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On the regional tracking problem of the bilinear wave equation subject to bounded controls. (English) Zbl 1534.93211

Summary: This research focuses on a regional optimal control problem of a bilinear wave equation evolving on a spatial domain \(\Omega\subset\mathbb{R}^d\), where \(d\geq 1\). The equation is excited by bounded controls that act on the velocity term. The main objective of this study is to minimize a functional cost, which involves tracking a desired state within a subregion \(\omega\) of \(\Omega\) and the energy term over the time interval \([0,T]\). We successfully prove the existence of an optimal control that we characterize as a solution to an optimality system. Additionally, an algorithm for the computation of such a control is given and successfully illustrated through simulations.

MSC:

93C35 Multivariable systems, multidimensional control systems
93C20 Control/observation systems governed by partial differential equations
35L05 Wave equation
93C10 Nonlinear systems in control theory
Full Text: DOI

References:

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