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Omatu, S.; Seinfeld, J. H.

Existence and comparison theorems for partial differential equations of Riccati type. (English) Zbl 0451.35009

J. Optimization Theory Appl. 36, 263-276 (1982).
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Cited in 6 Documents

MSC:

35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35A08 Fundamental solutions to PDEs

Keywords:

equation of Riccati type; optimal filtering error covariance function; linear distributed-parameter system; Dirac delta function; existence and uniqueness of a bounded solution; fundamental solution; successive approximation; comparison theorem
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References:

[1] Bensoussan, A.,Filtrage Optimal des Systemes Lineaires, Dunod, Paris, France, 1971. · Zbl 0231.93022
[2] Bensoussan, A.,Optimization of Sensor Location in a Linear Filtering Problem, Proceedings of the International Symposium on Stability of Dynamical Systems, Coventry, England, pp. 62-84, 1972.
[3] Datko, R.,A Linear Control Problem in Abstract Hilbert Space, Journal of Differential Equations, Vol. 9, pp. 346-359, 1971. · Zbl 0218.93011 · doi:10.1016/0022-0396(71)90087-8
[4] Lions, J. L.,Optimal Control of Systems Governed by Partial Differential Equations, Springer-Verlag, New York, New York, 1970. · Zbl 0231.35041
[5] Curtain, R. F., andPritchard, A. J.,The Infinite-Dimensional Riccati Equation, Journal of Mathematical Analysis and Applications, Vol. 47, pp. 43-57, 1974. · Zbl 0279.93048 · doi:10.1016/0022-247X(74)90035-3
[6] Omatu, S., Koide, S., andSoeda, T.,Optimal Sensor Location Problem for a Linear Distributed Parameter System, IEEE Transactions on Automatic Control, Vol. AC-23, pp. 665-673, 1978. · Zbl 0381.93045 · doi:10.1109/TAC.1978.1101826
[7] Sakawa, Y.,Optimal Filtering in Linear Distributed-Parameter Systems, International Journal of Control, Vol. 16, pp. 115-127, 1972. · Zbl 0236.93052 · doi:10.1080/00207177208932247
[8] Sawaragi, Y., Soeda, T., andOmatu, S.,Modeling, Estimation, and Their Applications for Distributed Parameter Systems, Springer-Verlag, Berlin, Germany, 1978. · Zbl 0392.93001
[9] Ito, S.,Partial Differential Equations (in Japanese), Baifukan, Tokyo, Japan, 1966.
[10] Yosida, K.,Functional Analysis, Springer-Verlag, New York, New York, 1968. · Zbl 0152.32102
[11] Omata, S., andSoeda, T.,Estimation Problems for a Linear Stochastic Differential Equation, Stochastic Differential Equations, Edited by K. Ito, Kinokuniya, Tokyo, Japan, 1978.
[12] Omatu, S., andSoeda, T.,Optimal Sensor Location in a Linear Distributed Parameter System, Proceedings of the IFAC Symposium on Environmental System Planning, Design, and Control, Kyoto, Japan, 1977.
[13] Omata, S., Soeda, T., andTomita, Y.,Linear Fixed-Point Smoothing by Using Functional Analysis, IEEE Transactions on Automatic Control, Vol. AC-22, pp. 9-18, 1977. · Zbl 0346.93045 · doi:10.1109/TAC.1977.1101400
[14] Kumar, S., andSeinfeld, J. H.,Optimal Location of Measurements for Distributed Parameter Estimation, IEEE Transactions on Automatic Control, Vol. AC-23, pp. 690-698, 1978. · Zbl 0381.93047 · doi:10.1109/TAC.1978.1101803
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