Control and Optimization
Reza Akbari; Leader Navaei; Mohammad Shahriari
Abstract
This paper presents an extension of the SEIR mathematical model for infectious disease transmission to a fractional-order model. The model is formulated using the Caputo derivative of order α ∈ (0, 1]. We study the stability of equilibrium points, including ...
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This paper presents an extension of the SEIR mathematical model for infectious disease transmission to a fractional-order model. The model is formulated using the Caputo derivative of order α ∈ (0, 1]. We study the stability of equilibrium points, including the disease-free equilibrium $(E_{f})$, and the infected steady-state equilibrium $(E_{e})$ using the stability theorem of Fractional Differential Equations. The model is also analyzed under certain conditions, and it is shown that the disease-free equilibrium is locally asymptotically stable. Additionally, the extended Barbalat’s lemma is applied to the fractional-order system, and a suitable Lyapunov functional is constructed to demonstrate the global asymptotic stability of the infected steady-state equilibrium. To validate the theoretical results, a numerical simulation of the problem is conducted.
Mohammad Reza Zarrabi
Abstract
Drones are among the most valuable and versatile technologies in the world, with applications in a vast number of fields such as traffic control, agriculture, firefighting and rescue, and filmmaking, to name a few. As ...
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Drones are among the most valuable and versatile technologies in the world, with applications in a vast number of fields such as traffic control, agriculture, firefighting and rescue, and filmmaking, to name a few. As the development of unmanned aerial vehicles (UAVs) accelerates, the safety of UAVs becomes increasingly important. In this paper, a robust adaptive controller is designed to improve the safety of a hexa-rotor UAV, and a robust adaptive controller is developed to control our system. In doing so, the wind parameters from the aerodynamic forces and moments acting on the hexa-rotor are estimated using an observer with the adaptive algorithm. This proposed controller guarantees stability and reliable function in the midst of parametric and non-parametric uncertainties. The process's global stability and tracking convergence are investigated using the Lyapunov theorem. The performance and effectiveness of the proposed controller are tested through two simulation studies, which take into account external disturbances that are a function of time.
