Korbicz, Józef State estimation in discrete-time distributed parameter systems under incomplete priori information about the system. (English) Zbl 0581.93056 Kybernetika 21, 470-479 (1985). An algorithm for state estimation is presented for linear discrete-time distributed parameter systems in case of incomplete priori information concerning system parameters and statistic characteristics of noises. The algorithm is based on the correction of the covariance matrix of the estimation error taking into consideration a real, not theoretical, error. Digital simulation results confirm the stability of the algorithm and its practical utility. MSC: 93E10 Estimation and detection in stochastic control theory 93C05 Linear systems in control theory 93C35 Multivariable systems, multidimensional control systems 93C55 Discrete-time control/observation systems 93E25 Computational methods in stochastic control (MSC2010) 93E11 Filtering in stochastic control theory 62M20 Inference from stochastic processes and prediction Keywords:state estimation; linear discrete-time distributed parameter systems; incomplete priori information; algorithm PDF BibTeX XML Cite \textit{J. Korbicz}, Kybernetika 21, 470--479 (1985; Zbl 0581.93056) Full Text: EuDML References: [1] N. T. Kuzovkov S. V. Karabanov, O. S. Salytchev: Continuous and Discrete Control Systems and Identification Methods. (in Russian). Mashinostroyenie, Moscow 1978. · Zbl 0451.93004 [2] K. Brammer, G. Siffling: Kalman-Bucy Filter; Deterministische Beobachtung und Stochastische Filterung. R. Oldenburg Verlag, Muchen-Wien 1974. · Zbl 0327.93029 [3] Y. Sawaragi T. Soeda, S. Omatu: Modeling, Estimation and Their Applications for Distributed Parameter Systems. (Lecture Notes in Control and Information Sciences 11.) Springer-Verlag, Berlin-Heidelberg-New York 1978. · Zbl 0392.93001 · doi:10.1007/BFb0112543 [4] Y. Sakawa: Optimal filtering in linear distributed-parameter systems. Internat. J. Control 76 (1972), 1, 115-127. · Zbl 0236.93052 · doi:10.1080/00207177208932247 [5] A. A. Krasovsky: Field estimation at the fuzzy measurements. (in Russian). Dokl. Akad. Nauk SSSR 256 (1981), 5, 1061-1064. [6] V. E. Kraskevitch, J. Korbicz: Supoptimal Kalman-filter for distributed parameter systems. System Science 6 (1980), 3, 225-234. · Zbl 0475.93070 [7] W. H. Ray: Distributed parameter state estimation algorithms and applications - A survey. Proc. 6th World Congress IFAC, Boston, 1975, 8.1/1-8.1/10. [8] G. K. Lausterer W. H. Ray, H. R. Martenes: Real time distributed parameter state estimation applied to a two dimensional heated ingot. Automatica 14 (1978), 4, 335 - 344. · Zbl 0391.93016 · doi:10.1016/0005-1098(78)90033-X [9] R. K. Mehra: On the identification of variances and adaptive Kalman filtering. IEEE Trans. Automat. Control AC-15 (1970), 2, 175-184. [10] J. Korbicz: Adaptive algorithm of the Kalman filter for the distributed parameter systems. Proc. Internat. Conference ”System Engineering”, Conventry, 1980, 266-274. [11] K. Watanabe T. Yoshimura, T. Soeda: A discrete-time adaptive filter for stochastic distributed parameter systems. Trans. ASME Ser. G J. Dynamic Systems Measurement Control 103 (1981), 3, 266-278. · Zbl 0464.93078 · doi:10.1115/1.3140638 [12] S. Omatu, J. H. Seinfeld: A unified approach to discrete-time distributed estimation by the least-squares method. Internat. J. Systems Sci. 12 (1981), 6, 665-686. · Zbl 0467.93060 [13] N. S. Raybman: Control of Technological Processes. (in Russian). Nauka, Moscow 1978. [14] H. Sriyananda: A simple method for the control of divergence in Kalman filter algorithms. Internát. J. Control 16 (1972), 6, 1101-1106. [15] S. G. Tzafestas: Innovation approach to distributed-parameter detection and estimation. Internat. J. Systems Sci. 9 (1978), 2, 147-184. · Zbl 0376.93025 · doi:10.1080/00207727808941687 [16] A. G. Butkovsky: Structural Theory of the Distributed Systems. (in Russian). Nauka, Moscow 1977. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.