Advertisement

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)

Abstract

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).

Keywords

Kalman Filter Open Loop Control Gaussian Random Vector Signal Flow Graph Discrete Time Case 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  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