Synchronization Control Of Chaotic Systems Research Articles

Dynamic Analysis and Sliding Mode Synchronization Control of Chaotic Systems with Conditional Symmetric Fractional-Order Memristors

In this paper, the characteristics of absolute value memristors are verified through the circuit implementation and construction of a chaotic system with a conditional symmetric fractional-order memristor. The dynamic behavior of fractional-order memristor systems is explored using fractional-order calculus theory and the Adomian Decomposition Method (ADM). Concurrently, the investigation probes into the existence of coexisting symmetric attractors, multiple coexisting bifurcation diagrams, and Lyapunov exponent spectra (LEs) utilizing system parameters as variables. Additionally, the system demonstrates an intriguing phenomenon known as offset boosting, where the embedding of an offset can adjust the position and size of the system’s attractors. To ensure the practical applicability of these findings, a fractional-order sliding mode synchronization control scheme, inspired by integer-order sliding mode theory, is designed. The rationality and feasibility of this scheme are validated through a theoretical analysis and numerical simulation.

Adaptive internal synchronization control of chaotic systems based on DNA strand displacement

AbstractIn the application of DNA‐based chaotic synchronization, the precise values of the system parameters are often complicated to attain due to the interference of external factors, thus weakening the performance of synchronization. In this paper, considering the case of unknown parameters in chaotic systems, a method of adaptive synchronization based on DNA strand displacement (DSD) is proposed. Firstly, the chain replacement reaction modules of emergence, activation and degradation are given through the design of DNA strand, which enable the realization of Yang chaotic system using the mass action dynamics law. Further, in order to achieve the estimation of the unknown parameters and the stability of the error system, the rules for identification of unknown parameters are derived and adaptive controllers are designed under the adaptive control principle. Finally, an internal synchronization approach is recommended to decompose the chaotic system into subsystems of different orders, which can freely choose subsystems to complete synchronization. Subsequently, numerical simulations show that DNA‐based adaptive controllers can fulfill the internal synchronization of Yang system with unknown parameters and are robust to parameter deviations. In addition, the strategy presented in this study can be extended to the synchronization control of other DSD‐based multivariable chaotic systems.

Chaotic synchronization based on improved global nonlinear integral sliding mode control☆

In order to avoid integral saturation of integral sliding mode surface, a new integral function which can magnify small errors and minify large errors is designed. Meanwhile, an attenuation function which can decay to zero in a finite time is designed to accelerate the convergence speed of global sliding mode surface. Then, an improved global nonlinear integral sliding mode surface (GNISMS) is constructed, and sliding mode control based on the proposed sliding mode surface is designed to accomplish the synchronization control of chaotic systems with external disturbances and internal parameters uncertainties. Simulation results show that the proposed sliding mode control method has good control performance, and it can be effectively applied to the chaotic secure communication system based on chaos synchronization control.

What is the most suitable Lyapunov function?

• Algorithm for Hamilton energy function in dynamical system is clarified. • Hamilton energy function is the most suitable Lyapunov function for dynamical control. • Control of energy flow is the most effective way to synchronization control of chaotic systems. Lyapunov function provides feasible estimation and prediction of nonlinear system stability, and useful guidance for adaptive control in chaos and synchronization approach. In case of synchronization and control of chaotic systems, the involvement of adjustable gains in the Lyapunov function can be effective to optimize the convergence of orbits to stability and controllers within finite transient period. As a result, shorter transient period and lower power consumption can be approached by detecting the most suitable gains in the controllers and parameter observers. In this paper, we claim that the most suitable Lyapunov function can be the Hamilton energy for chaotic systems and more nonlinear dynamical systems, and so the parameter region for stability and controllability can be detected exactly, in addition, the reliability of controllers can be confirmed in practical way. Furthermore, the Lorenz and improved Chua oscillators in chaotic states are presented to confirm the dependence of Hamilton energy and stability on the intrinsic parameters and variables. It indicates that control of energy flow can be an effective scheme to control chaos in nonlinear systems and synchronization realization between chaotic systems, neurons and networks.

Prescribed Performance Synchronization Control of Chaotic Systems with Unknown Control Gain Signs

For a class of uncertain nonlinear chaotic systems with unknown control gain signs and saturated input, by means of Nussbaum function, a scheme of finite-time prescribed performance synchronization control is proposed. Here, Nussbaum function is used to eliminate the influence of unknown control gain signs, and fuzzy logic systems are used to estimate unknown functions. Lyapunov theory is used to prove that all synchronization errors converge to a predefined small performance range under the designed control method. Finally, simulation results are provided to illustrate the feasibility of the proposed method.

Exponential Stability of Nonlinear Systems With Delayed Impulses and Applications

We consider a class of nonlinear impulsive systems with delayed impulses, where the time delays in impulses exist between two consecutive impulse instants. Based on the impulsive control theory and the ideas of average dwell time (ADT), a set of Lyapunov-based sufficient conditions for globally exponential stability are obtained. It is shown that the time delay in impulses exhibits double effects (i.e., negative or positive effects) on system dynamics, namely, it may destroy the stability and lead to undesired performance, and conversely, it may stabilize an unstable system and achieve better performance. Then, we apply the theoretical results to synchronization control of chaotic systems and design some impulsive controllers that are formalized in terms of linear matrix inequality and ADT-like conditions. Two numerical examples including chaotic cellular neural network and Chua's oscillator are given to illustrate the applicability of the presented impulsive control schemes. Our examples show that, under some conditions, the impulsive synchronization of chaotic systems can be achieved via the input delays in impulses.

Globally exponential multi switching-combination synchronization control of chaotic systems for secure communications

This article introduces the global exponential multi switching combination synchronization (GEMSCS) for three different chaotic systems with known parameters in the master-slave system configuration. The proposed GEMSCS scheme establishes the global exponential stability of the synchronization error at the origin with different combinations of state variables of the two master chaotic systems with the state variables of a slave chaotic system in diverse manners. Consequently, it increases the complexity level of the information signal in secure communications. To study the GEMSCS, an efficient nonlinear control algorithm is designed. The Lyapunov direct theorem is used to accomplish the global exponential stability of the synchronization error at the origin. The stability conditions are derived analytically. To show the effectiveness and advantages of the proposed GEMSCS control approach, two numerical examples are presented. The computer based simulation results are compared with the reported works in the relevant literature. This article also extends the idea of GEMSCS to the secure communication using the chaotic masking technique. Using the GEMSCS strategy, the information signal is recovered at the receiving system with good accuracy and high speed while the parameters of the transmitter and receiver systems mismatch. At the end, some future research problems related to this work are suggested.

Adaptive neural synchronization control of chaotic systems with unknown control directions under input saturation

In this paper, we investigate the synchronization problem of chaotic systems with unknown control direction under input saturation nonlinearity. By utilizing backstepping technique, an adaptive neural synchronization control scheme is developed via neural approximation technique and Nussbaum-type function method. To deal with the problem of sharp corner of saturation, a tangent function based smooth function is used to approximate input saturation. To facilitate controller design, an auxiliary signal is constructed to augment the plant. Two Nussbaum functions are respectively used to deal with unknown control direction and compensate for the time-varying gain arising from the partial differentiation of the smooth function of input saturation. Tracking-differentiator is introduced to handle the problem of “explosion of computation” in the backstepping design. Adaptive robust effects are designed to deal with the “disturbance-like” term and tracking-differentiator estimation error. Lyapunov based analysis gives the transient performance and convergence of synchronization errors. Finally, a simulation example is presented to verify the effectiveness of the proposed approach.

Study on Super-Twisting synchronization control of chaotic system based on U model

Study on Super-Twisting synchronization control of chaotic system based on U model

Synchronization Control of Chaotic Systems with Different Orders

The mixed function projective synchronization is proposed in this paper, which includes the full synchronization and the anti-synchronization and so on. We design an effective controller and parameters identification strategy to study the synchronization phenomena between systems with different orders and uncertain parameters. The analytic results are complemented with numerical simulations for two chaotic systems which are the new integer-order system and the fractional-order Chen system, respectively. Several results show the effectiveness of the presented scheme.

Sampled-data synchronization control of chaotic systems based on min-max approach

For the chaotic systems with disturbance, a sampled-data controller is designed to achieve chaotic synchronization. Firstly, to handle the discontinuity introduced by the sampling activities, the input-delay approach is introduced to transform the discontinuous chaotic systems into continuous ones. Secondly, the worst possible case of performance is considered according to min-max robust strategy. Then the sufficient conditions for global asymptotic synchronization of such chaotic systems are derived and expressed in terms of linear matrix inequality (LMI). The proposed algorithm can achieve synchronization of the sampled-data chaotic systems for all admissible disturbances at the pre-computed set of disturbance realizations. The effectiveness is finally illustrated via numerical simulations of chaotic Chuas circuit, and the simulation results show that the proposed algorithm is suitable for secure communication.

New results on global exponential stabilization of impulsive functional differential equations with infinite delays or finite delays

This paper studies the global exponential stabilization of impulsive functional differential equations with infinite delays or finite delays by using Lyapunov functions and improved Razumikhin technique. The results obtained in this paper improve and complement ones from some recent works. Moreover, the Razumikhin condition obtained is very simple and effective to implement in real problems and it is helpful for investigating the stability of control systems and synchronization control of chaotic systems. Finally, two examples and their simulations are given to show the effectiveness and advantages of our results.