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<p>This paper addresses the optimal control problem of a new class of bilinear systems, where both operators <i>A</i> and <i>B</i> generate a strongly continuous semigroup. We begin by formulating the assumptions and establishing a unique weak solvability result for this class, using the theory of evolution families. We then prove the existence of an optimal solution for the associated control problem. Thereby, a necessary optimality condition is established, by differentiating the minimized functional. Finally, we illustrate the applicability of our results through two examples: a population growth model and an epitaxial film model.</p>

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On the optimal control of bilinear systems governed by commuting semigroups

  • 期刊论文

  • 发表日期：

    2026年8月1日

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  • Samir E. L. Hajhouj,
  • Nihale E. L. Boukhari,
  • Hicham Benaissa

摘要

This paper addresses the optimal control problem of a new class of bilinear systems, where both operators A and B generate a strongly continuous semigroup. We begin by formulating the assumptions and establishing a unique weak solvability result for this class, using the theory of evolution families. We then prove the existence of an optimal solution for the associated control problem. Thereby, a necessary optimality condition is established, by differentiating the minimized functional. Finally, we illustrate the applicability of our results through two examples: a population growth model and an epitaxial film model.