Abstract
For an observed plant with delayed perturbations, an explicit formula for calculation of the linear quadratic filter in the Wiener–Kolmogorov problem was presented.The filter contains an integral over the delay interval. For replacement of the optimal filter by a suboptimal one designed disregarding the delay, an explicit expression for the increment of the performance functional was established. For small delays, the asymptotics was determined. For tracking a two-axle carriage whose model has a delay caused by the road imperfections acting first on the leading axle and then on the rear one, an example of filter calculation was presented.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
Petrov, O.A. and Fomin, V.N., Lineinaya fil'tratsiya sluchainykh protsessov(Linear Filtering of Random Processes), Leningrad: Leningr. Gos. Univ., 1991.
Andreeva, E.A., Kolmanovskii, V.B., and Shaikhet, L.E., Upravlenie sistemami s posledeistviem(Control of Aftereffect Systems), Moscow: Nauka, 1992.
Liptser, R.Sh. and Shiryaev, A.N., Teoriya martingalov, Moscow: Nauka, 1986. Translated under the title Theory of Martingales, Dordrecht: Kluwer, 1989.
Afanassieva, G.B., Barabanov, A.E., and Shtanenko, T.I., H-infinity Filtering of Linear Delayed Systems, Eur. Control Conf., Porto, Portugal, 2001, Section Th-E08, p. 5.
Åstrm, K.J. and Wittenmark, B., Computer Controlled Systems. Theory and Design, Englewood Cliffs: Prentice Hall, 1984. Translated under the title Sistemy upravleniya s EVM, Moscow: Mir, 1987.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Afanas'eva, G.B. Calculation of the Optimal Filter in Delayed Perturbation Systems. Automation and Remote Control 65, 1255–1264 (2004). https://doi.org/10.1023/B:AURC.0000038728.95761.1e
Issue Date:
DOI: https://doi.org/10.1023/B:AURC.0000038728.95761.1e