In this article, a new idea of chaos synchronization and chaos-based secure communication is developed. First, the chaotic master system is used as a transmitter in chaos-based secure communication, then a drive signal is constructed, and the information message is encrypted into the drive signal to form a transmitted signal for secure communication. Second, in the receiver, a recurrent Takagi–Sugeno–Kang (TSK) fuzzy brain emotional learning cerebellar model articulation controller (RTFBECAC) is developed to control the slave system to follow the master system in the transmitter. Third, after descripting the chaotic signal, the embedded information message can be recovered. Besides, the stability problem is analyzed in detail based on the stability theory. Finally, two simulation examples, including audio signal and image, are introduced to illustrate the effectiveness and the advantages of the proposed method.

Fractional-order four-wing (FO 4-wing) systems are of significant importance due to their complex dynamics and wide-ranging applications in secure communications, encryption, and nonlinear circuit design, making their control and stabilization a critical area of study. In this research, a novel model-free finite-time flexible sliding mode control (FTF-SMC) strategy is developed for the stabilization of a particular category of hyperchaotic FO 4-wing systems, which are subject to unknown uncertainties and input saturation constraints. The proposed approach leverages fractional-order Lyapunov stability theory to design a flexible sliding mode controller capable of effectively addressing the chaotic dynamics of FO 4-wing systems and ensuring finite-time convergence. Initially, a dynamic sliding surface is formulated to accommodate system variations. Following this, a robust model-free control law is designed to counteract uncertainties and input saturation effects. The finite-time stability of both the sliding surface and the control scheme is rigorously proven. The control strategy eliminates the need for explicit system models by exploiting the norm-bounded characteristics of chaotic system states. To optimize the parameters of the model-free FTF-SMC, a deep reinforcement learning framework based on the adaptive dynamic programming (ADP) algorithm is employed. The ADP agent utilizes two neural networks (NNs)—action NN and critic NN—aiming to obtain the optimal policy by maximizing a predefined reward function. This ensures that the sliding motion satisfies the reachability condition within a finite time frame. The effectiveness of the proposed methodology is validated through comprehensive simulations, numerical case studies, and comparative analyses.

This paper presents a new hybrid neural network controller for time series prediction and chaotic synchronization. The proposed controller is called as a wavelet interval type-2 Takagi-Kang-Sugeno (TSK) fuzzy brain emotional learning cerebellar model articulation controller (WIT2TFBCC), and it consists of a wavelet interval type-2 TSK fuzzy brain emotional learning controller (WIT2TFBELC), and a wavelet interval type-2 TSK fuzzy cerebellar model articulation controller (WIT2TFCMAC). The proposed WIT2TFBCC can serve both as a control signal for chaotic master-slave synchronization and as a prediction output signal for the time series predictor. Moreover, a robust compensator is used to achieve robust ability of the system. A Lyapunov function was used to establish the adaptive laws and effectively adjust the system parameters online. Finally, two examples of the application are presented to illustrate the performance of proposed method.

To prevent the distortion of the data transmission, the disturbance compensation method is highly required in the communication system. Therefore, the variations of parameters on both master and slave of secure communication and attacked signals all should be compensated to remain the sent data as its after decrypting. However, to reject these unwanted signals, the time varying disturbance rejection technique is requested. The time varying disturbance observer (DO) is able to reject both low and high frequency disturbances. Furthermore, the template of the sources of the disturbances are free. To meet the goal of robust control, first, the Liu chaotic system is used to represent the master and slave systems (MSSs). Second, the disturbance observer was proposed on the side of slave system together with the controller, which used to reject the parameters variations and disturbances on the public channels. Third, the sliding mode control was proposed to synchronize the slave and master systems. Final, the mathematical stability is provided based on the Lyapunov condition. Furthermore, to show the power and effectiveness of the given theory, the circuit realization was used to conduct the theoretical analysis. The sent and received messages were mostly identical, which is used to confirm that the proposed theory on the secure communication of chaotic circuits is good both in synchronization and disturbance rejection also.

This paper mainly proposes a new disturbance observer (DO) for a secure communication system (SCS) of the chaos-based system (CBS). First, the fractional-order (FO) Chen chaotic system is remodeled by a Takagi–Sugeno (T–S) fuzzy system with the aim of softening in calculation. Second, the robust fixed-time was designed to synchronize two nonidentical chaotic systems. Third, a new disturbance observer was proposed to compensate for the disturbance and uncertainty of the secure communication system. Fourth, the proof of the proposed method based on Lyapunov condition together with simulation are given to illustrate the correctness and effectiveness of the proposed theory. The tested disturbance on the public channel was mostly compensated by the appropriately estimated disturbance value. The states of master and slave systems (MSSs) were closed to each other in fixed-time. These factors are used to confirm that the symmetry of two chaotic systems were obtained by the proposed control methods.