Linear Quadratic Gaussian Control
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.
KeywordsClose Loop System State Feedback Riccati Equation Loop System Diophantine Equation
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- 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
- Grimble, M.J., Johnson, M.A., 1988. Optimal Control and Stochastic Estimation, vol. 2. John Wiley & Sons, Chichester.Google Scholar
- Kwakernaak, H., Sivan, R., 1982. Linear Optimal Control Systems. Wiley, New York.Google Scholar
- 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
- 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
- Glad, T., Ljung, L., 2000. Control Theory. Multivariable and Nonlinear Methods. Taylor and Francis, London.Google Scholar
- Goodwin, G.C., Graebe, S.F., Saigado, M.E., 2001. Control System Design. Prentice Hall, Upper Saddle River.Google Scholar
- Skogestad, S., Postlethwaite, I., 1996. Multivariable Feedback Control. John Wiley, New York, NY.Google Scholar
- 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
© Springer-Verlag London 2002