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Riccati Equations for the Bolza Problem Arising in Boundary/Point Control Problems Governed by C 0 Semigroups Satisfying a Singular Estimate

Author

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  • I. Lasiecka

    (University of Virginia)

  • A. Tuffaha

    (University of Virginia)

Abstract

We establish solvability of Riccati equations and optimal feedback synthesis in the context of Bolza control problem for a special class of control systems referred to in the literature as control systems with singular estimate. Boundary/point control problems governed by analytic semigroups constitute a very special subcategory of this class which was motivated by and encompasses many PDE control systems with both boundary and point controls that involve interactions of different types of dynamics (parabolic and hyperbolic) on an interface. We also discuss two examples from thermoelasticity and structure acoustics.

Suggested Citation

  • I. Lasiecka & A. Tuffaha, 2008. "Riccati Equations for the Bolza Problem Arising in Boundary/Point Control Problems Governed by C 0 Semigroups Satisfying a Singular Estimate," Journal of Optimization Theory and Applications, Springer, vol. 136(2), pages 229-246, February.
    • Handle: RePEc:spr:joptap:v:136:y:2008:i:2:d:10.1007_s10957-007-9307-9
    DOI: 10.1007/s10957-007-9307-9
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    1. ,, 1999. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 15(5), pages 777-788, October.
    2. ,, 1999. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 15(1), pages 151-160, February.
    3. ,, 1999. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 15(4), pages 629-637, August.
    4. ,, 1999. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 15(3), pages 427-432, June.
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    Cited by:

    1. Zhaoqiang Ge, 2022. "Linear Quadratic Optimal Control Problem for Linear Stochastic Generalized System in Hilbert Spaces," Mathematics, MDPI, vol. 10(17), pages 1-20, August.

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