A Review of the State and Parameter Estimation Theory in Distributed Systems

REFERENCES

• Butkovskii (A G) and Lerner (A Y). The Optimal Control of Systems with Distributed Parameters. Automation and Remote Control. 21, 6; 1960; 472–477.
   Google Scholar
• Kalman (R E). A New Approach to Linear Filtering and Prediction Problems. ASME Trans. J. Basic Engg. 82, series D, 1; 1960; 35–4.
   Google Scholar
• Kalman (R E) and Bucy (R S). New Results in Linear Filtering and Prediction Theory. Ibid. 83, 4; 1961; 95–107.
   Google Scholar
• Athans (M). Toward a Practical Theory for Distributed Parameter Systems. IEEE Trans. AC-15, 2; 1970; 245–247.
   Web of Science ®Google Scholar
• Meditch (J S). On State Estimation for Distributed Parameter Systems. J. Franklin Institute. 290, 1; 1970; 49–59.
   Google Scholar
• Forsythe (C E) and Wasow (W R). Finite-Difference Methods for Partial Differential Equations. 1967. John Wiley, New York.
   Google Scholar
• Polis (M P). On Problems of Parameter Identification for Distributed Systems with Results Using Galerkin's Criterion. 1972. Ph. D. Thesis, Purdue Univ. Lafayette, Indiana.
   Google Scholar
• Pous (M P), Goodson (R E) and Wozny (M J). On Parameter Identification for Distributed Systems using Galerkin's Criterion. Automatica. 9, 1; 1973; 53–64.
   Google Scholar
• Aguilar Martin (J), Alengrin (G) and Hernandez (C). Estimation of the Diffusion Co-efficient of a Fluidized Bed Catalytic Reactor Using Nonlinear Filtering Techniques. In Identification and System parameter Estimation, (Proc. 3rd IFAC Symposium), P. Eykhoff Ed., 1973, 255–264.
   Google Scholar
• Finlayson (B A) and Scriven (L G). The Method of Weighted Residuals—A review. Applied Mechanics Review. 19, 9; 1966; 735–748.
   Google Scholar
• Courant (R) and Hilbert (D). Methods of Mathematical Physics, Vol. II. 1962 Interscience.
   Google Scholar
• Carpenter (W T), Wozny (M J) and Goodson (R E). Distributed Parameter Identification Using the Method of Characteristics. ASME Trans., J. of Dynamic Systems, Measurement and Control, series G. 93, 2; 1971; 73–78.
   Google Scholar
• Goodson (R E). Distributed System Simulation Using Infinite Product Expansions. Simulation. 15, 6; 1970; 255–273.
   Google Scholar
• Ward (E) and Goodson (R E). Identification of Non linear Boundary Conditions in Distributed Systems with Linear Fields. ASME Trans. J. of Dynamic Systems Measurement and Control, series G. 95, 4, 1973; 390–395.
   Google Scholar
• Zienkiewicz (O C). The Finite-element Method in Engineering Science. 1971. McGraw-Hill, New York.
   Google Scholar
• Huebner (K H). The Finite-Element Method for Engineers. 1975. John Wiley, New York.
   Google Scholar
• Gallagher (R H). Finite Element Analyses: Fundamentals. 1975. Prentice Hall, Englewood.
   Google Scholar
• Reddy (K S). Studies of the State and Parameter Estimation in Distributed Systems. 1976. Ph. D. Thesis. Submitted to Indian Institute of Technology, Delhi.
   Google Scholar
• Wang (P K C). Control of Distributed Parameter Systems. Advances in Control Systems—I. Ed. C. T. Leondes, Academic Press, 1964. P 67–69.
   Google Scholar
• Goodson (R E) and Klein (R E). A Definition and Some Results for Distributed System Observability. IEEE Trans. AC-15, 2; 1970; 165–174.
   Web of Science ®Google Scholar
• Yu (T K) and Seinfeld (J H). Observability of a Class of Hyperbolic Distributed Parameter Systems. IEEE Trans. AC-16, 5; 1971; 495–196.
   Web of Science ®Google Scholar
• Yu (TK) and Seinfeld (J H). Observability and Optimal Measurement Location in Linear Distributed Systems. Int. J. Control. 18, 4; 1973; 785–799.
   Web of Science ®Google Scholar
• Thowson (A) and Perkins (W R). Observability Conditions for Two General Classes of Linear Flow Processes. IEEE Trans. AC-19, 4; 1974; 603–604.
   Web of Science ®Google Scholar
• Sendula (M). Observability of Linear Systems with Time-variable Delays. IEEE Trans. AC-19, 4; 1974; 604–605.
   Web of Science ®Google Scholar
• Cannon (J R) and Klein (R E). Optimal Selection of Measurement Locations in a Conductor for Approximate Determination of Temperature Distribution. Proc. JACC. 1970; 750–756.
   Google Scholar
• Kwakernaak (H). Optimal Filtering in Linear Systems with Time Delays. IEEE Trans. AC-12, 2; 1967; 169173.
   Google Scholar
• Balakrishnan (A V) and Lions (J L). State Estimation for Infinite Dimensional Systems. J. Computer and Systems Sci. 1, 4; 1967; 391–403.
   Google Scholar
• Falb (P L). Infinite Dimensional Filtering. The Kalman-Bucy Filter in Hilbert Space. Information and Control. 11, 1; 1967; 102–137.
   Google Scholar
• Tzafestas (S G) and Nightingale (J M). Optimal Filtering, Smoothing and Prediction in Linear Distributed Parameter Systems. Proc. IEEE. 115, 8; 1968a; 1207–1212.
   Google Scholar
• Tzafestas (S G) and Nightingale (J M). Concerning Optimal Filtering Theory for Linear Distributed Parameter Systems. Proc. IEE. 115, 11; 1968b; 1737–1742.
   Google Scholar
• Tzafestas (S G) and Nightingale (J M). Maximum Likelihood Approach to the Optimal Filtering of Distributed Systems. Proc. IEE. 116, 7; 1969; 1085–1093.
   Google Scholar
• Thau (F E). On Optimum Filtering for a Class of Linear Distributed Parameter Systems. ASME Trans. J. of Basic Engg. Series D. 91, 2; 1969; 173–178.
   Google Scholar
• Atre (S R) and Lamba (S S). Derivation of an Optimal Estimator for Distributed Parameter Systems via Maximum Principle. IEEE Trans. AC-17, 3; 1972a; 388–390.
   Web of Science ®Google Scholar
• Atre (S R) and Lamba (S S). Optimal Estimation in Distributed Processes Using the Innovations Approach. IEEE Trans. AC-17, 5; 1972b; 710–712.
   Web of Science ®Google Scholar
• Tzafestas (S G). Baysian Approach to Distributed Para meter Filtering and Smoothing. Int. J. Control. 15, 2; 1972a; 273–295.
   Web of Science ®Google Scholar
• Tzafestas (S G). On Optimum Distributed Parameters Filtering and Fixed-Interval Smoothing for Coloured Noise. IEEE Trans. AC-17, 4; 1972b; 448–58.
   Web of Science ®Google Scholar
• Kailath (T). An Innovations Approach to Least-Squares Estimation Part—I: Linear Filtering in Additive White Noise. IEEE Trans. AC-13, 6; 1968; 646–655.
   Web of Science ®Google Scholar
• Reddy (K S) and Rajamani (V S). Optimum Filtering for a Class of Distributed Parameter Systems with Coloured Measurement Noise. Int. J. Syst. Sci. 6, 7; 1975a; 615–620.
   Web of Science ®Google Scholar
• Reddy (K S) and Rajamani (V S). Optimal Estimation in Linear Distributed Systems with Time Delays: An Innovations Approach. Int. J. Syst. Sci. 6, 9; 1975b, 859–863.
   Google Scholar
• Kumar (G R V) and Sage (A P). Error Analysis Algorithms for Distributed Parameter Filtering. Automatica. 8, 3; 1972; 363–366.
   Web of Science ®Google Scholar
• Saka WA (Y). Optimal Filtering in Linear Distributed Parameter Systems. Int. J. Control. 16, 1; 1972; 115–127.
   Web of Science ®Google Scholar
• Reddy (K S) and Rajamani (V S). Least-Squares Estimation in Interacting Systems with Lumped and Distributed Parameters. Proc. National Systems Conference, held at Roorkee, Paper No. STA-14, 1976.
   Google Scholar
• Kailath (T). Some New Algorithms for Recursive Estimation in Constant Linear Systems. IEEE Trans. IT-9, 6; 1973; 750–760.
   Web of Science ®Google Scholar
• Casti (J) and Ljung (L). Some Analytic and Computa tional Results for Operator Riccati Equations. SIAM J. Control. 13, 4; 1975; 817–825.
   Web of Science ®Google Scholar
• Chandrasekhar (S). Radiative Transfer. 1960. Dover, New York.
   Google Scholar
• Seinfeld (J H). Nonlinear Estimation for Partial Differential Equations, Chsm. Engg. Sci. 24, 1; 1969; 75–83.
   Web of Science ®Google Scholar
• Seinfeld (J H), Gavalas (G R) and Hwang (M J). Non linear Filtering in Distributed Parameter Systems. ASME Trans. J. of Dynamic Systems, Measurement and Control. Series G. 93, 3; 1971; 157–163.
   Google Scholar
• Detchmendy (D) and Sridhar (R). Sequential Estimation of State and Parameters in Noisy Nonlinear Dynamical Systems. ASME Transactions, J. Basic Engg. Series D. 88, 2; 1966; 362–368.
   Google Scholar
• Seinfeld (J H). Identification of Parameters in Partial Differential Equations. Chemical Engineering Science. 24, 1; 1969; 65–74.
   Web of Science ®Google Scholar
• Lamont (G B). Estimation of States in Systems Described by Partial Differential Equations. Proc. 13th Midwest Symposium on Circuit Theory, Mineapolis, Min., 1970.
   Google Scholar
• Lamont (G B) and Kumar (K S P). Sequential Interpolating Estimator for Nonlinear Partial Differential Equations. Preprints, IFAC Symposium on the control of distributed parameter systems. Banff, Alberta, Canada, 1971; paper No. 8–5.
   Google Scholar
• Sehgal (R) and Webb (R P). Nonlinear Distributed Para meter Estimation. Proc. IEEE Decision and Control Conference, Neworlines, La., 1972; P 89–93.
   Google Scholar
• Yu (T K), Seinfeld (J H) and Ray (W H). Filtering in Nonlinear Time-Delay Systems. IEEE Trans. AC-19, 4; 1974; 324–333.
   Web of Science ®Google Scholar
• Reddy (K S) and Rajamani (V S). Application of Hierarchical Systems Theory to Sequential Estimation in Chemical Reactors. Presented at the IFAC Workshop in Sept. 1977 in France.
   Google Scholar
• Smith (N J) and Sage (A P). A Sequential Method for System Identification in Hierarchical Structure. Automatica. 9, 6; 1973; 677–688.
   Web of Science ®Google Scholar
• Ajinkya (M B), Ray (W H), Yu (T K) and Seinfeld (J H). The Application of an Approximate Nonlinear Filter to Systems Governed by Coupled Ordinary and Partial Differential Equations. Int. J. Sys. Sci. 6, 4; 1975a; 313–332.
   Web of Science ®Google Scholar
• Ray (W H) and Seinfeld (J H). Filtering in Distributed Parameter Systems with Moving Boundaries. Automatica. 11, 5; 1975; 509–515.
   Web of Science ®Google Scholar
• Dreifke (G E) and Houghen (J O). Experimental Determination of System Dynamics by Pulse Methods. Preprints JACC. 1963; 452–458.
   Google Scholar
• Astrom (K J) and Eykhoff (P). System Identification: A Survey. Automatica. 7, 2; 1971; 123–162.
   Google Scholar
• Jones JR (B F). The Determination of a Co-efficient in a Parabolic Differential Equation: Part I, Existence and Uniqueness. J. of Mathematics and Mechanics. 11, 6; 1962; 907–918.
   Google Scholar
• Douglas JR (J) and Jones JR (B F). The Determination of a Co-efficient in a Parabolic Differential Equation: Part II, Numerical Approximation. J. of Mathematics and Mechanics. 11, 6; 1962; 919–926.
   Google Scholar
• Beck (J V). Calculation of Thermal Diffusivity from Temperature Measurements. Trans. ASME, J. Heat Transfer, Series C. 85. 2; 1963; 181–182.
   Google Scholar
• Perdreauville (F J) and Goodson (R E). Identification of Systems Described by Partial Differential Equations. Trans. ASME, J. Basic Engg., Series D. 88, 2; 1966; 463–468.
   Google Scholar
• Tzafestas (S G). Identification of Stochastic Distributed Systems. Int. J. Control. 11, 4; 1970; 619–625.
   Web of Science ®Google Scholar
• Fairman (F W) and Shen (D W C). Parameter Identification for a Class of Distributed Systems. Ibid. 11, 6; 1970; 929–940.
   Google Scholar
• Zhivoglyadov (V P) and Kaipov (V K H). Identification of Distributed Parameter Plants in the Presence of Noise. Proc. IFAC Symposium on Identification of Automatic Control Systems, Prague, Czechoslovakia, paper No. 3–5, 1967.
   Google Scholar
• Collins (P L) and Khatri (H C). Identification of Distributed Parameter Systems Using Finite Differences—ASME Trans. J. Basic Engg., Series D. 91, 2; 1969; 239–245.
   Google Scholar
• Seinfeld (J H) and Chen (W H). Estimation of Parameters in Distributed Systems from Noisy Experimental Data. Chem. Engg. Sci. 26, 6; 1971; 753–766.
   Web of Science ®Google Scholar
• Chavent (G). Analyse Functionnelle et Identification de Co-efficients Repartis dans les Equations aux Denvers Partielles. Thesis Paris 1971.
   Google Scholar
• Vemuri (V) and Karplus (W J). Identification of Non linear Parameters of Ground Water Basins by Hybrid Computation. Water Resources Research. 5, 1; 1969; 172–185.
   Google Scholar
• Saridis (G N) and Badavas (P C). Identifying Solutions of Distributed Parameter Systems by Stochastic Approximation. IEEE Trans. AC-15, 3; 1970; 393–395.
   Web of Science ®Google Scholar
• Dale (B O) and Cohen (R). Multi-parameter Identification in Linear Continuous Vibratory Systems. ASME Trans. J. of Dynamics Systems, Measurement and Control. 93, 1; 1971; 45–52.
   Google Scholar
• Ruban (A I). Identification of Distributed Dynamic Objects on the Basis of a Sensitivity Algorithm. Engineering Cybernetics. 9, 6; 1971; 1137–1142.
   Google Scholar
• Wozny (M J), Carpenter (W T) and Stein (G). Identification of Green's Function for Distributed Parameters Systems. IEEE Trans. AC-15, 1; 1970; 155–157.
   Web of Science ®Google Scholar
• Luckinbill (D L) and Childs (B). Parameter Identification by Newton-Raphson Expansions for Partial Differential Equations. Proc. IFAC Symposium on the control of distributed parameter systems. Alberta, Canada, 1971, Paper No. 13–3.
   Google Scholar
• Kozhinsky (O S) and Rajbman (N S). Identification of Distributed Plants. Preprints IFAC Symposium on the control of distributed parameter systems. Alberta, Canada, 1971; paper No. 8–3.
   Google Scholar
• Hamza (H M) and Sheirah (M A). On-line Identification of Distributed Parameter Systems. Automatica. 9, 6; 1973; 689–698.
   Web of Science ®Google Scholar
• Collins (J D), Young (J P) and Kiefling (L). Methods and Application of System Identification in Shock Vibration, System Identification of Vibrating Structures, ASME publication of the 1972 Winter annual meeting.
   Google Scholar
• Chaudhuri (S P). A Class of Distributed Parameter System Identification via Differential Approximation and Quasi-Linearization. 5th Hawaii, International Conference on System Sciences, University of Hawaii, 1973.
   Google Scholar
• Meditch (J S). Least-Squares Filtering and Smoothing for Linear Distributed Parameter Systems. Automatica. 7, 3; 1971; 315–320.
   Web of Science ®Google Scholar
• Tzafestas (S G). On the Distributed Parameter Least-Squares State Estimation Theory. Int. J. Syst. Sci. 4, 6; 1973; 833–858.
   Google Scholar
• Padmanabhan (L). On Filtering in Delay Systems with Continuous Dynamics and Discrete Time Observations. Proc. 1972 JACC. P 826–830.
   Google Scholar
• Perlis (H J) and Okunseinde (B). Multiple Kalman Filters in a Distributed Stream Monitoring System. Proc. 1974 Joint Automatic Control. P 615.
   Google Scholar
• Atre (S R). A Note on the Kalman-Bucy Filtering for Linear Distributed Parameter Systems. IEEE Trans. AC-17, 5; 1972; 712–714.
   Web of Science ®Google Scholar
• Ajinkya (M B), Kohne (M), Mader (H F) and Ray (W H). The Experimental Implementation of a Distributed Parameter Filter. Automatica. 11, 6; 1975 b; 571–577.
   Web of Science ®Google Scholar
• Ajinkya (M B), Ray (W H) and Froment (G F). On line Estimation of Catalyst-Activity Profiles in Packed Bed Reactors Having Catalyst Decay. I and EC Process Design and Development. 13. 2; 1974; 107–112.
   Google Scholar
• Bankoff (S G) and Hanzevack (E L). Real Time Adaptive Air Pollution Modelling. Proceedings Joint AICHE- EFCHE Meeting, Munich, Sept. 1974.
   Google Scholar
• Ray (W H). An Optimal Control Scheme for Tubular Chemical Reactors Suffering Catalyst Decay. Proc. IFAC Symposium on Distributed Parameter Systems, Banff, 1971; Paper No. 10.
   Google Scholar
• Yu (T K) and Seinfeld (J H). Control of Stochastic Distributed Parameter Systems. J. Opt. Theory. App. 10, 6; 1972; 362–380.
   Google Scholar
• McGreavy (C) and Vago (A). Estimation of Spatially Distributed Decay Parameters in a Chemical Reactor. Proc. IFAC. Symposiym on Identification and System Parameter Est., Hague, 1973; 307–310.
   Google Scholar
• Goldman (S F) and Sargent (R W H). Applications of Linear Estimation Theory to Chemical Processes: A Feasibility Study. Chem. Eng. Sci. 26, 12; 1971; 1535–1537.
   Web of Science ®Google Scholar
• Joffe (B L) and Sargent (R W). The Design of an On line Control Scheme for a Tubular Catalytic Reactor. Trans. Inst. Chem. Engg. 50, 3; 1972; 270–275.
   Google Scholar
• Seinfeld (J H). Current Problems in the Modelling and Control of Urban Air Pollution. Proceedings 1972, JACC. P 717.
   Google Scholar
• Seinfeld (J H). Determination of Air Pollution Control Strategies. Proceedings 1974, JACC. P 554.
   Google Scholar
• Gould (L A), Schweppe (F C) and Desalu (A A). Dynamic Estimation of Air Pollution. IEEE Trans. AC-19, 6; 1974; 904–910.
   Google Scholar
• Special Issue on Linear-Quadratic-Gaussian Problem, IEEE Trans. AC-16, 6; 1971.
   Google Scholar
• Special Issue on System Identification and Time Series Analysis. IEEE Trans. AC-19, 6; 1974.
   Google Scholar