Optimal Actuator Location of the Norm Optimal Controls for Degenerate Parabolic Equations

Yuanhang Liu (), Weijia Wu () and Donghui Yang ()
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Yuanhang Liu: Central South University
Weijia Wu: Central South University
Donghui Yang: Central South University

Journal of Optimization Theory and Applications, 2024, vol. 202, issue 3, No 14, 1326-1358

Abstract: Abstract This paper focuses on investigating the optimal actuator location for achieving minimum norm controls in the context of approximate controllability for degenerate parabolic equations. We propose a formulation of the optimization problem that encompasses both the actuator location and its associated minimum norm control. Specifically, we transform the problem into a two-person zero-sum game problem, resulting in the development of four equivalent formulations. Finally, we establish the crucial result that the solution to the relaxed optimization problem serves as an optimal actuator location for the classical problem.

Keywords: Degenerate parabolic equation; Norm optimal control; Optimal location; Game theory; 35K05; 49J20; 90C47; 93C20 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10957-024-02498-z

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