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Sensors and controllers location in distributed systems - A survey. (English) Zbl 0555.93035
A survey of the field of optimal sensors and/or controllers location for dynamical distributed parameter systems modelled by partial differential equations is presented. The recent contributions in this field are grouped according to the main goal for which the location problem is developed, namely: system identification, state estimation, and optimal control. In order to pose the sensors and controllers location problem, the semigroup approach for modelling distributed linear systems is briefly reviewed together with its equivalent (infinite dimensional) and approximate (finite dimensional) Fourier expansion representations. After presenting a concise general review of several methods considered in the current literature, a classification of methods is also proposed. The main classifying factor concerns the use of N-modal approximation schemes, and the different stages of the optimization procedure in which they are required.

MSC:
93C20 Control/observation systems governed by partial differential equations
93-02 Research exposition (monographs, survey articles) pertaining to systems and control theory
93B30 System identification
42C15 General harmonic expansions, frames
93C25 Control/observation systems in abstract spaces
93E12 Identification in stochastic control theory
47D03 Groups and semigroups of linear operators
93C05 Linear systems in control theory
93E10 Estimation and detection in stochastic control theory
93E20 Optimal stochastic control
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[1] Ahmed, N.U.; Teo, K.L., ()
[2] Aidarous, S.E., Optimal allocation of pointwise controllers in stochastic distributed systems, () · Zbl 0312.93048
[3] Aidarous, S.E.; Gevers, M.R.; Installé, M.J., Optimal sensors allocation strategies for a class of stochastic distributed systems, Int. J. control, 22, 197, (1975) · Zbl 0311.93056
[4] Aidarous, S.E.; Gevers, M.R.; Installé, M.J., Optimal pointwise discrete control and controllers location strategies for stochastic distributed systems, Int. J. control, 24, 493, (1976) · Zbl 0332.93084
[5] Aidarous, S.E.; Gevers, M.R.; Installé, M.J., On the asymptotic behaviour of sensors’ allocation algorithm in stochastic distributed systems, () · Zbl 0379.93056
[6] Akhiezer, N.I.; Glazman, I.M., ()
[7] Ames, W.F., ()
[8] Amouroux, M., Sur une méthode de détermination de l’emplacement optimal de points d’action pour une classe de systèmes linéaire à paramètres répartis, C.R. acad. sci. Paris, 277, 193, (1973) · Zbl 0274.93017
[9] Amouroux, M.; Babary, J.P., Sur la commandabilité de système linéaire à paramètres répartis et sons utilization pour la determination de points d’action optimaux, R.a.i. r.o., J-3, 120, (1973) · Zbl 0273.93015
[10] Amouroux, M.; Babary, J.P., Optimal pointwise control for a class of distributed parameter systems, (), 1-2 · Zbl 0391.49006
[11] Amouroux, M.; Babary, J.P., On the optimal pointwise control and parametric optimization of distributed parameter systems, Int. J. control, 28, 789, (1978) · Zbl 0391.49006
[12] Amouroux, M.; Babary, J.P., On optimization of zones of action for an optimal control problem for distributed parameter systems, Int. J. control, 29, 861, (1979) · Zbl 0444.49004
[13] Amouroux, M.; Babary, J.P.; Malandrakis, C., Optimal location for linear stochastic distributed parameter systems, () · Zbl 0392.93030
[14] Amouroux, M.; Di Pillo, G.; Grippo, L., Optimal selection of sensors and control location for a class of distributed parameter systems, Ric. automatica, 7, 92, (1976)
[15] Athans, M., Toward a practical theory of distributed parameter systems, IEEE trans aut. control, AC-15, 245, (1970)
[16] ()
[17] Balakrishnan, A.V., ()
[18] Banks, H.T.; Kunisch, K., An approximation theory for nonlinear partial differential equations with applications to identification and control, SIAM J. control & optimiz., 20, 815, (1982) · Zbl 0503.93016
[19] Bencala, K.E.; Seinfeld, J.H., Distributed parameter filtering: boundary noise and discrete observations, Int. J. syst. sci., 10, 493, (1979) · Zbl 0404.93043
[20] Bensoussan, A., ()
[21] Bensoussan, A., Optimization of sensors location in a distributed parameter system, ()
[22] Bensoussan, A., Control of stochastic partial differential equations, () · Zbl 0548.35037
[23] Burger, J., Determination de l’emplacement optimal des actioneurs ponctuels dans un système regi par une équation aux derivée partielles linéaire, C.R. acad. sci. Paris, 280, 161, (1975) · Zbl 0299.93021
[24] Burger, J., Emplacement optimal des actionneurs ponctuels ou par zones dans un système gouverné par une équation linéaire d’evolution du premier ordre, R.a.i.r.o., J-5, 87, (1976) · Zbl 0332.93049
[25] Burger, J.; Chavent, G., Identification de paramètre repartis dans LES équations aux dérivés partielles, R.A.I.R.O. syst. anal. & control, 13, 115, (1979) · Zbl 0405.93017
[26] Butkovskiy, A.G., ()
[27] Cannon, J.R.; Klein, R.E., Optimal selection of measurement location in a conductor for approximate determination of temperature distribution, (), 750-756
[28] Cannon, J.R.; Klein, R.E., Optimal selection of measurement locations in a conductor for approximate determination of temperature distributions, Trans. ASME, J. dyn. syst. meas. & control, 93-G, 193, (1971)
[29] Caravani, P.; Di Pillo, G.; Grippo, L., Optimal location of a measurement point in a diffusion process, (), 3-8
[30] Carotenuto, L.; Raiconi, G., Identifiability and identification of a Galerkin approximation for a class of distributed parameter systems, Int. J. syst. sci., 11, 1035, (1980) · Zbl 0494.93013
[31] Carotenuto, L.; Raiconi, G., On the identification of a random parameter function in the one-dimensional diffusion equation and related location, (), 76-81 · Zbl 0526.93062
[32] Chavent, G., About the stability of the optimal control solution of inverse problems, () · Zbl 0436.93018
[33] Chavent, G., Identification of distributed parameter systems: about the output least squares methods, its implementation, and identifiability, (), 85-97
[34] Chavent, G., Local stability of the output least square parameter estimation technique, Mat. aplic. comp., 2, 3, (1983) · Zbl 0567.93017
[35] Chen, W.H.; Seinfeld, J.H., Optimal location of process measurements, Int. J. control, 21, 1003, (1975) · Zbl 0322.93042
[36] Courant, R.; Friedrichs, K.O., ()
[37] Courant, R.; Hilbert, D., ()
[38] Courdesses, M., Optimal sensors and controllers allocation in output feedback control for a class of distributed parameter systems, (), 735-740
[39] Courdesses, M.; Amouroux, M., Identifiabilité et identification des systèmes à paramètres repartis, (), XXI.1-XXI.6
[40] Courdesses, M.; Amouroux, M.; Polis, M.P., Sur des conditions d’identifiabilité des paramètres d’un système distribué de type parabolique, R.A.I.R.O., syst., anal. & control, 15, 347, (1981) · Zbl 0469.93041
[41] Courdesses, M.; Polis, M.P.; Amouroux, M., On identifiability of parameters in a class of parabolic distributed systems, IEEE trans aut. control, AC-26, 474, (1981) · Zbl 0487.93016
[42] Crouch, P.E.; Kubrusly, C.S.; Pritchard, A.J., Systems identification: some fundamental aspects, ()
[43] Curtain, R.F., A survey of infinite dimensional filtering, SIAM rev., 17, 395, (1975) · Zbl 0308.60022
[44] Curtain, R.F., A semigroup approach to the L.Q.G. problem for infinite dimensional systems, IEEE trans circ. & syst., CAS-25, 713, (1978) · Zbl 0402.93045
[45] Curtain, R.F., Compensators for infinite dimensional linear systems, J. franklin inst., 315, 331, (1983) · Zbl 0518.93045
[46] Curtain, R.F., Tracking and regulation for distributed parameter systems, Mat. aplic. comp., 2, 199, (1983) · Zbl 0535.93036
[47] Curtain, R.F., Finite dimensional compensators for parabolic distributed systems with unbounded control and observation, SIAM J. control & optimiz., 22, 255, (1984) · Zbl 0542.93056
[48] Curtain, R.F.; Ichikawa, A., Optimal location of sensors for filtering for distributed systems, () · Zbl 0398.93059
[49] Curtain, R.F.; Pritchard, A.J., ()
[50] Curtain, R.F.; Pritchard, A.J., Infinite dimensional linear systems theory, () · Zbl 0352.49003
[51] Davis, M.H.A., ()
[52] Dunford, N.; Schwartz, J.T., ()
[53] El Jai, A., Sur la commande avec estimation de l’etat initial d’une classe de système a paramètres répartis, considérations pratiques, R.A.I.R.O., syst., anal. & control, 11, 313, (1977) · Zbl 0385.93025
[54] Ewing, D.J.; Higgins, T.J., A sensor location algorithm for distributed parameter systems, ()
[55] Friedman, A., ()
[56] Fuhrmann, P.A., ()
[57] Garabedian, P.R., ()
[58] Goodson, R.E.; Klein, R.E., A definition and some results of distributed systems observability, IEEE trans aut. control, AC-15, 165, (1970)
[59] Goodson, R.E.; Polis, M.P., Identification of parameters in distributed systems, () · Zbl 0298.00029
[60] Gustafson, K.E., ()
[61] Helton, J.W., Systems with infinite dimensional state space: the Hilbert space approach, (), 145
[62] Hille, E.; Phillips, R.S., Functional analysis and semigroups, AMS colloq. publ., vol. XXXI, (1957), Providence · Zbl 0078.10004
[63] Ichikawa, A.; Ryan, E.P., Filtering and control of distributed parameter systems with point observations and inputs, (), 347-357 · Zbl 0408.93045
[64] Ichikawa, A.; Ryan, E.P., Sensor and controller location problems for distributed parameter systems, Automatica, 15, 347, (1979) · Zbl 0408.93045
[65] John, F., ()
[66] Johnson, T.L., Progress in modelling and control of flexible spacecraft, J. franklin inst., 315, 495, (1983) · Zbl 0519.93043
[67] Kaiser, K.W., A method of determining the heat-sensor configuration in temperature distribution controllers, (), 1-3
[68] Kato, T., ()
[69] Kitamura, S.; Nakagiri, S., Identifiability of spatially-varying and constant parameters in distributed systems of parabolic type, SIAM J. control & optimiz., 15, 785, (1977) · Zbl 0354.93020
[70] Kitamura, S.; Taniguchi, Y., Parameter estimation of one- and two-dimensional heat conduction processes using a minicomputer, Int. J. control, 34, 955, (1981)
[71] Klein, R.E., Non well-posed problems in the sense of Hadamard and their relationship to distributed parameter state reconstructor problems, ()
[72] Koivo, A.J.; Kruh, P., On the design of approximately optimal feedback controllers for a distributed parameter system, Int. J. control, 10, 53, (1969) · Zbl 0174.14504
[73] Kubrusly, C.S., Distributed parameter system identification: a survey, Int. J. control, 26, 509, (1977) · Zbl 0405.93012
[74] Kubrusly, C.S., Linear DPS identification in a stochastic environment, R.A.I.R.O. system anal. & control, 14, 343, (1980) · Zbl 0477.93064
[75] Kubrusly, C.S., On identifiability of linear dynamical systems, Mat. aplic. comp., 3, 219, (1984) · Zbl 0558.93021
[76] Kumar, S.; Seinfeld, J.H., Optimal location of measurements for distributed parameter estimation, IEEE trans aut. control, AC-23, 690, (1978) · Zbl 0381.93047
[77] Kumar, S.; Seinfeld, J.H., Optimal location of measurements in tubular reactors, Chem. engng. sci., 33, 1507, (1978)
[78] Le Pourhiet, A.; Le Letty, L., Optimization of sensors location in distributed parameter system identification, (), 1581-1591
[79] Lee, M.H.; Koppel, L.B.; Lim, H.C., Optimal sensor locations and controller settings for class of counter current processes, (), 36
[80] Leigh, J.R., ()
[81] Lions, J.L., ()
[82] Lions, J.L., Some aspects of the optimal control of distributed parameter systems, () · Zbl 0275.49001
[83] Lions, J.L., Optimal control of deterministic distributed parameter system, () · Zbl 0275.49001
[84] Lions, J.L., On the foundations of the optimal control of distributed systems, () · Zbl 0451.49009
[85] Malandrakis, C.G., Optimal sensor and controller allocation for a class of distributed parameter systems, Int. J. syst. sci., 10, 1283, (1979) · Zbl 0439.93034
[86] Mikhlin, S.G., ()
[87] Morari, M.; O’Dowd, J., Optimal sensors location in the presence of nonstationary noise, Automatica, 16, 463, (1980) · Zbl 0441.93038
[88] Nakagiri, S-I., Identifiability of linear systems in Hilbert spaces, SIAM J. control & optimiz., 21, 501, (1983)
[89] Nakamori, Y.; Miyamoto, S.; Ikeda, S.; Sawaragi, Y., Measurement optimization with sensitivity criteria for distributed parameter systems, IEEE trans aut. control, AC-25, 889, (1980) · Zbl 0444.93027
[90] Naylor, A.W.; Sell, G.R., ()
[91] Omatu, S.; Koide, S.; Soeda, T., Optimal sensor location problem for linear distributed parameter systems, IEEE trans aut. control, AC-23, 665, (1978) · Zbl 0381.93045
[92] Omatu, S.; Seinfeld, J.H., Optimization of sensor and actuator location in a distributed parameter system, J. franklin inst., 315, 407, (1983) · Zbl 0528.93068
[93] Phillipson, G.A., ()
[94] Polis, M.P., The distributed system parameter identification problem: a survey of recent results, (), SP.45-SP.58
[95] Polis, M.P.; Goodson, R.E., Parameter identification in distributed systems: a synthesizing overview, (), 45
[96] Polis, M.P.; Goodson, R.E.; Wozny, M.J., On parameter identification of distributed systems using Galerkin’s criterion, Automatica, 9, 56, (1973)
[97] Pritchard, A.J., Infinite-dimensional linear system theory, (), 641
[98] Qureshi, Z.H.; Ng, T.S.; Goodwin, G.C., Optimum experimental design for identification of distributed parameter systems, Int. J. control, 31, 21, (1980) · Zbl 0431.93017
[99] Rafajlłowicz, E., Design of experiments for eignvalue identification in distributed-parameter systems, Int. J. control, 34, 1079, (1981)
[100] Rafajlłowicz, E., Optimal experimental design for identification of linear distributed-parameter systems: frequency domain approach, IEEE trans aut. control, AC-28, 806, (1983)
[101] Ray, W.H., Distributed parameter state estimation algorithms and applications—a survey, (), 1-8
[102] Ray, W.H., Some recent applications of distributed parameter systems theory—a survey, Automatica, 14, 281, (1978) · Zbl 0375.93030
[103] ()
[104] Robinson, A.C., A survey of optimal control of distributed parameter systems, Automatica, 7, 371, (1971) · Zbl 0218.49001
[105] ()
[106] Sakawa, Y., Observability and related problems of partial differential equations of parabolic type, SIAM J. control, 13, 14, (1975) · Zbl 0296.93006
[107] Sawaragi, Y.; Soeda, T.; Omatu, S., Modelling, estimation and their applications for distributed parameter systems, () · Zbl 0392.93001
[108] Schechter, M., ()
[109] Seinfeld, J.H.; Chen, W.H., Estimation of parameters in partial differential equations from noisy experimental data, Chem. engng. sci., 26, 753, (1971)
[110] Showalter, R.E., ()
[111] Sokollik, F., Identifikation von systemen mit verteilten parametern, Messen. steuern. regeln., 17, 271, (1974)
[112] Sokollik, F., Zur parameterschätzung von systemen mit verteilten parametern mittels on-line-verfahren, Messen. steuern. regeln., 19, 84, (1976)
[113] Sokollik, F., Zur optimalen wahl der meßorte bei der parameterschätzung von systemen mit verteilten parametern, Messen. steuern. regeln., 19, 194, (1976)
[114] (), Parts I/II
[115] Treves, F., ()
[116] Tzafestas, S.G., Distributed parameter state estimation, () · Zbl 0275.93053
[117] ()
[118] ()
[119] Tzafestas, S.G.; Stavroulakis, P., Recent advances in the study of distributed parameter systems, J. franklin inst., 315, 285, (1983) · Zbl 0517.93037
[120] Wang, P.K.C., Control of distributed parameter systems, () · Zbl 0204.17202
[121] Weidmann, J., ()
[122] Weinberger, H.F., ()
[123] Yosida, K., ()
[124] Yu, T.K.; Seinfeld, J.H., Observability of a class of hyperbolic distributed parameter systems, IEEE trans aut. control, AC-16, 495, (1971)
[125] Yu, T.K.; Seinfeld, J.H., Observability and optimal measurement location in linear distributed parameter systems, Int. J. control., 18, 785, (1973) · Zbl 0263.93010
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