Complete Synchronization and Partial Anti-Synchronization of Complex Lü Chaotic Systems by the UDE-Based Control Method

Abstract

The presence of uncertainty and disturbance can lead to asymmetric control of nonlinear systems, and this asymmetric control can lead to a decrease in the productivity of the engineered system. In order to improve the control speed of the improved nonlinear system, complete synchronization and partial anti-synchronization of complex Lü chaotic systems with uncertainty and disturbance are investigated in the present paper. First, a new UDE-based dynamic feedback control method is proposed for the complete synchronization problem of the system. The method unites the dynamic gain feedback control method and the uncertainty and perturbation estimator (UDE) control method, where the dynamic gain feedback controller is used to achieve asymptotic stability of the nominal system and the UDE controller is used to handle a given controlled system with uncertainty and disturbance. Second, for the partial desynchronization problem of this system, a new UDE-based linear-like feedback control method is proposed, which consists of two controllers: a linear-like feedback controller used to achieve the asymptotic stabilization of the nominal system and the other UDE controller is designed to handle the given controlled system with uncertainty and disturbance. Finally, numerical simulations are performed to verify the correctness and stability of the theoretical results.

Fixed time function combination synchronization of perturbed chaotic systems via adaptive control

“…Remark The control gains in References 5,11,12,16–22 are static which mean that once the control schemes are formulated the control gains are invariant during the system's operation. While in our work, the control gains are generated by the adaptive laws which implies that the control gains can be regulated based on the actual system's situation.…”

“…In addition, various noticeable control techniques on systems have been presented, for instance, feedback control, 7 adaptive technique, 8 impulsive control, 9 sliding mode technique, 10 observer-based method. 11 In the meantime, there are some deferent synchronization concepts in the chaotic systems, for instance, the complete synchronization (PC), 12,13 projective synchronization (PS), 14 function projective synchronization (FPS). 15 Nevertheless, most of synchronization criteria are restricted to two chaotic systems.…”

“…The main contributions and innovative of this paper are as follows: Differ from the existing works, 19–24 this paper presents a new fixed time stability theorem which plays an important role on the synchronization scheme. Furthermore, the estimation of convergence time can be determined by a simple calculate formula. The scaling functions given in References 16–22 are constants or fixed functions, while the scaling functions in our combination synchronization are governed by the chaotic dynamic systems, which can improve the security of information transformation to some extent. Compare to the traditional synchronization schemes in References 5,12–22, a novel fixed time function combination synchronization scheme for the chaotic systems is developed in this work via adaptive control, and the upper bound of convergence time is fixed which is determined by the control parameters regardless of initial conditions. …”

“…Compare to the traditional synchronization schemes in References 5,12–22, a novel fixed time function combination synchronization scheme for the chaotic systems is developed in this work via adaptive control, and the upper bound of convergence time is fixed which is determined by the control parameters regardless of initial conditions.…”

A memristive system: dynamics, synchronization, parameter modulation and demodulation

“…The fractional-order delayed memristive fuzzy neural networks was investigated in [13]. Additionally, many synchronization schemes for memristive system have been studied, such as finite-time quantized synchronization method was studied in [14], UDE-based complete synchronization and antisynchronization method was proposed in [15], switching SMC combina tion synchronization and parameter identification method was considered in [16], finite-time H ∞ synchronization method was described in [17], adaptive fuzzy-impulsive synchronization method was focused in [18], active projective synchronization method was described in [19], passive-constrained synchronization control method was given in [20], inverse matrix projective difference synchronization method and its application were investigated in [21], and other synchronization control schemes were described in [22][23][24][25][26]. An image encryption method employing memristive map was introduced in [27].…”