Abstract
A fixed-point smoothing algorithm is proven for discretetime systems with additive and multiplicative noise in the plant and measurement equations. Such systems, although linear, differ in a number of aspects from systems with only additive noise. The algorithm depends on the multiplicative terms, as expected. Steady-state results are derived.
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References
Sagirow, P.,Stochastic Methods in the Dynamics of Satellites, Lecture Notes, CISM, Udine, Italy, 1970.
Bernstein, D. S., andHyland, D. C.,The Optimal Projection Maximum Entropy Approach to Designing Low-Order, Robust Controllers for Flexible Structures, Proceedings of the 24th Conference on Decision and Control, Fort Lauderdale, Florida, pp. 745–752, 1985.
Phillis, Y. A.,A Smoothing Algorithm for Systems with Multiplicative Noise, IEEE Transactions on Automatic Control, Vol. AC-33, pp. 401–403, 1988.
Phillis, Y. A.,Estimation and Control of Discrete Multiplicative Systems with Unknown Second-Order Statistics (to appear).
Jazwinski, A. H.,Stochastic Processes and Filtering Theory, Academic Press, New York, New York, 1970.
Meditch, J. S.,Stochastic Optimal Linear Estimation and Control, McGraw-Hill, New York, New York, 1969.
Kwakernaak, H., andSivan, R.,Linear Optimal Control Systems, Wiley, New York, New York, 1972.
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Communicated by C. T. Leondes
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Phillis, Y.A. Fixed-point smoothing algorithm for discrete multiplicative systems. J Optim Theory Appl 62, 333–339 (1989). https://doi.org/10.1007/BF00941062
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DOI: https://doi.org/10.1007/BF00941062