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<p>This article addresses the optimal control problem involving a new class of bilinear systems with unbounded control operators, namely those who are bounded from a space <i>V</i> to its dual <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10957_2025_2751_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="23" /> </InlineMediaObject> <EquationSource Format="TEX">\(V^*\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>V</mi> <mo>∗</mo> </msup> </math></EquationSource> </InlineEquation> w.r.t a pivot space <i>X</i>. The analysis begins with the optimal control problem over a finite time interval, applied to endpoint problems, and then extends to the infinite time interval case with applications to stabilization problems. The study also includes applications to reaction-diffusion equations involving various types of control actions.</p>

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Optimal Control for a New Class of Unbounded Non-Homogeneous Bilinear Systems

  • 期刊论文

  • 发表日期：

    2025年6月15日

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  • Soufiane Yahyaoui,
  • Mohamed Ouzahra

摘要

This article addresses the optimal control problem involving a new class of bilinear systems with unbounded control operators, namely those who are bounded from a space V to its dual \(V^*\) V ∗ w.r.t a pivot space X. The analysis begins with the optimal control problem over a finite time interval, applied to endpoint problems, and then extends to the infinite time interval case with applications to stabilization problems. The study also includes applications to reaction-diffusion equations involving various types of control actions.