEEE Trans. on Automatic Control, 2011, 56(12): 2991–2996.
D. Marelli, K. You, and M. Fu, Identification of ARMA models using intermittent and quantized output observations, Proceedings of the 36th International Conference on Acoustics, Speech and Signal Processing, Prague, Czech Republic, 2011.
L. Y. Wang, G. Yin, J. F. Zhang, and Y. L. Zhao, System Identification with Quantized Observations, Boston: Birkhüser, 2010.
L. Y. Wang, J. F. Zhang, and G. Yin, System identification using binary sensors, IEEE Trans. on Automatic Control, 2003, 48: 1892–1907.
K. You, L. H. Xie, S. Sun, and W. Xiao, Multiple-level quantized innovation Kalman filter, Proceedings of the 17th IFAC World Congress, Korea, July 6–11, 2008.
Y. L. Zhao, J. Guo, and J. F. Zhang, Adaptive tracking control of linear systems to periodic target with set-valued information, Proceedings of the 30th Chinese Control Conference, Yantai, July 22–24, 2011.
L. Y. Wang, G. H. Xu, and G. Yin, State reconstruction for linear time-invariant systems with binary-valued output observations, Systems & Control Letters, 2008, 57: 958–963.
L. Y. Wang, Y. Kim, and J. Sun, Prediction of oxygen storage capacity and stored NOx using HEGO sensor model for improved LNT control strategies, Proceedings of ASME International Mechanical Engineering Congress and Exposition, New Orleans, November 17–22, 2002.
I. Akyildiz, W. Su, Y. Sankarasubramaniam, and E. Cayirci, Wireless sensor networks: A survey, Computer Networks, 2002, 38: 393–422.
N. Dokuchaev and A. Savkin, A new class of hybrid dynamical systems: state estimators with bit-rate constraints, International Journal of Hybrid Systems, 2001, 1(1): 33–50.
A. Ribeiro, G. Giannakis, and S. Roumeliotis, SOI-KF: Distributed Kalman filtering with low-cost communications using the sign of innovations, IEEE Trans. on Signal Processing, 2006, 54(12): 4782–4795.
L. Y. Wang, C. Y. Li, G. Yin, L. Guo, and C. Z. Xu, State observability and observers of lineartime-invariant systems under irregular sampling and sensor limitations, IEEE Trans. Automatic Control, 2011, 56(11): 2639–2654.
Y. L. Zhao and J. Guo, Quantization system identification under a class of persistent excitations, Proceedings of the 29th Chinese Control Conference, Beijing, July 29–31, 2010.
L. Guo, Time-Varying Stochastic Systems — Stability, Estimation and Control, Jilin Science and Technology Press, Changchun, China, 1993.
Y. S. Chow and H. Teicher, Probability Theory: Independence, Interchangeability, Martingales, Springer-Verlag, New York, 3rd Edition, 1997.
H. F. Chen, Stochastic Approximation and Its Application, Kluwer Academic Publishers, Dordrecht, 2002.
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This research was supported by the National Natural Science Foundation of China under Grant Nos. 60934006, 61174042, and 61120106011.
This paper was recommended for publication by Editor Gang George YIN
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Guo, J., Zhang, JF. & Zhao, Y. Adaptive tracking of a class of first-order systems with binary-valued observations and fixed thresholds. J Syst Sci Complex 25, 1041–1051 (2012). https://doi.org/10.1007/s11424-012-1257-0
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DOI: https://doi.org/10.1007/s11424-012-1257-0