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Kalman on dynamics and contro, Linear System Theory, Optimal Control, and Filter

Author

Listed:
  • Pierre Bernhard

    (Université Côte d'Azur, INRIA)

  • Marc Deschamps

    (Université de Bourgogne Franche-Comté, CRESE)

Abstract

Rudolf Emil Kalman (R.E.K.) passed away on July, 2nd, 2016. Among contemporary economists Kalman is mainly remembered for his filter, an algorithm that allows recursive estimation of unobserved time varying variables in a system. However, he has also a key part on the whole of recursive macroeconomic theory as is notably expressed by Lars Ljungqvist's and Thomas Sargent's book [Ljunqvist and Sargent, 2012]. Our paper is a contribution to show the links between Kalman's works on filtering, linear quadratic optimal control, and system theory. We also provide a model on cooperative advertising to show that Kalman's works on dynamics and control can be useful in macroeconomics as in microeconomics, a domain where his contributions seem to be unfortunately less used.

Suggested Citation

  • Pierre Bernhard & Marc Deschamps, 2017. "Kalman on dynamics and contro, Linear System Theory, Optimal Control, and Filter," Working Papers 2017-10, CRESE.
    • Handle: RePEc:crb:wpaper:2017-10
    as

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    File URL: https://crese.univ-fcomte.fr/uploads/wp/WP-2017-10.pdf
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    References listed on IDEAS

    as
    1. Jørgensen, Steffen & Zaccour, Georges, 2014. "A survey of game-theoretic models of cooperative advertising," European Journal of Operational Research, Elsevier, vol. 237(1), pages 1-14.
    2. Richard Bellman, 1957. "On a Dynamic Programming Approach to the Caterer Problem--I," Management Science, INFORMS, vol. 3(3), pages 270-278, April.
    3. Ljungqvist, Lars & Sargent, Thomas J., 2012. "Recursive Macroeconomic Theory, Third Edition," MIT Press Books, The MIT Press, edition 3, volume 1, number 0262018748, December.
    4. Petit,Maria Luisa, 2009. "Control Theory and Dynamic Games in Economic Policy Analysis," Cambridge Books, Cambridge University Press, number 9780521127158.
    5. Weber, Thomas A., 2011. "Optimal Control Theory with Applications in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262015730, December.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Dynamic Programming; System Theory; Linear Quadratic Optimal Control; Kalman Filter; Riccati Equation;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics

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