Modified Function Projective Lag Synchronization Research Articles

Complex Modified Function Projective Lag Synchronization With Fixed-Time Stability Guarantees for Hyperchaotic Systems via a Fixed-Time Control Proposal

Our paper investigates complex modified function projective lag synchronization with fixed-time stability guarantees for hyperchaotic systems via a FxTC proposal. The synchronization of complex hyperchaotic systems and the desired performance are definitely guaranteed within a period of bounded time. The synchronization interval can be predefined without demanding the information of the initial conditions from the systems where the synchronization is performed. Furthermore, the fixed-time stability guarantees of the control scheme are achieved according to the Lyapunov principle and the settling time is calculated by solving the differential equations. In MATLAB/SIMULINK environment, synchronization performance from two simulation examples is performed in many cases with the change of initial values and time delay of the system to reveal the feasibility and the efficacy of the control proposal.

Robust modified function projective lag synchronization between two nonlinear complex networks with different-dimensional nodes and disturbances

This paper is concerned with a theoretical investigation on the robust modified function projective lag synchronization (MFPLS) between two complex networks with nonlinear couplings, different-dimensional nodes, parameter disturbances and external disturbances. Some novel robust hybrid controllers are designed to address such synchronization problems for networks with and without disturbances, in which adaptive updated laws of disturbances are adopted to attenuate the disturbances occurred in networks. By utilizing Lyapunov functional method, synchronization criteria are derived by strict theoretical proof. Compared with existing jobs, the proposed model and synchronization type are more general. Two examples are presented to verify our results.

Adaptive Modified Function Projective Lag Synchronization of Memristor-Based Five-Order Chaotic Circuit Systems

The modified function projective lag synchronization of the memristor-based five-order chaotic circuit system with unknown bounded disturbances is investigated. Based on the LMI approach and Lyapunov stability theorem, an adaptive control law is established to make the states of two different memristor-based five-order chaotic circuit systems asymptotically synchronized up to a desired scaling function matrix, while the parameter controlling strength update law is designed to estimate the parameters well. Finally, the simulation is put forward to demonstrate the correctness and effectiveness of the proposed methods. The control method involved is simple and practical.

Fixed-Time Complex Modified Function Projective Lag Synchronization of Chaotic (Hyperchaotic) Complex Systems

A novel fixed-time controller is proposed to perform fixed-time complex modified function projective lag synchronization of chaotic (hyperchaotic) complex systems. The synchronization is obtained after a finite time that could be preestablished without the knowledge of the initial states of both synchronized chaotic (hyperchaotic) complex systems. The global fixed-time stability of the closed-loop systems is rigorously proven based on Lyapunov analysis. Some simulation examples are provided to demonstrate the effectiveness and feasibility of the proposed method and verify the theoretical results.

Continuous adaptive finite-time modified function projective lag synchronization of uncertain hyperchaotic systems

This paper introduces an adaptive control method for finite-time modified function projective lag synchronization of uncertain hyperchaotic systems. Based upon novel nonsingular terminal sliding mode surfaces and the adaptive super-twisting algorithm, a controller is proposed to provide robustness, high precision and fast and finite-time modified function projective lag synchronization without the knowledge of the upper bound of uncertainties and unknown external disturbances. In addition, chattering is significantly attenuated due to the inherited continuity of the proposed controller. The global stability and finite-time convergence are rigorously proven. Numerical simulation is presented to demonstrate the effectiveness and feasibility of the proposed strategy and to verify the theoretical results.

Modified function projective lag synchronization of uncertain complex networks with time-varying coupling strength

In this article, we investigate the issue on modified function projective lag synchronization (MFPLS) of dynamical complex networks with disturbance and unknown parameters, the dynamical network is a complex network model containing uncertainty and coupling delay, the coupling strength is time-varying in the complex networks. Theoretical analysis and numerical simulations about MFPLS of uncertain complex networks are presented, not only unknown parameters of the networks are estimated, but also unknown bounded disturbances can be simultaneously conquered by adaptive laws and adaptive coupling strength obtained from Lyapunov stability theory.

Universal function projective lag synchronization of chaotic systems with uncertainty by using active sliding mode and fuzzy sliding mode control

In this paper, a novel synchronization scheme, universal function projective lag synchronization (UFPLS), is proposed. The synchronization scheme is a generalization of universal function projective synchronization and modified function projective lag synchronization. An active sliding mode controller is introduced for UFPLS of chaotic systems. By using the integral sliding surface, the determination of sliding parameters become easier than using the classical one. Furthermore, based on the consideration of reality, the systems with uncertainty and the system contaminated by noise are investigated. Theoretical proof is achieved with the Lyapunov stability theory. A fuzzy active sliding control method is presented by using a fuzzy system to adjust the coefficient of switch term so that the chattering can be weakened. Simulation results verify the effectiveness of the introduced schemes and illustrate that the application of fuzzy system eliminates the chattering effectively.

Adaptive Modified Function Projective Lag Synchronization for Two Different Chaotic Systems with Stochastic Unknown Parameters

In this paper, we investigate the modified function projective lag synchronization for two different stochastic chaotic systems using adaptive control method. We design an adaptive controller to make the mean square of synchronization error convergence to an arbitrarily small bound around zero depending on the controller feedback gain according to the Lyapunov stability theory. One example is presented to demonstrate the effectiveness of the proposed controller.

Adaptive modified function projective lag synchronization of hyperchaotic complex systems with fully uncertain parameters

In this article, a novel synchronization scheme, modified function projective lag synchronization (MFPLS), between identical and nonidentical hyperchaotic complex systems with fully uncertain parameters, is proposed. In the proposed general method, the states of two hyperchaotic complex systems with unknown parameters are asymptotically synchronized up to a desired scaling function matrix with time delay, and all of the unknown parameters are identified. The adaptive controller and laws of parameters are designed to achieve MFPLS between the drive and response systems. Theoretical proof and numerical simulations demonstrate the effectiveness and feasibility of the proposed scheme.

Modified function projective lag synchronization in fractional-order chaotic (hyperchaotic) systems

In this paper, a novel modified function projective lag synchronization (MFPLS) for fractional-order chaotic (hyperchaotic) systems is proposed. Considering fractional derivatives do not satisfy the Leibniz product rule, as it is known in integer-order calculus, it is difficult to achieve the synchronization with a scaling function between the drive and response systems in the time domain. In this paper, we construct the equivalent integer-order systems based on the Laplace transform and make numerical calculation. By means of the Lyapunov stability theory, an adaptive controller is designed to achieve MFPLS for the transformed systems. According to the mapping relationship between the original and transformed systems, MFPLS for the fractional-order chaotic systems is achieved. Theoretical proof and numerical simulations demonstrate the effectiveness and feasibility of the proposed scheme.

Hybrid robust modified function projective lag synchronization in two different dimensional chaotic systems

In this article, a novel synchronization scheme, modified function projective lag synchronization (MFPLS) in two different dimensional chaotic systems with parameter perturbations, is proposed. In the proposed method, the states of two nonidentical chaotic systems with different orders are asymptotically lag synchronized up to a desired scaling function matrix by means of reduced order and increased order, respectively. Furthermore, based on the reality situation, the parameter perturbations are involved, which are assumed to appear in both drive and response systems. With the Lyapunov stability theory, an adaptive controller is designed to achieve MFPLS. Theoretical proof and numerical simulations demonstrate the effectiveness and feasibility of the proposed scheme.

Adaptive Modified Function Projective Lag Synchronization of Uncertain Hyperchaotic Dynamical Systems with the Same or Different Dimension and Structure

Modified function projective lag synchronization (MFPLS) of uncertain hyperchaotic dynamical systems with the same or different dimensions and structures is studied. Based on Lyapunov stability theory, a general theorem for controller designing, parameter update rule designing, and control gain strength adapt law designing is introduced by using adaptive control method. Furthermore, the scheme is applied to four typical examples: MFPLS between two five-dimensional hyperchaotic systems with the same structures, MFPLS between two four-dimensional hyperchaotic systems with different structures, MFPLS between a four-dimensional hyperchaotic system and a three-dimensional chaotic system and MFPLS between a novel three-dimensional chaotic system, and a five-dimensional hyperchaotic system. And the system parameters are all uncertain. Corresponding numerical simulations are performed to verify and illustrate the analytical results.

Modified function projective lag synchronization of chaotic systems with disturbance estimations

This paper addresses the modified function projective lag synchronization (MFPLS) for a class of chaotic systems with unknown external disturbances. The disturbances are supposed to be generated by the exogenous systems. By using the disturbance-observer-based control and the linear matrix inequality approach, the disturbance observers are developed to ensure the boundedness of the disturbance error dynamics. Then by employing the sliding mode control (SMC) technique, an active SMC law is established to guarantee the disturbance rejection and realize MFPLS between the master and slave systems. And the corresponding numerical simulation is provided to illustrate the effectiveness of the proposed method.

Modified function projective lag synchronization for multi-scroll chaotic system with unknown disturbances

In this paper, we treat the modified function projective lag synchronization between two non-identical multi-scroll chaotic systems with unknown disturbances. By utilizing the lyapunov stability theory, the fuzzy adaptive controller and parameter update law are derived to make the state of chaotic system achieve modified function projective lag synchronization. The controller can keep the systems stable even when the disturbance changes. Finally numerical simulations are performed to show the effectiveness of the proposed method.

A general method for modified function projective lag synchronization in chaotic systems

The modified function projective lag synchronization (MFPLS) is proposed in this Letter, in which the states of two chaotic systems are asymptotically lag synchronized up to a desired scaling function matrix. Based on Lyapunov stability theory, a general method of MFPLS is investigated. The scheme is successfully applied to two groups examples, which are the MFPLS between Lorenz system and Lü system, and two identical hyper-chaotic Chen system. Corresponding numerical simulations are performed to verify and illustrate the analytical results.