Optimal Feedback Arising in a Third-Order Dynamics with Boundary Controls and Infinite Horizon
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 Ω with L2(0 , ∞; L2(Γ)) -Robin boundary control on one part Γ of the boundary Γ , and damping in the Neumann BC on the complementary part 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.
Publication Title
Journal of Optimization Theory and Applications
Recommended Citation
Lasiecka, I., & Triggiani, R. (2022). Optimal Feedback Arising in a Third-Order Dynamics with Boundary Controls and Infinite Horizon. Journal of Optimization Theory and Applications, 193 (1-3), 831-855. https://doi.org/10.1007/s10957-022-02017-y
