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Optimal Control Problems for Lipschitz Dissipative Systems with Boundary-Noise and Boundary-Control

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  • Desheng Yang

    (Central South University)

Abstract

This paper studies the infinite-horizon optimal control problems for Lipschitz dissipative systems with boundary-control and boundary-noise of Neumann type. By introducing Sobolev spaces based on the invariant measure and using the m-dissipativity of the Kolmogorov operator, corresponding to the uncontrolled system, we prove the existence of a unique mild solution of the associated stationary Hamilton–Jacobi–Bellman equation under the general cost functional and obtain the optimal control in the feedback law.

Suggested Citation

  • Desheng Yang, 2015. "Optimal Control Problems for Lipschitz Dissipative Systems with Boundary-Noise and Boundary-Control," Journal of Optimization Theory and Applications, Springer, vol. 165(1), pages 14-29, April.
    • Handle: RePEc:spr:joptap:v:165:y:2015:i:1:d:10.1007_s10957-014-0612-9
    DOI: 10.1007/s10957-014-0612-9
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    References listed on IDEAS

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    1. Goldys, B. & Gozzi, F., 2006. "Second order parabolic Hamilton-Jacobi-Bellman equations in Hilbert spaces and stochastic control: approach," Stochastic Processes and their Applications, Elsevier, vol. 116(12), pages 1932-1963, December.
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    Cited by:

    1. Giorgio Fabbri & Fausto Gozzi & Andrzej Swiech, 2017. "Stochastic Optimal Control in Infinite Dimensions - Dynamic Programming and HJB Equations," Post-Print hal-01505767, HAL.

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