Ph. D. Project
Title:
Modeling and control of fractional dynamic systems using AI techniques
Dates:
2026/01/12 - 2029/01/11
Student:
Supervisor(s):
Other supervisor(s):
Professeur Adraoui, Professeur Lotfi
Description:
Fractional dynamic systems constitute an emerging branch of applied mathematics and complex system modeling. The importance of these systems
lies in their ability to capture nonlinear and unpredictable phenomena observed in many natural and artificial systems, often overlooked or poorly
represented by models based on integer derivatives.
Research work, in the context of this thesis, focuses on three main aspects:
- Developing new fractional operators and studying their mathematical properties to construct efficient solution methods. Fractional epidemiological
models will serve as study and comparison models. They allow for the consideration of memory effects in disease transmission, more precise
modeling of population heterogeneity, and the incorporation of non-exponential behaviors for a better representation of epidemiological dynamics.
- The second aspect involves modeling these phenomena using Physics-Informed Neural Networks (PINNs) to evaluate their performance in terms of
computation, accuracy, speed, and stability compared to methods developed in the first aspect.
- Lastly, developing generic AI-based control strategies for this class of systems when the model is known or unknown. One of the major challenges
is establishing the conditions for existence and stabilization, an aspect that has been largely unexplored to date.
References :
1 - Podlubny, I. (1999). Fractional differential equations: An introduction to fractional derivatives, fractional differential equations, to methods of
their solution, and some of their applications. Academic Press.
2 - Singh, H., Kumar, D., & Baleanu, D. (2023). A review on epidemic models in sight of fractional calculus. Alexandria Engineering Journal, 77,
81-113.
3 - Kharazmi, E., Cai, M., Zheng, X., Zhang, Z., Lin, G., & Karniadakis, G. E. (2021). Identifiability and predictability of integer- and fractional-
order epidemiological models using physics-informed neural networks. Nature Computational Science, 1, 744-753.
4 - Sweilam, N. H., Al-Mekhlafi, S. M., & Baleanu, D. (2022). Application of fractional optimal control theory for the mitigating of novel
coronavirus in Algeria. Chaos, Solitons & Fractals, 158, 112041.
lies in their ability to capture nonlinear and unpredictable phenomena observed in many natural and artificial systems, often overlooked or poorly
represented by models based on integer derivatives.
Research work, in the context of this thesis, focuses on three main aspects:
- Developing new fractional operators and studying their mathematical properties to construct efficient solution methods. Fractional epidemiological
models will serve as study and comparison models. They allow for the consideration of memory effects in disease transmission, more precise
modeling of population heterogeneity, and the incorporation of non-exponential behaviors for a better representation of epidemiological dynamics.
- The second aspect involves modeling these phenomena using Physics-Informed Neural Networks (PINNs) to evaluate their performance in terms of
computation, accuracy, speed, and stability compared to methods developed in the first aspect.
- Lastly, developing generic AI-based control strategies for this class of systems when the model is known or unknown. One of the major challenges
is establishing the conditions for existence and stabilization, an aspect that has been largely unexplored to date.
References :
1 - Podlubny, I. (1999). Fractional differential equations: An introduction to fractional derivatives, fractional differential equations, to methods of
their solution, and some of their applications. Academic Press.
2 - Singh, H., Kumar, D., & Baleanu, D. (2023). A review on epidemic models in sight of fractional calculus. Alexandria Engineering Journal, 77,
81-113.
3 - Kharazmi, E., Cai, M., Zheng, X., Zhang, Z., Lin, G., & Karniadakis, G. E. (2021). Identifiability and predictability of integer- and fractional-
order epidemiological models using physics-informed neural networks. Nature Computational Science, 1, 744-753.
4 - Sweilam, N. H., Al-Mekhlafi, S. M., & Baleanu, D. (2022). Application of fractional optimal control theory for the mitigating of novel
coronavirus in Algeria. Chaos, Solitons & Fractals, 158, 112041.
Department(s):
| Control Identification Diagnosis |