Quantized Feedback Control under Dynamic Logarithmic Quantization Schemes

Abstract:

This paper addresses the quantized feedback stabilization problem for networked control systems with unbounded process disturbance, where sensors, controllers and plants are connected by digital communication channels. A dynamic logarithmic quantization policy is proposed to stabilize the unstable plant. It is derived that the quantization policy can maintain stabilization in the presence of unbounded and possibly non-Gaussian process disturbance. Simulation results show the validity of the proposed scheme.

• Periodical: Advanced Materials Research (Volumes 433-440)
• Pages: 6235-6241
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.433-440.6235
• Online since: January 2012
• Authors: Qing Quan Liu
• Keywords: Digital Communication Channel, Feedback Stabilization, Networked Control System (NCS), Quantization Policy

References

[1] E. Fridman and U. Shaked, An improved stabilization method for linear time-delay systems, IEEE Trans. Automat. Control, vol. 47, no. 11, pp.1931-1937, (2002).

DOI: 10.1109/tac.2002.804462

[2] W. S. Wong and R. W. Brockett, Systems with finite communication bandwidth constraints II: Stabilization with limited information feedback, IEEE Transactions on Automatic Control, vol. 44, PP. 1049-1053, (1999).

DOI: 10.1109/9.763226

[3] H. shii and C. R. Francis, Quadratic stabilization of sampled-data systems with quantization, Automatica, vol. 39, pp.1793-1800, (2003).

DOI: 10.1016/s0005-1098(03)00179-1

[4] K. Li and J. Baillieul, Robust quantization for digital finite communication bandwidth (DFCB) control, IEEE Transactions on Automatic Control, vol. 49, no. 9, pp.1573-1597, (2004).

DOI: 10.1109/tac.2004.834106

[5] K. Li and J. Baillieul, Robust and efficient quantization and coding for control of multidimensional linear systems under data rate constraints, International Journal of Robust and Nonlinear Control, vol. 17, pp.898-920, (2007).

DOI: 10.1002/rnc.1142

[6] S. Graf and H. Luschgy, Foundations of Quantization for Probability Distributions, Springer-Verlag New York, Inc, Secaucus, NJ, (2000).

[7] G. N. Nair and R. J. Evans, Stabilizability of Stochastic Linear Systems with Finite Feedback Data Rates, SIAM Journal on Control and Optimization, vol. 43, no. 2, pp.413-436, (2004).

DOI: 10.1137/s0363012902402116

[8] D. Liberzon, On stabilization of linear systems with limited information, IEEE Transactions on Automatic Control, vol. 48, no. 2, pp.304-307, (2003).

DOI: 10.1109/tac.2002.808487

[9] R. W. Brockett and D. Liberzon, "Quantized feedback stabilization of linear systems, IEEE Transactions on Automatic Control, vol. 45, no. 7, pp.1279-1289, (2000).

DOI: 10.1109/9.867021

[10] D. Liberzon and D. Nesic, Input-to-state stabilization of linear systems with quantized state measurements, IEEE Transactions on Automatic Control, vol. 52, pp.767-781, (2007).

DOI: 10.1109/tac.2007.895850

[11] F. Fagnani and S. Zampieri, Quantized stabilization of linear systems: Complexity versus performance, IEEE Transactions on Automatic Control, vol. 49, no. 9, pp.1534-1548, (2004).

DOI: 10.1109/tac.2004.834111

[12] T. Kameneva and D. Nesic, Robustness of quantized control systems with mismatch between coder initializations, Automatica, (2009).

DOI: 10.1016/j.automatica.2008.10.020

[13] A. S. Matveev and A. V. Savkin, An Analogue of Shannon Information Theory for Detection and Stabilization via Noisy Discrete Communication Channels, SIAM Journal on Control and Optimization, vol. 46, no. 4, pp.1323-1367, September (2007).

DOI: 10.1137/040621697

[14] A. S. Matveev and A. V. Savkin, Shannon zero error capacity in the problems of state estimation and stabilization via noisy communication channels, International Journal of Control. vol. 80, pp.241-255, (2007).

DOI: 10.1080/002071706000981775

[15] J. Baillieul, Feedback designs in information based control, In Stochastic Theory and Control Proceedings of a Workshop Held in Pasik-Duncan, Ed. New York: Springer-Verlag, pp.35-57, (2001).

DOI: 10.1007/3-540-48022-6_3

[16] S. Yksel and T. Basar, Communication constraints for decentralized stabilizability with time-invariant policies, IEEE Trans. Automat. Control, vol. 52, no. 6, pp.1060-1066, Jun. (2007).

DOI: 10.1109/tac.2007.899085

[17] N. Elia, When Bode meets Shannon: Control-oriented feedback communication schemes, IEEE Trans. Automat. Control, vol. 49, no. 9, pp.1477-1488, Sep. (2004).

DOI: 10.1109/tac.2004.834119

[18] S. Tatikonda and S. K. Mitter, Control under communication constraints, IEEE Trans. Automat. Control, vol. 49, no. 7, pp.1056-1068, Jul. (2004).

DOI: 10.1109/tac.2004.831187

[19] H. Ishii and B. A. Francis, Quadratic stabilization of sampled-data systems with quantization, Automatica, vol. 39, no. 10, pp.1793-1800, (2003).

DOI: 10.1016/s0005-1098(03)00179-1

[20] D. F. Coutinho, M. Fu and C. Souza, Input and output quantized feedback linear systems, IEEE Trans. Automat. Control, vol. 55, no. 3, pp.761-766, (2004).

DOI: 10.1109/tac.2010.2040497