Robust filtering in discrete stochastic systems with jump parameters and interval uncertainty
A robust filtering algorithm for a discrete stochastic system with interval parameters depending of the hidden Markov chain is considered. To represent the interval parameters, a probabilistic approach is used, which is based on the replacement of indeterminate interval-type parameters with independent random variables with a uniform distribution. Recurrent Kalman filtering schemes and algorithms for estimating the state of jump parameter are used. An example is provided to illustrate the proposed approach. Contribution of the authors: the authors contributed equally to this article. The authors declare no conflicts of interests.
Keywords
robust filtering,
interval uncertainty,
hidden Markov chainAuthors
Kim Konstantin S. | Tomsk State University | kks93@rambler.ru |
Smagin Valery I. | Tomsk State University | vsm@mail.tsu.ru |
Всего: 2
References
Ugrinovskii V.A., Pota H.R. Decentralized control of power systems via robust control of uncertain Markov jump parameter systems // Int. J. Control. 2005. V. 78. P. 662-677.
Sales-Setien E., Penarrocha-Alos I. Markovian jump system approach for the estimation and adaptive diagnosis of decreased power generation in wind farms // let Control Theory and Applications, 2019. V. 13 (18). P. 3006-3018.
Zhu Y., Zhong Z., Zheng W.X. et al. HMM-based H-infinity filtering for discrete-time Markov jump LPV systems over unreliable communication channels // IEEE Transactions on Systems Man Cybernetics-Systems. 2018. V. 48, is. 12. P. 2035-2046.
Wang J., Yao F., Shen H. Dissipativity-based state estimation for Markov jump discrete-time neural networks with unreliable communication links // Neurocomputing. 2014. V. 139/SI. P. 107-113.
Yao X., Wu L., Zheng W.X. Fault detection filter design for Markovian jump singular systems with intermittent measurements // IEEE Transactions on Signal Processing. 2011. V. 59/7. P. 3099-3109.
Gagliardi G., Casavola A., Famularo D.A. Fault detection and isolation filter design method for Markov jump linear parameter-varying systems // Int. Journal of Adaptive Control and Signal. Processing, 2012, V. 26, is. 3/SI. P. 241-257.
Costa O.L.V., Benites G.R.A.M. Linear minimum mean square filter for discrete-time linear systems with Markov jumps and multiplicative noises // Automatica. 2011. V. 47 (3). P. 466-476.
Liu W. On state estimation of discrete-time linear systems with multiplicative noises and markov jumps // 32nd Chinese Control Conference. Xian, CHINA. July 26-28, 2013. P. 3744-3749.
Costa O.L.V., Benites G.R.A.M. Robust mode-independent filtering for discrete-time Markov jump linear systems with multiplicative noises // Int. J. of Control. 2013. V. 86 (5). P. 779-793.
Ломакина С.С., Смагин В.И. Робастная фильтрация в непрерывных системах со скачкообразными изменениями параметров в случайные моменты времени // Автометрия. 2005. Т. 41, № 2. С. 36-43.
Ким К.С., Смагин В.И. Фильтрация и диагностика в дискретных стохастических системах со скачкообразными параметрами и мультипликативными возмущениями // Вестник Томского государственного университета. Управление, вычислительная техника и информатика. 2020. № 51. С. 79-86.
Janczak D., Grishin Y. State estimation of linear dynamic system with unknown input and uncertain observation using dynamic programming // Control and Cybernetics. 2006. V. 35 (4). P. 851-862.
Gillijns S., Moor B. Unbiased minimum-variance input and state estimation for linear discrete-time systems // Automatica. 2007. V. 43. P. 111-116.
Smagin V., Koshkin G., Udod V. State estimation for linear discrete-time systems with unknown input using nonparametric technique // ACSR-Advances in Computer Science Research. 2015. V. 18. P. 675-677.
Smagin V., Koshkin G. Kalman filtering and conrol algorithms for systems with unknown disturbances and parameters using nonparametric technique // Proc. 20th International Conference on Methods and Models in Automation and Robotics (MMAR 2015), 24-27 August 2015, Miedzyzdroje, Poland. P. 247-251.
Koshkin G., Smagin V. Kalman filtering and forecasting algorithms with use of nonparametric functional estimators // Springer Proc. in Mathematical Statistics / R. Cao et al. (Eds.). 2016. V. 175. P. 75-84.
Kim K.S., Smagin V.I. Robust filtering for discrete systems with unknown inputs and jump parameters // Automatic Control and Computer Sciences. 2020. V. 54 (1). P. 1-9.
Barmish B.R., Polyak B.T. A new approach to open robustness problems based on probabilistic predication formulae // Proc. 13th World IFAC Congr., 30 June - 5 July, San Francisco, USA. 1996. V. H. P. 1-6.
Athans M. The matrix minimum principle // Information and Control. 1968. V. 11. P. 592-606.