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

Irena Lasiecka () and Roberto Triggiani ()
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Irena Lasiecka: University of Memphis
Roberto Triggiani: University of Memphis

Journal of Optimization Theory and Applications, 2022, vol. 193, issue 1, No 34, 855 pages

Abstract: 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.

Keywords: Optimal boundary control; Absorbing boundary conditions; Non-standard Riccati equations; Feedback synthesis; High-intensity focused ultrasound (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10957-022-02017-y

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