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On Infinite Dimensional Linear-Quadratic Problem with Fixed Endpoints. Continuity Question

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  • Przyłuski, K. Maciej

Abstract

In a Hilbert space setting, necessary and sufficient conditions for the minimum norm solution u to the equation Su = Rz to be continuously dependent on z are given. These conditions are used to study continuity of the minimum energy and linear-quadratic control problems for infinite dimensional linear systems with fixed endpoints.

Suggested Citation

  • Przyłuski, K. Maciej, 2014. "On Infinite Dimensional Linear-Quadratic Problem with Fixed Endpoints. Continuity Question," MPRA Paper 57430, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:57430
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    File URL: https://mpra.ub.uni-muenchen.de/57430/1/MPRA_paper_57430.pdf
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    References listed on IDEAS

    as
    1. Lars Ljungqvist & Thomas J. Sargent, 2004. "Recursive Macroeconomic Theory, 2nd Edition," MIT Press Books, The MIT Press, edition 2, volume 1, number 026212274x, December.
    2. Salvatore Federico, 2011. "A stochastic control problem with delay arising in a pension fund model," Finance and Stochastics, Springer, vol. 15(3), pages 421-459, September.
    3. Sent,Esther-Mirjam, 2006. "The Evolving Rationality of Rational Expectations," Cambridge Books, Cambridge University Press, number 9780521027717.
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    More about this item

    Keywords

    Minimum norm problem; linear-quadratic control and linear-quadratic economies; controllability and approximate controllability; null-controllability; continuity of optimal control.;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • E60 - Macroeconomics and Monetary Economics - - Macroeconomic Policy, Macroeconomic Aspects of Public Finance, and General Outlook - - - General

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