The research area of control over networks has attracted great interest in recent years. Inserted in this research area is the study of control feedback limitations imposed by the presence of a communication channel. In this paper we analyze the fundamental limitations in control feedback stabilizability imposed by a class of Signal-to-Noise Ratio (SNR) constrained communication channels. We solve the SNR constrained control over network problem as a linear quadratic Gaussian (LQG) optimization with loop transfer recovery (LTR). If the communication channel is located on the feedback path then the LTR is said to be performed at the output. Vice versa, if the communication channel is on the control path, then the recovery is said to be performed at the input. In the present paper we address both cases, namely the LQG optimization with LTR at the output and the LQG optimization with LTR at the input to solve an LTI SNR constrained problem. We then explore the link between these two solutions.
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B. Anderson and J. Moore, Optimal Filtering, Dover publications, NY, 2005.
K. J. Åström, Introduction to Stochastic Control Theory, Academic Press, 1970.
J. H. Braslavsky, R. H. Middleton, and J. S. Freudenberg, “Feedback stabilisation over signal-to-noise ratio constrained channels,” Proc. of the American Control Conf., pp. 4903–4908, 2004.
J. H. Braslavsky, R. H. Middleton, and J. S. Freudenberg, “Feedback stabilisation over signal-to-noise ratio constrained channels,” IEEE Trans. on Automatic Control, vol. 52, no. 8, pp. 1391–1403, August 2007.
T. M. Covers and J. A. Thomas, Elements of Information Theory, John Wiley & Sons, 1991.
J. S. Freudenberg, R. H. Middleton, and J. H. Braslavsky, “Control over signal-to-noise ratio constrained channels: stabilization and performance,” Proc. of the 44th IEEE Conf. on Decision and Control and European Control Conf., pp. 191–196, 2005.
R. G. Gallager, Principles of Digital Communication, Cambridge University Press, 2008.
M. Kinnaert and Y. Peng, “Discrete-time LQG/LTR techniques for systems with time delays,” Syst. Contr. Lett., vol. 15, no. 4, pp. 303–311, November 1990.
J. M. Maciejowski, “Asymptotic recovery for discrete-time systems,” IEEE Trans. on Automatic Control, vol. 30, no. 6, pp. 602–605, June 1985.
G. N. Nair and R. J. Evans, “Stabilizability of stochastic linear systems with finite feedback data rates,” SIAM J. Control and Optimization, vol. 43, no. 2, pp. 413–436, July 2004.
G. N. Nair, F. Fagnani, S. Zampieri, and R. J. Evans, “Feedback control under data rate constraints: an overview,” Proc. of the IEEE, vol. 95, no. 1, pp. 108–137, January 2007.
A. J. Rojas, J. H. Braslavsky, and R. H. Middleton, “Output feedback stabilisation over bandwidth limited, signal to noise ratio constrained communication channels,” Proc. of the American Control Conference, pp. 2789–2794, 2006.
A. J. Rojas, J. S. Freudenberg, J. H. Braslavsky, and R. H. Middleton, “Optimal signal to noise ratio in feedback over communication channels with memory,” Proc. of the 45th IEEE Conf. on Decision and Control, pp. 1129–1134, 2006.
A. J. Rojas, J. S. Freudenberg, and R. H. Middleton, “Infimal feedback capacity for a class of additive coloured gaussian noise channels,” Proc. of the 17th IFAC World Congress, pp. 5173–5178, 2008.
A. J. Rojas, R. H. Middleton, J. S. Freudenberg, and J. H. Braslavsky, “Input disturbance rejection in channel signal-to-noise ratio constrained feedback control,” Proc. of the American Control Conference, pp. 3100–3105, 2008.
A. J. Rojas, Feedback Control over Signal to Noise Ratio Constrained Communication Channels, Ph.D. Thesis, The University of Newcastle, 2006.
A. Saberi, B. M. Chen, and P. Sannuti, Loop Transfer Recovery: Analysis and Design, Springer-Verlag, 1993.
U. Shaked, “Explicit solution to the singular discrete-time stationary linear filtering problem,” IEEE Trans. on Automatic Control, vol. 30, no. 1, pp. 34–47, January 1985.
P. Antsaklis and J. Baillieul (editors), “Special issue on networked control systems,” IEEE Trans. on Automatic Control, vol. 49, no. 9, September 2004.
G. Stein and M. Athans, “The LQG/LTR procedure for multivariable feedback control design,” IEEE Trans. on Automatic Control, vol. 32, no. 2, pp. 105–114, February 1987.
Z. Zhang, Loop Transfer Recovery for Nonminimum Phase Plants and Ill-Conditioned Plants, Ph.D. Thesis, The University of Michigan, 1990.
Z. Zhang and J. S. Freudenberg, “Discrete-time loop transfer recovery for systems with Nonminimum phase zeros and time delays,” Automatica, vol. 29, no. 2, pp. 351–363, March 1993.
K. Zhou, J. C. Doyle, and K. Glover, Robust and Optimal Control, Prentice Hall, 1996.
Recommended by Editorial Board member Young Soo Suh under the direction of Editor Young-Hoon Joo.
Alejandro J. Rojas received the Ingeniero Civil Electrónico and Magister en Ingeniería Electrónica degrees from the Universidad Técnica Federico Santa María, Chile, in 2001. In 2007 he received the Ph.D. in Electrical Engineering from the University of Newcastle. He is currently a research academic at the ARC Centre for Complex Dynamic Systems and Control at the University of Newcastle. His research interests are in control over network, fundamental limitations, control applications and system biology.
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Rojas, A.J. Linear quadratic gaussian optimization approach for signal-to-noise ratio constrained control over network. Int. J. Control Autom. Syst. 7, 971 (2009). https://doi.org/10.1007/s12555-009-0614-9
- Control over networks
- fundamental limitations
- linear quadratic gaussian optimization
- loop transfer recovery
- signal-to-noise ratio