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<p>In this paper, we address the infinite-horizon optimal control problem for a class of bilinear systems described by the Fokker–Planck equation. The study focuses on systems where control actions are localized within a specific region of the domain. The aim is to minimize a quadratic cost function comprising state and control variables over an infinite time horizon. For this problem, we discuss the well-posedness of the state equation for both finite and infinite time horizons. Furthermore, we establish the existence of optimal controls and derive first- and second-order optimality conditions. Finally, we validate our findings with numerical examples supporting the proposed control strategy.</p>

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Infinite-horizon optimal control of a locally controlled Fokker–Planck equation

  • 期刊论文

  • 发表日期：

    2025年5月8日

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  • El Mezegueldy Redouane,
  • Yahyaoui Soufiane,
  • Ouzahra Mohamed

摘要

In this paper, we address the infinite-horizon optimal control problem for a class of bilinear systems described by the Fokker–Planck equation. The study focuses on systems where control actions are localized within a specific region of the domain. The aim is to minimize a quadratic cost function comprising state and control variables over an infinite time horizon. For this problem, we discuss the well-posedness of the state equation for both finite and infinite time horizons. Furthermore, we establish the existence of optimal controls and derive first- and second-order optimality conditions. Finally, we validate our findings with numerical examples supporting the proposed control strategy.