The anisotropy-based estimation problem for time invariant systems: the left asymptotics
- Authors: Belov I.R.1, Kustov A.Y.1
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Affiliations:
- V.A. Trapeznikov Institute of Control Sciences of RAS
- Issue: No 103 (2023)
- Pages: 94-120
- Section: Control systems analysis and design
- URL: https://ogarev-online.ru/1819-2440/article/view/363798
- DOI: https://doi.org/10.25728/ubs.2023.103.4
- ID: 363798
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Abstract
The anisotropy-based estimation problem for linear discrete time invariant system is considered in the paper. The asymptotic formulas for estimator matrices, estimation error covariance matrice and anisotropic norm of estimation error system under the condition of small values of mean anisotropy of input disturbance are demonstrated. Also the maximum edge of external disturbance anisotropy, providing the prescribed accuracy of anisotropy-based estimator approximation by Kalman filter, is determined in the article. The stated problems solution is demonstrated in the graphical results of numerical modelling for linear discrete time invariant stable system.
About the authors
Ivan Romanovich Belov
V.A. Trapeznikov Institute of Control Sciences of RAS
Author for correspondence.
Email: ivanb1993@mail.ru
Moscow
Arkadiy Yur'evich Kustov
V.A. Trapeznikov Institute of Control Sciences of RAS
Email: arkadiykustov@yandex.ru
Moscow
References
- Владимиров И. Г., Курдюков А. П., Семенов А. В. Асимптотика анизотропийной нормы линейных стационарных систем // Автоматика и телемеханика. – 1999. – № 3. – С. 78–87.
- Тимин В. Н., Курдюков А. П. Синтез робастной системы управления на режиме посадки самолета в условиях сдвига ветра // Известия РАН. Техническая кибернетика. – 1993. – № 6. – С. 200–208.
- Anderson B. D. O., Moore J. B. Optimal Filtering. – New Jersey: Prentice Hall, 1979.
- Belov I. R., Yurchenkov A. V., Kustov A. Yu. Anisotropy-Based Bounded Real Lemma for Multiplicative Noise Systems: the Finite Horizon Case // Proc. of the 27th Mediterranean Conference on Control and Automation (MED). – 2019.
- Dey S., Moore J. B. Risk-sensitive filtering and smoothing via reference probability methods // IEEE Trans. on Automatic Control. – 1997. – Vol. 42, No. 11. – P. 1587–1591.
- Hassibi B., Sayed A., Kailath T. Indefinite Quadratic Estimation and Control: A Unified Approach to ℋ2 and ℋ∞ Theories. – Philadelphia: SIAM, 1999.
- Kailath T. A view of three decades of linear filtering theory // IEEE Trans. on Information Theory. – 1974. – Vol. 20, No. 2. – P. 146–181.
- Kalman R. E. A New Approach to Linear Filtering and Prediction Problems // J. Basic Eng., Trans. ASME, Series D. – 1960. – Vol. 82, No. 1. – P. 35–45.
- Korotina M., Aranovskiy S., Bobtsov A. Disturbance Frequency Estimation for an LTV System // IFAC-PapersOnLine. – 2022. – Vol. 55, Is. 12. – P. 318–323.
- Kustov A. Yu., Timin V. N., Yurchenkov A. V. Anisotropic Norm Computation for Time-invariant Random System // Proc. of the 15th Int. Conf. on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy’s Conference) (STAB). – 2020.
- Kustov A. Yu., Yurchenkov A. V. Anisotropic Estimator Design for Time Varying System with Measurement Dropouts // Proc. of the 15th Int. Conf. on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy’s Conference) (STAB). – 2020.
- Kwon O.-K., De Souza C. E., Ryu H.-S. Robust ℋ∞ FIR filter for discrete-time uncertain systems // Proc. of 35th IEEE Conf. on Decision and Control. – 1996. – Vol. 4. – P. 4819–4824.
- Oppenheim A. V., Schafer R. W. Digital Signal Processing. – Prentice Hall, Inc., Englewood Cliffs, N.J., 1975.
- Polyak B. T., Khlebnikov M. V. Filtering with nonrandom noise: invariant ellipsoids technique // IFAC Proc. Volumes (IFAC Papers-OnLine). – 2008. – Vol. 41.
- Pyrkin A., Bobtsov A., Ortega R., Isidori A. An adaptive observer for uncertain linear time-varying systems with unknown additive perturbations // Automatica. – 2023. – Vol. 147.
- Semyonov A. V., Vladimirov I. G., Kurdjukov A. P. Stochastic approach to ℋ∞-optimization // Proc. of the 33rd Conf. on Decision and Control, Florida, USA. – December 14–16, 1994. – Vol. 3. – P. 2249–2250.
- Simon D. Optimal State Estimation: Kalman, ℋ∞, and Nonlinear Approaches. – New Jersey: Wiley, 2006.
- Terman F. E. Electronic and Radio Engineering. – McGraw-Hill Book Company, New York, 1955.
- Theodor Y., Shaked U. Robust discrete-time minimum-variance filtering // IEEE Trans. on Signal Processing. – 1996. – Vol. 44, No. 2. – P. 181–189.
- Vladimirov I. G., Kurdjukov A. P., Semyonov A. V. Anisotropy of Signals and the Entropy of Linear Stationary Systems // Dokl. Math. – 1995. – Vol. 51. – P. 388–390.
- Vladimirov I. G., Kurdjukov A. P., Semyonov A. V. On Computing the Anisotropic Norm of Linear Discrete-Time-Invariant Systems // Proc. 13 IFAC World Congress. – 1996. – P. 179–184.
- Vladimirov I. G., Kurdjukov A. P., Semyonov A. V. State-space solution to anisotropy-based stochastic ℋ∞-optimization problem // Proc. of the 13th IFAC World Congress, San Francisco, California, USA. – June 30 – July 5, 1996. – V. H, Paper IFAC-3d-01.6. – P. 427–432.
- Xie L., Soh Y. C., De Souza C. E. Robust Kalman filtering for uncertain discrete-time systems // IEEE Trans. Automat. Contr. – 1994. – Vol. 39. – P. 1310–1314.
- Yurchenkov A. V. Lemma on Boundedness of Anisotropic Norm for Systems with Multiplicative Noises under a Noncentered Disturbance // Automation and Remote Control. – 2021. – P. 51–62.
- Yurchenkov A. V., Kustov A. Yu. Anisotropy-Based Approach to Communication Tuning for a Time-Varying Sensor Network System // Dokl. Math. – 2022. – Vol. 104. – P. 311–315.
- Yurchenkov A. V., Kustov A. Yu., Timin V. N. Anisotropy-based Approach of Sensors Network Filtration: Nonzero Mean Disturbance Case // Proc. of the 16th Int. Conf. on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy’s Conference) (STAB). – 2022.
- Yurchenkov A. V., Kustov A. Yu., Timin V. N. The sensor network estimation with dropouts: Anisotropy-based approach // Automatica. – 2023. – Vol. 151.
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