Synchronization of Delayed Fractional Order Chaotic Systems Based on Controller with Non-Linear Fractional Order PID Structure

Subject Areas : Fractional order systems

Mohammad Rasouli ¹ , Assef Zare ² , Majid Hallaji ³

1 - Faculty of Electrical Engineering- Gonabad Branch, Islamic Azad University, Gonabad, Iran
2 - Research Center of Intelligent Technologies in Electrical Industry- Gonabad Branch, Islamic Azad University, Gonabad, Iran
3 - Faculty of Electrical Engineering- Neyshabure Branch, Islamic Azad University, Neyshabure, Iran

Received: 2022-11-10 Accepted : 2023-03-08 Published : 2025-08-06

Keywords: fractional order chaotic synchronization, sliding mode control, uncertainty, unknown time delay,

Abstract :

In this paper, a new control approach for robust synchronization of chaotic systems with uncertainty, unknown parameters such as indefinite time delay and external disturbances is presented. Uncertain time delay as an important factor that increases the complexity of the control problem and overcoming it is stated in this article. By using the structure of nonlinear proportional-integral-derivative control­lers of fractional order, a sliding surface of fractional order has been introduced to design the control strategy of the said sliding mode. Then, using Lyapunov's theory, robust adaptive rules are designed in such a way that the estimation error of the unknown parameters of the fractional order system with an indefinite time delay tends to zero by the proposed control mechanism. Also, by using Lyapunov stability standard the stability analysis of the proposed robust control approach has been proved. Finally, the performance evaluation of the proposed mechanism, the synchronization of two Jerk chaotic systems with uncertainty along an indefinite time delay and disturbance, has been simulated by the presented control approach, the results of which show the robust and favorable performance of the simulation.

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