The LQG-Problem: A Brief Tutorial Exposition

  • Jan C. Willems
Conference paper
Part of the NATO Advanced Study Institutes Series book series (ASIC, volume 78)


The purpose of this article is to provide a brief tutorial exposition of the formal setting, the main ideas, and the formulas for the linear quadratic gaussian stochastic optimal control problem (the so-called LQG-problem).


Covariance Estima 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Kalman, R.E. (1960), Contributions to the theory of optimal control, Bol. Soc. Mat. Mexicana, Vol. 5, pp. 102–119.MathSciNetGoogle Scholar
  2. [2]
    Kalman, R.E. (1960), A new approach to linear filtering and prediction problems, J. Basic Eng. (Trans, ASME Ser. D), Vol. 82, pp. 34–35.Google Scholar
  3. [3]
    Kalman, R.E. and Bucy, R.S. (1961), New results in linear filtering and prediction theory, J. Basic Eng. (Trans. ASME Ser. D), Vol. 83, pp. 95–107.MathSciNetGoogle Scholar
  4. [4]
    Willems, J.C. (1978), Recursive filtering, Statistica Neerlandica, Vol. 32, pp. 1–39.MathSciNetCrossRefGoogle Scholar
  5. [5]
    Kwakernaak, H, and Sivan R. (1972), Linear Optimal Control Systems, Wiley.MATHGoogle Scholar
  6. [6]
    Kailath, T. (1974), A view of three decades of linear filtering, IEEE Trans, on Information Theory, Vol. IT-20, pp. 146–130.Google Scholar
  7. [7]
    Special Issue on the Linear-Quadratic-Gaussian Problem, IEEE Trans, on Automatic Control, Vol. AC-16, 1971.Google Scholar
  8. [8]
    Willems, J.C. (1971), The Analysis of Feedback Systems, HIT Press.MATHGoogle Scholar
  9. [9]
    Wonham, W.M. (1970), Random differential equations in control theory, in Probabilistic Methods in Applied Mathematics, A.T. Barucha — Reid, Ed., pp. 131–212, Academic Press.Google Scholar
  10. [10]
    Kalman, R.E., Falb, P.L. and Arbib, M.A. (1969), Topics in Mathematical Systems Theory, McGraw Hill.Google Scholar
  11. [11]
    Willems, J.C., Systems theory models for the analysis of physical systems, Ricerche di Automatica, Vol. 10, to appear.Google Scholar

Copyright information

© D. Reidel Publishing Company 1981

Authors and Affiliations

  • Jan C. Willems
    • 1
  1. 1.Mathematics InstituteGroningenThe Netherlands

Personalised recommendations