Review of Control and Estimation Theory
Chapter
Abstract
The purpose of this chapter is to provide a review of control and estimation theory. It is expected that the reader has some basic knowledge of dynamical systems and probability theory. Several of the concepts shown in this chapter are used throughout the text. First a basic review of system modeling using differential equations is shown. This is followed by linear and nonlinear control theory. Then estimation concepts, such as maximum likelihood and the Kalman filter, are reviewed. The reader is encouraged to read the several cited texts in this chapter for further information.
References
- 1.Arnold, W.F., Laub, A.J.: Generalized eigenproblem algorithms and software for algebraic Riccati equations. Proc. IEEE 72(12), 1746–1754 (1984)CrossRefGoogle Scholar
- 2.Bierman, G.J.: Factorization Methods for Discrete Sequential Estimation. Academic Press, Orlando (1977)zbMATHGoogle Scholar
- 3.Chen, C.T.: Linear System Theory and Design. Holt, Rinehart and Winston, New York (1984)Google Scholar
- 4.Crassidis, J.L., Junkins, J.L.: Optimal Estimation of Dynamic Systems, 2nd edn. CRC Press, Boca Raton (2012)zbMATHGoogle Scholar
- 5.Dorf, R.C., Bishop, R.H.: Modern Control Systems. Addison Wesley Longman, Menlo Park (1998)Google Scholar
- 6.Fagin, S.L.: Recursive linear regression theory, optimal filter theory, and error analysis of optimal systems. In: 1964 IEEE International Convention Record, pp. 216–240 (1964)Google Scholar
- 7.Franklin, G.F., Powell, J.D., Workman, M.: Digital Control of Dynamic Systems, 3rd edn. Addison Wesley Longman, Menlo Park (1998)Google Scholar
- 8.Gelb, A. (ed.): Applied Optimal Estimation. MIT Press, Cambridge (1974)Google Scholar
- 9.Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore (1996)zbMATHGoogle Scholar
- 10.Jazwinski, A.H.: Stochastic Processes and Filtering Theory. Academic Press, New York (1970)zbMATHGoogle Scholar
- 11.Kalman, R.E., Bucy, R.S.: New results in linear filtering and prediction theory. J. Basic Eng. 95–108 (1961)MathSciNetCrossRefGoogle Scholar
- 12.LePage, W.R.: Complex Variables and the Laplace Transform for Engineers. Dover Publications, New York (1980)zbMATHGoogle Scholar
- 13.Lewis, F.L.: Optimal Estimation with an Introduction to Stochastic Control Theory. Wiley, New York (1986)zbMATHGoogle Scholar
- 14.Lizarralde, F., Wen, J.T.Y.: Attitude control without angular velocity measurement: A passivity approach. IEEE Trans. Automat. Contr. 41(3), 468–472 (1996)MathSciNetCrossRefGoogle Scholar
- 15.Markley, F.L., Carpenter, J.R.: Generalized linear covariance analysis. J. Astronaut. Sci. 57(1 & 2), 233–260 (2009)CrossRefGoogle Scholar
- 16.Marquardt, D.W.: An algorithm for least-squares estimation of nonlinear parameters. J. Soc. Ind. Appl. Math. 11(2), 431–441 (1963)MathSciNetCrossRefGoogle Scholar
- 17.Maybeck, P.S.: Stochastic Models, Estimation, and Control, vol. 1. Academic Press, New York (1979)zbMATHGoogle Scholar
- 18.Moler, C., van Loan, C.: Nineteen dubious ways to compute the exponential of a matrix. SIAM Rev. 20(4), 801–836 (1978)MathSciNetCrossRefGoogle Scholar
- 19.Palm, W.J.: Modeling, Analysis, and Control of Dynamic Systems, 2nd edn. Wiley, New York (1999)Google Scholar
- 20.Phillips, C.L., Nagle, H.T.: Digital Control System Analysis and Design, 2nd edn. Prentice Hall, Englewood Cliffs (1990)Google Scholar
- 21.Psiaki, M.L., Martel, F., Pal, P.K.: Three-axis attitude determination via Kalman filtering of magnetometer data. J. Guid. Contr. Dynam. 13(3), 506–514 (1990)CrossRefGoogle Scholar
- 22.Rao, S.S.: Engineering Optimization: Theory and Practice, 3rd edn. Wiley, New York (1996)Google Scholar
- 23.Rauch, H.E., Tung, F., Striebel, C.T.: Maximum likelihood estimates of linear dynamic systems. AIAA J. 3(8), 1445–1450 (1965)MathSciNetCrossRefGoogle Scholar
- 24.Sedlack, J., Hashmall, J.: Accurate magnetometer/gyroscope attitudes using a filter with correlated sensor noise. In: Proceedings of the Flight Mechanics/Estimation Theory Symposium, pp. 293–303. NASA-Goddard Space Flight Center, Greenbelt (1997)Google Scholar
- 25.Slotine, J.J.E., Li, W.: Applied Nonlinear Control. Prentice Hall, Englewood Cliffs (1991)Google Scholar
- 26.Sorenson, H.W.: Parameter Estimation, Principles and Problems. Marcel Dekker, New York (1980)Google Scholar
- 27.Stengel, R.F.: Optimal Control and Estimation. Dover Publications, New York (1994)zbMATHGoogle Scholar
- 28.Żak, S.H.: Systems and Control. Oxford University press, New York (2003)Google Scholar
Copyright information
© Springer Science+Business Media New York 2014