Linear Quadratic Gaussian Control

  • T. Söderström
Part of the Advanced Textbooks in Control and Signal Processing book series (C&SP)


The problem to be coped with in this chapter will lead to the celebrated separation theorem. The basic setup has three essential ingredients:
  • the system is linear

  • the criterion is quadratic

  • the disturbances are Gaussian.


Close Loop System State Feedback Riccati Equation Loop System Diophantine Equation 
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  1. Extended Kalman filtering is a classical subject. Two major sources are Anderson, B.D.O., Moore, J.B., 1989. Optimal Control. Linear Quadratic Methods. Prentice Hall International, Hemel Hempstead, UK.Google Scholar
  2. Aström, K.J., 1970. Introduction to Stochastic Control. Academic Press, New York.MATHGoogle Scholar
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  6. Including some more terms in the generalized minimum variance criterion, treated in Exercise 11.5, and thus also penalizing future output deviations and control actions is often called generalized predictive control. See Bitmead, R.R., Gevers, M., Wertz, V., 1990. Adaptive Optimal Control. The Thinking Man’s GPC. Prentice Hall International, Hemel Hempstead, UK.MATHGoogle Scholar
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  8. Clarke, D.W., Mohtadi, C., Tuffs, P.S., 1987. Generalized predictive control-Part II. Extensions and interpretations. Automatica, vol. 23, 149–160.CrossRefMATHGoogle Scholar
  9. for this design method. There are numerous books dedicated to control system design. The above texts on LQG design include many such aspects. Modern treatments of the design in a general setting include Doyle, J.C., Francis, B.A., Tannenbaum, A.R., 1992. Feedback Control Theory. Macmillan, New York.Google Scholar
  10. Glad, T., Ljung, L., 2000. Control Theory. Multivariable and Nonlinear Methods. Taylor and Francis, London.Google Scholar
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  13. Skogestad, S., Postlethwaite, I., 1996. Multivariable Feedback Control. John Wiley, New York, NY.Google Scholar
  14. The paper Bitmead, R.R., Gevers. M., Wertz, V., 1989. Adaptation and robustness in predictive control. Proceedings of 28th IEEE Conference on Decision and Control, Tampa, FL. summarizes many useful results on LTR, particularly in connection with discrete time LQG control.Google Scholar

Copyright information

© Springer-Verlag London 2002

Authors and Affiliations

  • T. Söderström
    • 1
  1. 1.Department of Systems and Control, Information TechnologyUppsala UniversityUppsalaSweden

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