Optimal control problems governed by a class of nonlinear systems

Maawiya Ould Sidi; Rabie Zine; Sid Ahmed Ould Ahmed Mahmoud; Hadi Obaid Alshammari; Sid Ahmed Ould Beinane; Maawiya Ould Sidi; Rabie Zine; Sid Ahmed Ould Ahmed Mahmoud; Hadi Obaid Alshammari; Sid Ahmed Ould Beinane

doi:10.3934/math.2024024

AIMS Mathematics

2024, Volume 9, Issue 1: 440-452. doi: 10.3934/math.2024024

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Optimal control problems governed by a class of nonlinear systems

1.
Mathematics Department, College of Science, Jouf University, P.O. Box 2014, Sakaka, Saudi Arabia
2.
School of Science and Engineering, Al Akhawayn University in Ifrane, Ifrane, Morocco

Received: 29 August 2023 Revised: 15 November 2023 Accepted: 23 November 2023 Published: 30 November 2023
MSC : 35L10, 34K35, 93C20, 93C95

This article suggested a solution to a flow control problem governed by a class of nonlinear systems called bilinear systems. The problem was initially well-posed, and after it was established that an optimal control solution existed, its characteristics were stated. After that, we demonstrated how to use various bounded feedback controls to make a plate equation's flow close to the required profile. As an application, we resolved the plate equation-governed partial flow control issue. The findings bring up a variety of system applications, which can be employed in engineering advancement.
- nonlinear systems,
- bilinear systems,
- optimal control,
- adjoint method,
- partial method
Citation: Maawiya Ould Sidi, Rabie Zine, Sid Ahmed Ould Ahmed Mahmoud, Hadi Obaid Alshammari, Sid Ahmed Ould Beinane. Optimal control problems governed by a class of nonlinear systems[J]. AIMS Mathematics, 2024, 9(1): 440-452. doi: 10.3934/math.2024024

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Abstract

This article suggested a solution to a flow control problem governed by a class of nonlinear systems called bilinear systems. The problem was initially well-posed, and after it was established that an optimal control solution existed, its characteristics were stated. After that, we demonstrated how to use various bounded feedback controls to make a plate equation's flow close to the required profile. As an application, we resolved the plate equation-governed partial flow control issue. The findings bring up a variety of system applications, which can be employed in engineering advancement.

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