Abstract
The purpose of this chapter is to study the behaviour of discrete-time dynamical systems under the influence of external effects which can be described in a statistical way. It can be argued that all real systems operate in a stochastic environment where they are subject to noise (unknown disturbances) and, in addition, the controller has to rely, in practice, on imperfect measurements. The noise may arise due to unpredictable changes at the input end of the system, and/or due to inaccurate measurements at the output end. In either case, exact information about the state of the system is not available, and we should therefore seek methods to estimate the state of the system on the basis of statistically related data. This leads to the state estimation problem. In other applications, the coefficients of the models need to be determined on the basis of the input and output records which are corrupted by noise components. This defines the parameter estimation problem. Both these problems are examined in this chapter and techniques for their solutions are developed.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Sage, A.P. and J.L. Melsa, “Estimation Theory with Applications to Communications and Control”, McGraw-Hill, N.Y., 1971.
Astrom, K.J., “Introduction to Stochastic Control Theory”, Academic Press, N.Y., 1970.
Anderson, B.D.O. and J.B. Moore, “Optimal Filtering”, Prentice Hall, N.J., 1979.
Meditch, J.S., “Stochastic Optimal Linear Estimation and Control”, McGraw-Hill, N.Y., 1969.
Jazwinski, A.H., “Stochastic Processes and Filtering Theory”, Academic Press, N.Y., 1970.
Brogan, W.L., “Modern Control Theory”, Quantum Publishing Inc., N.Y., 1974.
Cox, H., “On the Estimation of State Variables and Parameters for Noisy Dynamic Systems”, IEEE Trans. Autom. Contr., vol. AC-9, pp. 5–12, 1964.
Kalman, R.E., “A New Approach to Linear Filtering and Prediction Problems”, Trans. ASME, Ser. D: J. Basic Engineering, vol. 82, pp. 35–45, 1960.
Kalman, R.E. and R.S. Bucy, “New Results in Linear Filtering and Prediction Theory”, Trans. ASME, Ser. D: J. Basic Engineering, vol. 83, pp. 95–108, 1961.
Singh, M.G. and A. Titli, “Systems: Decomposition, Control and Optimization”, Pergamon Press, Oxford, 1978.
Bryson, A.E. and Y.C. Ho, “Applied Optimal Control”, Ginn and Co., Massachusetts, 1969.
Athans, M. and E. Tse, “A Direct Derivation of the Optimal Linear Filter Using the Maximum Principle”, IEEE Trans. Autom. Contr., vol. AC-12, pp. 690–698, 1967.
Sorenson, H.W., “Least-Squares Estimation: from Gauss to Kalman”, IEEE Spectrum, vol. 7, pp. 63–68, 1970.
Balakrishnan, A.V., “A Martingale Approach to Linear Recursive State Estimation”, SIAM J. Control, vol. 10, pp. 754–766, 1972.
Bierman, G.J., “A Comparison of Discrete Linear Filtering Algorithms” IEEE Trans. Aerospace and Electronic Systems, vol. AES-9, pp. 28–37, 1973.
Pearson, J.D., “Dynamic Optimization Techniques”, in Optimization Methods for Large Scale Systems, edited by D.A. Wismer, McGraw-Hill, N.Y., 1971.
Singh, M.G., “Multi-level State Estimation”, Int. J. Systems Sciences, vol. 6, pp. 535–555, 1975.
Hassan, M.F., “Optimal Kalman Filter for Large Scale Systems Using the Prediction Approach”, IEEE Trans. Systems, Man and Cybern., vol. SMC-6, pp., 1976.
Shah, M., “Suboptimal Filtering Theory for Interacting Control Systems”, Ph.D. Thesis, Cambridge University, 1971.
Hassan, M.F., G. Salut, M.G. Singh and A. Titli, “A Decentralized Computational Algorithm for the Global Kalman Filter”, IEEE Trans. Autom. Contr., vol. AC-23, pp. 262–267, 1978.
Luenberger, D.G., “Optimization by Vector Space Methods”, J. Wiley, N.Y., 1969.
Darwish, M.G. and J. Fantin, “An Approach for Decomposition and Reduction of Dynamical Models for Large Scale Power Systems”, Int. J. Systems Science, vol. 7, pp. 1101–1112, 1976.
Eykoff, P., “System Identification”, J. Wiley and Sons, N.Y., 1974.
Hassan, M.F., M.S. Mahmoud, M.G. Singh and M.P. Spathopolous, “A Two-Level Parameter Estimation Algorithm Using the Multiple Projection Approach”, CSC Report No.518, UMIST, Manchester, UK, and also Automatica, vol. 18, pp. 621–630, 1982.
Clarke, D.W., “Generalized Least-Squares Estimation of the Parameters of a Dynamic Model”, IFAC Symposium - Identification in Automatic Control Systems, Prague Paper # 3. 17, 1967.
Hasting-James, R. and M.W. Sage, “Recursive Generalized Least-Squares Procedure for On-Line Identification of Process Parameters”, Proc. IEE, vol. 116, pp. 2057–2062, 1969.
Arafeh, S. and A.P. Sage, “Multilevel Discrete-Time System Identification in Large Scale Systems”, Int. J. Systems Science, vol. 8, pp. 753–791, 1974.
Arafeh, S. and A.P. Sage, “Hierarchical System Identification of States and Parameters in Interconnected Power Systems”, Int. J. Systems Science, vol. 9, pp. 817–846, 1975.
Fry, C.M. and A.P. Sage, “Identification of Aircraft Stability and Control Parameters Using Hierarchical State Estimation”, IEEE Trans. Aero. Elect. Syst., vol. AES-10, pp. 255–264, 1974.
Guinzy, N.J. and A.P. Sage, “System Identification in Large Scale Systems with Hierarchical Structures”, J. Computers and Elect. Eng., vol. 1, pp. 23–43, 1973.
Lee, E.S., “Quasilinearisation and Invariant Imbedding”, Academic Press, N.Y., 1968.
Chemoul, P., M.R. Katebi, D. Sastry and M.G. Singh, “Maximum a posteriori Parameter Estimation in Large-Scale Systems”, Automatica, vol. 17, pp. 845–851, 1981.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1984 Springer-Verlag Berlin, Heidelberg
About this chapter
Cite this chapter
Mahmoud, M.S., Singh, M.G. (1984). State and Parameter Estimation. In: Discrete Systems. Communications and Control Engineering Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-82327-5_6
Download citation
DOI: https://doi.org/10.1007/978-3-642-82327-5_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-82329-9
Online ISBN: 978-3-642-82327-5
eBook Packages: Springer Book Archive