×
Watanabe, Keigo

Optimal partitioned filter of stochastic distributed parameter dynamical systems with unknown initial state. (English) Zbl 0517.93055

J. Franklin Inst. 315, 347-385 (1983).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0517.93055

Cited in 2 Documents

MSC:

93E11 Filtering in stochastic control theory
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
93E25 Computational methods in stochastic control (MSC2010)
93E10 Estimation and detection in stochastic control theory
60B11 Probability theory on linear topological spaces
46C99 Inner product spaces and their generalizations, Hilbert spaces
60G35 Signal detection and filtering (aspects of stochastic processes)
93C25 Control/observation systems in abstract spaces
62M20 Inference from stochastic processes and prediction

Keywords:

stochastic distributed parameter systems; partitioned filter; parallel processing; numerical solution of partial differential Riccati equation
Cite Review PDF
Full Text: DOI

References:

[1] Bensoussan, A., Filtrage Optimal des Systèmes Linéaires (1971), Dunod, Paris · Zbl 0231.93022
[2] Balakrishnan, A. V., Applied Functional Analysis (1976), Springer: Springer Berlin · Zbl 0333.93051
[3] Ajinkya, M. B.; Köhne, M.; Mäder, H. F.; Ray, W. H., The experimental implementation of a distributed parameter filter, Automatica, Vol. 11, 571-577 (1975)
[4] Koda, M.; Seinfeld, J. H., Estimation of urban air pollution, Automatica, Vol. 14, 583-595 (1978) · Zbl 0385.92020
[5] Yoshimura, T.; Okamoto, Y.; Soeda, T., Prediction of air pollutant concentrations in Tokushima prefecture, Japan, Automatica, Vol. 17, 493-508 (1981) · Zbl 0468.93075
[6] Yoshimura, T.; Okamoto, Y.; Watanabe, K.; Soeda, T., Construction of a diffusion model for the prediction of \(SO_2\) concentration, Trans. Soc. Inst. Contr. Engrs, Vol. 17, 461-466 (1981), (in Japanese).
[7] Seinfeld, J. H.; Gavalas, G. R.; Hwang, M., Nonlinear filtering in distributed parameter systems, Trans. ASME, J. Dynamic Systems Meas. Control, Vol. 93, 157-163 (1971)
[8] Ajinkya, M. B., The application of an approximate nonlinear filter to systems governed by coupled ordinary and partial differential equations, Int. J. Syst. Sci., Vol. 6, 313-332 (1975) · Zbl 0306.93029
[9] Thau, F. E., On optimal filtering for a class of linear distributed parameter systems, Trans. ASME, Series D, J. bas. Engng, Vol. 91, 173-178 (1969)
[10] Ray, W. H.; Seinfeld, J. H., Filtering in distributed parameter systems with moving boundaries, Automatica, Vol. 11, 509-515 (1975)
[11] Lausterer, G. K.; Ray, W. H.; Martens, H. R., Real time distributed parameter state estimation applied to a two dimensional heated ingot, Automatica, Vol. 14, 335-344 (1978) · Zbl 0391.93016
[12] Greiss, F. K.; Ray, W. H., Stochastic control of processes having moving boundaries—An experimental study, Automatica, Vol. 16, 157-166 (1980) · Zbl 0433.93054
[13] Tzafestas, S. G., Innovation approach to distributed-parameter detection and estimation, Int. J. Syst. Sci., Vol. 9, 147-184 (1978) · Zbl 0376.93025
[14] Tzafestas, S. G.; Nightingale, J. M., Stochastic distributed filtering approach to gamma-ray imaging, Int. J. Syst. Sci., Vol. 7, 1249-1274 (1976)
[15] Sunahara, Y.; Ohsumi, A.; Imamura, M., A method of parameter identification for linear distributed parameter systems, Automatica, Vol. 12, 245-256 (1976) · Zbl 0331.93072
[16] Ray, W. H.; Lainiotis, D. G., Identification, estimation and control of distributed parameter systems (1978), Marcel Dekker: Marcel Dekker New York · Zbl 0476.00031
[17] Balas, M. J., Feedback control of flexible systems, IEEE Trans. Aut. Control, Vol. AC-23, 673-679 (1978) · Zbl 0381.93012
[18] Balas, M. J., Modal control of certain flexible dynamic systems, SIAM J. Control Optiz., Vol. 16, 450-462 (1978) · Zbl 0384.93036
[19] Meirovitch, L.; Öz, Modal-space control of distributed gyroscopic systems, AIAA J. Guidance Control, Vol. 3, 140-150 (1980) · Zbl 0435.93004
[20] Smith, G. L.; Green, R. N.; Young, G. R., Statistical interpretation of pollution data from satellite, J. Spacecraft, Vol. 12, 374-380 (1975)
[21] Lions, J. L., Optimal Control of Systems Governed by Partial Differential Equations (1971), Springer · Zbl 0203.09001
[22] Lainiotis, D. G., Optimal adaptive estimation: structure and parameter adaption, IEEE Trans. Aut. Control, Vol. AC-16, 160-170 (1971)
[23] Omatu, S.; Soeda, T.; Tomita, Y., Linear fixed-point smoothing by using functional analysis, IEEE Trans. Aut. Control, Vol. AC-22, 9-18 (1977) · Zbl 0346.93045
[24] Omatu, S.; Soeda, T., Optimal estimation problems for a linear distributed parameter systems, Int. J. Syst. Sci., Vol. 9, 753-771 (1978) · Zbl 0389.93047
[25] Kailath, T., An innovation approach to least-squares estimation, Part I: Linear filtering in additive white noise, IEEE Trans. Aut. Control, Vol. AC-13, 646-655 (1968)
[26] Sawaragi, Y.; Soeda, T.; Omatu, S., Modeling, estimation, and their applications for distributed parameter systems, Lecture Notes in Contr. and Inf. Sci., Vol. 11 (1978), Springer · Zbl 0392.93001
[27] Kailath, T., A general likelihood-ratio formula for random signals in Gaussian noise, IEEE Trans. Inf. Theory, Vol. IT-15, 350-361 (1969) · Zbl 0172.42805
[28] Lainiotis, D. G., Optimal nonlinear estimation, Int. J. Control, Vol. 14, 1137-1148 (1971) · Zbl 0225.93034
[29] Lainiotis, D. G., Partitioned estimation algorithms, I: Nonlinear estimation, Inf. Science, Vol. 7, 203-235 (1974) · Zbl 0301.62050
[30] Lainiotis, D. G., Partitioned estimation algorithms, II: Linear estimation, Inf. Science, Vol. 7, 317-340 (1974) · Zbl 0301.62051
[31] Lainiotis, D. G., A unifying framework for linear estimation: Generalized partitioned algorithms, Inf. Science, Vol. 10, 243-278 (1976) · Zbl 0341.93029
[32] Ljung, L.; Kailath, T., Efficient change of initial conditions, dual Chandrasekhar equations, and some applications, IEEE Trans. Aut. Control, Vol. AC-22, 443-447 (1977) · Zbl 0354.93066
[33] Bucy, R. S.; Joseph, P. D., Filtering for Stochastic Processes with Application to Guidance (1968), Wiley: Wiley New York · Zbl 0174.21903
[34] Balakrishnan, A. V., Identification-inverse problems for partial differential equations: A stochastic formulation, Lecture Notes in Computer Science, Vol. 27 (1975), Springer: Springer Berlin · Zbl 0313.93025
[35] Tzafestas, S. G., Parameter adaptive control of stochastic distributed systems, Int. J. Syst. Sci., Vol. 11, 1397-1433 (1980) · Zbl 0455.93039
[36] Watanabe, K.; Yoshimura, T.; Soeda, T., Optimal non-linear estimation for distributed-parameter systems via the partition theorem, Int. J. Syst. Sci., Vol. 11, 1113-1130 (1980) · Zbl 0449.93054
[37] Watanabe, K., An alternative approach to the derivation of distributed-type partitioned filters, Int. J. Syst. Sci., Vol. 12, No. 3, 351-356 (1981) · Zbl 0468.93074
[38] Watanabe, K.; Yoshimura, T.; Soeda, T., A discrete-time adaptive filter for stochastic distributed parameter systems, Trans. ASME, J. Dynamic Syst. Meas. Control, Vol. 103, 266-278 (1981) · Zbl 0464.93078
[39] Watanabe, K.; Yoshimura, T.; Soeda, T., Optimal adaptive estimation and stochastic control for distributed-parameter systems, IEEE Trans. Aut. Control, Vol. AC-27, 216-219 (1982) · Zbl 0471.93060
[40] Lainiotis, D. G.; Deshpande, J. G.; Upadhyay, T. N., Optimal adaptive control: A non-linear separation theorem, Int. J. Control, Vol. 15, 877-888 (1972) · Zbl 0234.93031
[41] Falb, P. L., Infinite-dimensional filtering: The Kalman-Bucy filter in Hilbert space, Inf. Control, Vol. 11, 102-137 (1967) · Zbl 0178.18902
[42] Bensoussan, A.; Viot, M., Optimal control of stochastic linear distributed parameter systems, SIAM J. Control, Vol. 13, 904-926 (1975) · Zbl 0276.93058
[43] Curtain, R. F., Infinite-dimensional filtering, SIAM J. Control, Vol. 13, 89-104 (1975) · Zbl 0296.93036
[44] Curtain, R. F., Estimation theory for abstract evolution equations excited by general white noise processes, SIAM J. Control Optimiz., Vol. 14, 1124-1150 (1976) · Zbl 0344.93064
[45] Curtain, R. F.; Pritchard, A. J., Infinite dimensional linear systems theory, Lecture Notes in Contr. and Inf. Sci., Vol. 8 (1978), Springer · Zbl 0426.93001
[46] Curtain, R. F.; Falb, P. L., Ito’s lemma in infinite dimensions, J. Math. Anal. Appl., Vol. 31, 434-448 (1970) · Zbl 0233.60051
[47] Kailath, T., Some new algorithms for recursive estimation in constant linear systems, IEEE Trans. Inf. Theory, Vol. IT-19, 750-760 (1973) · Zbl 0342.93053
[48] Tzafestas, S. G., On the distributed parameter least-squares state estimation theory, Int. J. Syst. Sci., Vol. 4, 833-858 (1973) · Zbl 0275.93053
[49] Wang, P. K.C., Control of distributed parameter systems, (Leondes, C. T., Advances in Control Systems, Vol. 1 (1964), Academic Press: Academic Press New York) · Zbl 0204.17202
[50] Nakamori, Y.; Miyamoto, S.; Ikeda, S.; Sawaragi, Y., Measurement optimization with sensitivity criteria for distributed parameter systems, IEEE Trans. Aut. Control, Vol. AC-25, 889-901 (1980) · Zbl 0444.93027
[51] Koda, M., Finite difference implementation of distributed parameter filters, Automatica, Vol. 15, 687-692 (1979) · Zbl 0416.93091
[52] Sakawa, Y., Optimal filtering in linear distributed-parameter systems, Int. J. Control, Vol. 16, 115-127 (1972) · Zbl 0236.93052
[53] Watanabe, K., Optimal filtering and smoothing algorithms for linear distributed-parameter systems with pointwise observation, Int. J. Syst. Sci., Vol. 12, 325-349 (1981) · Zbl 0457.93053
[54] Lainiotis, D. G., Partitioned Riccati solution and integration-free doubling algorithms, IEEE Trans. Aut. Control, Vol. AC-21, 677-689 (1976) · Zbl 0344.93063
[55] Tzafestas, S. G., Eigenvalue and eigenfunction sensitivity of distributed-parameter systems (DPS), IEEE Trans. Aut. Control, Vol. AC-20, 172-174 (1975) · Zbl 0298.93004
[56] Mizohata, S., The Theory of Partial Differential Equations (1973), Cambridge University Press: Cambridge University Press London · Zbl 0263.35001
[57] Sidhu, G. S.; Bierman, G. J., Integration-free interval doubling for Riccati equation solutions, IEEE Trans. Aut. Control, Vol. AC-22, 831-834 (1977) · Zbl 0362.49026
[58] Kumar, S.; Seinfeld, J. H., Optimal location of measurements for distributed parameter estimation, IEEE Trans. Aut. Control, Vol. AC-23, 690-698 (1978) · Zbl 0381.93047
[59] Omatu, S.; Koide, S.; Soeda, T., Optimal sensor location problem for linear distributed parameter systems, IEEE Trans. Aut. Control, Vol. AC-23, 665-673 (1978) · Zbl 0381.93045
[60] Malandrakis, C. G., Optimal sensor and controller allocation for a class of distributed parameter systems, Int. J. Syst. Sci., Vol. 10, 1283-1290 (1979) · Zbl 0439.93034
[61] Ichikawa, A.; Ryan, E. P., Sensor and controller location problems for distributed parameter systems, Automatica, Vol. 15, 347-352 (1979) · Zbl 0408.93045
[62] Morari, M.; O’Dowd, M. J., Optimal sensor location in the presence of non-stationary noise, Automatica, Vol. 16, 463-480 (1980) · Zbl 0441.93038
[63] Watanabe, K., Generalized Chandrasekhar algorithms for distributed-parameter filtering problem with pointwise colored measurement noise, Int. J. Syst. Sci., Vol. 13, 619-637 (1982) · Zbl 0487.93070
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.