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

Author

Listed:
  • Irena Lasiecka

    (University of Memphis
    Polish Academy of Sciences)

  • Roberto Triggiani

    (University of Memphis)

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 $$\Omega $$ Ω with $$L_2(0,\infty ; L_2(\Gamma _0))$$ L 2 ( 0 , ∞ ; L 2 ( Γ 0 ) ) -Robin boundary control on one part $$ \Gamma _0$$ Γ 0 of the boundary $$ \Gamma $$ Γ , and damping in the Neumann BC on the complementary part $$ \Gamma _1$$ Γ 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.

Suggested Citation

  • Irena Lasiecka & Roberto Triggiani, 2022. "Optimal Feedback Arising in a Third-Order Dynamics with Boundary Controls and Infinite Horizon," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 831-855, June.
    • Handle: RePEc:spr:joptap:v:193:y:2022:i:1:d:10.1007_s10957-022-02017-y
    DOI: 10.1007/s10957-022-02017-y
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