The problem of -optimal reconstruction of a continuous-time signal using a stable sampled-data filter is considered. The signal is corrupted by additive noise and is measured with preview of τ, i.e., it is known in advance over the interval τ. This problem is equivalent to delayed signal reconstruction. A rigorous solution of the problem is presented on the basis of the parametric transfer function approach. Explicit expressions are given for the order of the optimal filter. A lower bound is obtained for the cost function for τ→∞, and it is shown that this bound depends on the ratio of the preview interval to the sampling period.
Issue Section:
Technical Papers
1.
Khargonekar, P. P., and Yamamoto, Y., 1996, “Delayed Signal Reconstruction Using Sampled-Data Control,” Proc. of 35th IEEE CDC, pp. 1259–1263.
2.
Yamamoto, Y., and Hara, S., 1998, “Performance Lower Bound for a Sampled-Data Signal Reconstruction,” Open Problems in Mathematical Systems and Control Theory, V. Blondel, E. Sontag, M. Vidyasagar, and J. Willems, eds., Springer, London, pp. 277–279.
3.
Chen, T., and Francis, B. A., 1995, Optimal Sampled-Data Control Systems, Springer-Verlag, Berlin-Heidelberg-New York.
4.
Hagiwara
, T.
, and Araki
, M.
, 1995
, “FR-Operator Approach to the H2-Analysis and Synthesis of Sampled-Data Systems
,” IEEE Trans. Autom. Control
, 40
(8
), pp. 1411
–1421
.5.
Grimble
, M. J.
, 1990
, “LQG-Predictive Optimal Control for Adaptive Applications
,” Automatica
, 26
(6
), pp. 949
–961
.6.
Halpern, M. E., 1991, “Optimal Tracking With Previewed Commands,” IEE Proc., Pt. D, 138(3), pp. 237–241.
7.
Halpern
, M. E.
, 1994
, “Preview Tracking for Discrete-Time SISO Systems
,” IEEE Trans. Autom. Control
, 39
(3
), pp. 589
–592
.8.
Grimble, M. J., 1994, Robust Industrial Control: Optimal Design Approach for Polynomial Systems, Prentice Hall International (UK) Ltd, Hemel Hempstead, Hertfordshire.
9.
Fridman
, E.
, and Shaked
, U.
, 2001
, “A New H∞ Filter Design for Linear Time Delay Systems
,” IEEE Trans. Signal Process.
, SP-49
, pp. 2839
–2843
.10.
Motorola Inc., Semiconductor Technical Data: MC 145483/D, 3V 13 Bit Linear PCM Codec-Filter, http://www.mot.com/SPS.
11.
Kim
, W. S.
, and Bejczy
, A. K.
, 1993
, “Demonstration of a High-Fidelity Predictive/Preview Display Technique for Telerobotic Servicing in Space
,” IEEE Trans. Rob. Autom.
, 9
(5
), pp. 698
–702
.12.
Rosenwasser, E. N., and Lampe, B. P., 2000, Computer-Controlled Systems: Analysis and Design With Process-Orientated Models, Springer, London.
13.
Rosenwasser
, Y.
, Polyakov
, K.
, and Lampe
, B.
, 1997
, “Frequency Method for H2-Optimization of Time-Delayed Sampled-Data Systems
,” Automatica
, 33
(7
), pp. 1387
–1392
.14.
Rosenwasser
, E.
, Polyakov
, K.
, and Lampe
, B.
, 1999
, “Application of Laplace Transformation for Digital Redesign of Continuous Control Systems
,” IEEE Trans. Autom. Control.
, 44
(4
), pp. 883
–886
.15.
Chen
, T.
, and Francis
, B. A.
, 1995
, “Design of Multirate Filter Banks by H∞—Optimization
,” IEEE Trans. Signal Process.
, 43
(12
), pp. 2822
–2830
.16.
Polyakov, K., Rosenwasser, E., and Lampe, B., 1999, “DirectSD—A Toolbox for Direct Design of Sampled-Data Systems,” Proc. of IEEE Int. Symp. CACSD’99, Kohala Coast, Island of Hawaii, Hawaii, pp. 357–362.
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