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All Journal Journal of Robotics and Control (JRC)
Ouannas, Adel
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Aerospace Engineering Computer Science & IT Control & Systems Engineering Electrical & Electronics Engineering Mechanical Engineering

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Solvability and Weak Controllability of Fractional Degenerate Singular Problem Fatma, Achab; Batiha, Iqbal; Imad, Rezzoug; Takieddine, Oussaeif; Ouannas, Adel
Journal of Robotics and Control (JRC) Vol 5, No 2 (2024)
Publisher : Universitas Muhammadiyah Yogyakarta

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18196/jrc.v5i2.20474

Abstract

In this paper, our objective is to investigate the unique solvability and the weak controllability of the fractional degenerate and singular problem. The energy inequality method is gives a sufficient conditions for the existence and the uniqueness of the strong solution of our problem. This problem is ill-posed in the sense of Hadamard. To address this, we attempt regularization through a fractional Tikhonov regularization method, which not only establishes weak controllability but also provides a full characterization of the optimal control.
On New Results of Stability and Synchronization in Finite-Time for Fitiz-Nagamo Model Using Grownal Inequality and Lyapunov Function Batiha, Iqbal M.; Bendib, Issam; Ouannas, Adel; Jebril, Iqbal H.; Alkhazaleh, Shawkat; Momani, Shaher
Journal of Robotics and Control (JRC) Vol. 5 No. 6 (2024)
Publisher : Universitas Muhammadiyah Yogyakarta

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18196/jrc.v5i6.23211

Abstract

Ionic diffusion across cytomembranes plays a critical role in both biological and chemical systems. This paper reexamines the FitzHugh-Nagumo reaction-diffusion system, specifically incorporating the influence of diffusion on the system’s dynamics. We focus on the system’s finite-time stability, demonstrating that it achieves and maintains equilibrium within a specified time interval. Unlike asymptotic stability, which ensures long-term convergence, finite-time stability guarantees rapid convergence to equilibrium, a crucial feature for real-time control applications. We prove that the equilibrium point of the FitzHugh-Nagumo system exhibits finite-time stability under certain conditions. In particular, we provide a criterion for finite-time stability and derive results using new lemmas and a theorem to guide the system’s design for reliable performance. Additionally, the paper discusses finite-time synchronization in reaction-diffusion systems, emphasizing its importance for achieving coherent dynamics across distributed components within a finite time. This approach has significant implications for fields requiring precise control and synchronization, such as sensor networks and autonomous systems. Practical simulations are presented to elucidate the theoretical principles discussed earlier, using the finite difference method (FDM) implemented in MATLAB.
Co-Authors Alkhazaleh, Shawkat Batiha, Iqbal Batiha, Iqbal M. Bendib, Issam Fatma, Achab Imad, Rezzoug Jebril, Iqbal H. Momani, Shaher Takieddine, Oussaeif