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Linear Quadratic Optimal Control Problem for Linear Stochastic Generalized System in Hilbert Spaces

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  • Zhaoqiang Ge

    (School of Mathematics and Statistics, Xi’an Jiaotong University, No. 28, Xianning West Road, Xi’an 710049, China)

Abstract

A finite-horizon linear stochastic quadratic optimal control problem is investigated by the GE-evolution operator in the sense of the mild solution in Hilbert spaces. We assume that the coefficient operator of the differential term is a bounded linear operator and that the state and input operators are time-varying in the dynamic equation of the problem. Optimal state feedback along with the well-posedness of the generalized Riccati equation is obtained for the finite-horizon case. The results are also applicable to the linear quadratic optimal control problem of ordinary time-varying linear stochastic systems.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:17:p:3118-:d:902255
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    References listed on IDEAS

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    1. 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.
    2. Thomas Johnson, 1985. "A Continuous Leontief Dynamic Input‐Output Model," Papers in Regional Science, Wiley Blackwell, vol. 56(1), pages 177-188, January.
    3. Frankowska, Hélène & Zhang, Xu, 2020. "Necessary conditions for stochastic optimal control problems in infinite dimensions," Stochastic Processes and their Applications, Elsevier, vol. 130(7), pages 4081-4103.
    4. Ying Hu & Hanqing Jin & Xun Yu Zhou, 2017. "Time-Inconsistent Stochastic Linear--Quadratic Control: Characterization and Uniqueness of Equilibrium," Post-Print hal-01139343, HAL.
    5. Zhaoqiang Ge, 2021. "Review of the Latest Progress in Controllability of Stochastic Linear Systems and Stochastic GE-Evolution Operator," Mathematics, MDPI, vol. 9(24), pages 1-42, December.
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