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Optimal Feedback Arising in a Third-Order Dynamics with Boundary Controls and Infinite Horizon

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Abstract

We study the optimal control problem over an infinite time horizon for the third-order JMGT equation, defined on a 3-d bounded domain \(\Omega \) with \(L_2(0,\infty ; L_2(\Gamma _0))\)-Robin boundary control on one part \( \Gamma _0\) of the boundary \( \Gamma \), and damping in the Neumann BC on the complementary part \( \Gamma _1\). The pathology present in the corresponding abstract model impacts on the final theory. It results in several new features including: (i) a non-standard pointwise feedback representation of the optimal control in terms of the optimal solution that involves a non-trivial inverse and (ii) a new Riccati operator that satisfies a non-standard algebraic Riccati equation with unbounded coefficients.

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Acknowledgements

The authors would like to thank the referees for useful comments. This research was partially supported by the NSF Grant DMS-1713506.

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Authors and Affiliations

  1. University of Memphis, Memphis, TN, USA

    Irena Lasiecka & Roberto Triggiani

  2. IBS, Polish Academy of Sciences, Warsaw, Poland

    Irena Lasiecka

Authors
  1. Irena Lasiecka
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  2. Roberto Triggiani
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Correspondence to Irena Lasiecka.

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Communicated by Boris. S. Mordukovich.

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Lasiecka, I., Triggiani, R. Optimal Feedback Arising in a Third-Order Dynamics with Boundary Controls and Infinite Horizon. J Optim Theory Appl 193, 831–855 (2022). https://doi.org/10.1007/s10957-022-02017-y

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  • DOI: https://doi.org/10.1007/s10957-022-02017-y

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