Sliding-Mode Synchronization Control for Uncertain Fractional-Order Chaotic Systems with Time Delay

Abstract

Specifically setting a time delay fractional financial system as the study object, this paper proposes a single controller method to eliminate the impact of model uncertainty and external disturbances on the system. The proposed method is based on the stability theory of Lyapunov sliding-mode adaptive control and fractional-order linear systems. The controller can fit the system state within the sliding-mode surface so as to realize synchronization of fractional-order chaotic systems. Analysis results demonstrate that the proposed single integral, sliding-mode control method can control the time delay fractional power system to realize chaotic synchronization, with strong robustness to external disturbance. The controller is simple in structure. The proposed method was also validated by numerical simulation.

Combination Synchronization of Three Different Fractional‐Order Delayed Chaotic Systems

“…Proof. A � K + I is the coefficient matrix for the fractionalorder delayed error system (12). Because k i < (− 1/sin(απ/2)), α ∈ (0, 1), the eigenvalues of A are…”

“…e fractional-order delayed Liu system was presented and the existence of chaos was investigated in [8], and the impulsive synchronization and robust predictive synchronization were investigated in [9,10], respectively. e nonlinear dynamics and chaos were studied for the fractional-order delayed nancial system in [11], and the sliding-mode synchronization was investigated in [12]. In [13], hybrid projective synchronization between the two aforementioned systems was done.…”

Fractional Order Memristor No Equilibrium Chaotic System with Its Adaptive Sliding Mode Synchronization and Genetically Optimized Fractional Order PID Synchronization

“…Because of high sensitivity to initial conditions two identical chaotic systems may have exponentially diverging state trajectories. Many methods have been proposed in the literature such as active control method [17,18], adaptive control method [19,20], extended back stepping control [21,22], sliding mode control [23,24], and adaptive sliding mode [25][26][27].…”

“…Fraction chaotic systems have been investigated by many researchers [28][29][30][31][32][33][34][35]. Fractional order controllers [24][25][26][27][36][37][38] are more effective compared to its integer order models especially in chaos control and synchronization. Fractional order systems with no equilibrium are announced and investigated by Li and Chen [39].…”

Fuzzy Adaptive Repetitive Control for Periodic Disturbance with Its Application to High Performance Permanent Magnet Synchronous Motor Speed Servo Systems

“…To enhance the system performance, in recent years, many advanced information theories has been developed for the control system, such as input-output linearization control [15]; adaptive control [18]; robust control [19]; sliding mode control [20], which has been applied for a fractional order chaotic system [21,22]; fractional order theory is also novel and interesting for researchers [23]; nonlinear model predictive control has been proposed for hydropower system [24]; back-stepping control [25]; finite-time control [26]; neural network methods are used in motion control system and a fruit classification system [27,28]; fuzzy theory [29,30], etc. These information theories can improve system performance from different aspects.…”