Abstract
The problem to be coped with in this chapter will lead to the celebrated separation theorem. The basic setup has three essential ingredients:
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the system is linear
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the criterion is quadratic
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the disturbances are Gaussian.
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References
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.
Aström, K.J., 1970. Introduction to Stochastic Control. Academic Press, New York.
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Maybeck, P.S., 1982. Stochastic Models, Estimation and Control, vol. 3. Academic Press, New York.
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.
Clarke, D.W., Mohtadi, C., Tuffs, P.S., 1987. Generalized predictive control-Part I. The basic algorithm. Automatica, vol. 23, 137–148.
Clarke, D.W., Mohtadi, C., Tuffs, P.S., 1987. Generalized predictive control-Part II. Extensions and interpretations. Automatica, vol. 23, 149–160.
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.
Glad, T., Ljung, L., 2000. Control Theory. Multivariable and Nonlinear Methods. Taylor and Francis, London.
Goodwin, G.C., Graebe, S.F., Saigado, M.E., 2001. Control System Design. Prentice Hall, Upper Saddle River.
Maciejowski, J.M., 1989. Multivariable Feedback Design. Addison-Wesley, Wokingham, UK.
Skogestad, S., Postlethwaite, I., 1996. Multivariable Feedback Control. John Wiley, New York, NY.
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.
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Söderström, T. (2002). Linear Quadratic Gaussian Control. In: Discrete-time Stochastic Systems. Advanced Textbooks in Control and Signal Processing. Springer, London. https://doi.org/10.1007/978-1-4471-0101-7_11
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DOI: https://doi.org/10.1007/978-1-4471-0101-7_11
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