Abstract
The number m0 of thresholds is a measure of space complexity, whereas the observation length N is a measure of time complexity that quantifies how fast uncertainty can be reduced. The significance of understanding space and time complexities can be illustrated by the following example. For computer information processing of a continuous-time system, its output must be sampled (e.g., with a sampling rate N Hz) and quantized (e.g., with a precision word-length of B bits). Consequently, its output observations carry the data-flow rate of NB bits per second (bps). For instance, for 8- bit precision and a 10-KHz sampling rate, an 80K-bps bandwidth of data transmission resource is required. In a sensor network in which a large number of sensors must communicate within the network, such resource demand is overwhelming especially when wireless communications of data are involved.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
L.Y. Wang, G. Yin, Y. Zhao, and J.F. Zhang, Identification input design for consistent parameter estimation of linear systems with binary-valued output observations, IEEE Trans. Automat. Control, 53 (2008), 867–880.
M. Casini, A. Garulli, and A. Vicino, Time complexity and input design in worst-case identification using binary sensors, in Proc. 46th IEEE Conf. Decision Control, 5528–5533, 2007.
T.M. Cover and J.A. Thomas, Elements of Information Theory, John Wiley, New York, 1991.
M.A. Dahleh, T. Theodosopoulos, and J.N. Tsitsiklis, The sample complexity of worst-case identification of FIR linear systems, Sys. Control Lett., 20 (1993), 157–166.
A.N. Kolmogorov, On some asymptotic characteristics of completely bounded spaces, Dokl. Akad. Nauk SSSR, 108 (1956), 385–389.
M. Milanese and A. Vicino, Information-based complexity and nonparametric worst-case system identification, J. Complexity, 9 (1993), 427–446.
K. Poolla and A. Tikku, On the time complexity of worst-case system identification, IEEE Trans. Automat. Control, 39 (1994), 944–950.
A.M. Sayeed, A signal modeling framework for integrated design of sensor networks, in IEEE Workshop Statistical Signal Processing, 7, 2003.
J.F. Traub, G.W. Wasilkowski, and H. Wozniakowski, Information-Based Complexity, Academic Press, New York, 1988.
G. Zames, On the metric complexity of causal linear systems: ε-entropy and ε-dimension for continuous time, IEEE Trans. Automat. Control, 24 (1979), 222–230.
G. Zames, L. Lin, and L.Y. Wang, Fast identification n-widths and uncertainty principles for LTI and slowly varying systems, IEEE Trans. Automat. Control, 39 (1984), 1827–1838.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2010 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Wang, L.Y., Yin, G.G., Zhang, JF., Zhao, Y. (2010). Space and Time Complexities, Threshold Selection, Adaptation. In: System Identification with Quantized Observations. Systems & Control: Foundations & Applications. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4956-2_14
Download citation
DOI: https://doi.org/10.1007/978-0-8176-4956-2_14
Published:
Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-4955-5
Online ISBN: 978-0-8176-4956-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)