Control Theory & Systems
Mohammad Rashki-Ghalehno; Seyed Mehdi Mirhosseini-Alizamini; Bashir Naderi
Abstract
This paper introduces a robust hybrid adaptive control framework for stabilizing chaotic systems under persistent, potentially large time delays. The controller is based on an enhanced Lyapunov–Krasovskii functional that integrates an energy-capturing integral term with a bounded trigonometric ...
Read More
This paper introduces a robust hybrid adaptive control framework for stabilizing chaotic systems under persistent, potentially large time delays. The controller is based on an enhanced Lyapunov–Krasovskii functional that integrates an energy-capturing integral term with a bounded trigonometric term. The integral term accounts for historical effects by quantifying cumulative energy over the delay period, while the trigonometric term attenuates nonlinear oscillations. Embedding these components in a single control law yields stabilization of all state variables to the equilibrium despite substantial delays. We establish Uniform Ultimate Boundedness, showing that trajectories enter a compact neighborhood of the equilibrium after a finite transient and subsequently converge. Adjustable gains enable practitioners to determine the convergence radius and the size of the attraction region according to practical requirements. The method is validated on the delayed Lorenz system; simulations with a 20-second delay demonstrate rapid convergence to a small neighborhood of the equilibrium, with the Lyapunov functional derivative remaining non-positive. A comparative study with established controllers underscores the proposed approach’s favorable trade-offs among computational cost, oscillation suppression, and explicit stability guarantees. Overall, the proposed framework delivers a practical, robust, and high-performance solution for controlling chaotic systems in the presence of large time delays.
Hossein Kheiri; Mehdi Zavieh; Bashir Naderi
Abstract
In this paper, we use a graphical algorithm to control and synchronization of a chaotic system. Most of the controllers designed for synchronizing chaotic systems are complex, but the controllers designed using contraction and graphical methods are often simple and linear. ...
Read More
In this paper, we use a graphical algorithm to control and synchronization of a chaotic system. Most of the controllers designed for synchronizing chaotic systems are complex, but the controllers designed using contraction and graphical methods are often simple and linear. Therefore, we explain the relationship between contraction analysis and the graphical method for controlling and synchronizing chaotic systems. We apply this approach to control and synchronize the chaotic Genesio-Tesi system. The stability of the error system in synchronization is investigated using the contraction method. Finally, we provide numerical simulations to demonstrate the effectiveness of the proposed method.
)