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

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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.

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Acknowledgments

This research was partly supported by the NSF Grant 11371190.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Central South University, Changsha, 410083, China

    Desheng Yang

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  1. Desheng Yang
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Correspondence to Desheng Yang.

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Communicated by Viorel Barbu.

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Yang, D. Optimal Control Problems for Lipschitz Dissipative Systems with Boundary-Noise and Boundary-Control. J Optim Theory Appl 165, 14–29 (2015). https://doi.org/10.1007/s10957-014-0612-9

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  • DOI: https://doi.org/10.1007/s10957-014-0612-9

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