A general nonlinear adaptive control scheme for finite-time synchronization of chaotic systems with uncertain parameters and nonlinear inputs

In this paper, the problem of finite-time chaos synchronization between two different uncertain chaotic systems with unknown parameters and input nonlinearities is investigated. It is assumed that both master and slave systems are perturbed by unknown model uncertainties, external disturbances, and fully unknown parameters. Proper update laws are proposed to estimate the systems?? unknown parameters. Based on the update laws and finite-time control technique, a robust adaptive controller is introduced to guarantee the convergence of the slave system trajectories to the trajectories of the master system in a given finite time. Two illustrative examples are presented to illustrate the effectiveness and applicability of the proposed finite-time controller and to validate the theoretical results of the paper.     

Adaptive control for electromechanical systems considering dead-zone phenomenon

The electromechanical gyrostat is a fourth-order nonautonomous system that exhibits very rich behavior such as chaos. In recent years, synchronization of nonautonomous chaotic systems has found many useful applications in nonlinear science and engineering fields. On the other hand, it is well known that the finite-time control techniques demonstrate good robustness and disturbance rejection properties. This paper studies the potential application of the finite-time control techniques for synchronization of nonautonomous chaotic electromechanical gyrostat systems in finite time. It is assumed that all the parameters of both drive and response systems are unknown parameters in advance. Moreover, the effects of dead-zone nonlinearities in the control inputs are also taken into account. Some adaptive controllers are introduced to synchronize two gyrostat systems in different scenarios within a given finite-time. Two illustrative examples are presented to demonstrate the efficiency and robustness of the proposed finite-time synchronization strategy.     

Chaos control and modified projective synchronization of unknown heavy symmetric chaotic gyroscope systems via Gaussian radial basis adaptive backstepping control

This paper proposes the chaos control and the modified projective synchronization methods for unknown heavy symmetric chaotic gyroscope systems via Gaussian radial basis adaptive backstepping control. Because of the nonlinear terms of the gyroscope system, the system exhibits chaotic motions. Occasionally, the extreme sensitivity to initial states in a system operating in chaotic mode can be very destructive to the system because of unpredictable behavior. In order to improve the performance of a dynamic system or avoid the chaotic phenomena, it is necessary to control a chaotic system with a regular or periodic motion beneficial for working with a particular condition. As chaotic signals are usually broadband and noise-like, synchronized chaotic systems can be used as cipher generators for secure communication. Obviously, the importance of obtaining these objectives is specified when the dynamics of gyroscope system are unknown. In this paper, using the neural backstepping control technique, control laws are established which guarantees the chaos control and the modified projective synchronization of unknown chaotic gyroscope system. In the neural backstepping control, Gaussian radial basis functions are utilized to on-line estimate the system dynamic functions. Also, the adaptation laws of the on-line estimators are derived in the sense of Lyapunov function. Thus, the unknown chaotic gyroscope system can be guaranteed to be asymptotically stable. Also, the control objectives have been achieved.     

Adaptive finite-time outer synchronization between two complex dynamical networks with noise perturbation

Nonlinear Dynamics - In this paper, the finite-time outer synchronization between two complex dynamical networks with noise perturbation is considered. Combing the adaptive and finite-time control...     

Robust adaptive synchronization for a class of chaotic systems with actuator failures and nonlinear uncertainty

This paper is concerned with the robust adaptive synchronization problem for a class of chaotic systems with actuator failures and unknown nonlinear uncertainty. Combining adaptive method and linear matrix inequality (LMI) technique, a novel type of robust adaptive reliable synchronization controller is proposed, which can eliminate the effect of actuator fault and nonlinear uncertainty on systems. After solving a set of LMIs, synchronization error between the master chaotic and slave chaotic systems can converge asymptotically to zero. Finally, illustrate examples about chaotic Chua’s circuit system and Lorenz systems are provided to demonstrate the effectiveness and applicability of the proposed design method.     

Generalized finite-time synchronization between coupled chaotic systems of different orders with unknown parameters

This letter investigates the adaptive finite-time synchronization of different coupled chaotic (or hyperchaotic) systems with unknown parameters. The sufficient conditions for achieving the generalized finite-time synchronization of two chaotic systems are derived based on the theory of finite-time stability of dynamical systems. By the adaptive control technique, the control laws and the corresponding parameters update laws are proposed such that the generalized finite-time synchronization of nonidentical chaotic (or hyperchaotic) systems is to be obtained. These results obtained are in good agreement with the existing one in open literature and it is shown that the technique introduced here can be further applied to various finite-time synchronizations between dynamical systems. Finally, numerical simulations are given to demonstrate the effectiveness of the proposed scheme.     

Robust synchronization of a chaotic mechanical system with nonlinearities in control inputs

Centrifugal flywheel governors are known as chaotic non-autonomous mechanical devices used for automatic control of the speed of engines. The main characteristic of them is avoiding the damage caused by sudden change of the load torques. In this paper, the problem of robust finite-time synchronization of centrifugal flywheel governor systems is studied. The effects of unknown parameters, model uncertainties, external noises, and input nonlinearities are fully taken into account. We propose some adaptive laws to overcome the side effects of the unknown parameters of the system on the synchronization performance. Then, a robust adaptive switching controller is introduced to synchronize centrifugal flywheel governors with nonlinear control inputs in a given finite time. The finite-time fast convergence property of the proposed scheme is analytically proved and numerically illustrated.     

Spatiotemporal chaos synchronization between uncertain complex networks with diverse structures

Spatiotemporal chaos synchronization between uncertain complex networks with diverse structures is investigated. The identification law of unknown parameters and the adaptive law of the configuration matrix element in state equations of network nodes are determined based on stability theory, and the conditions of realizing spatiotemporal chaos synchronization between uncertain complex networks with different structures are discussed and obtained. Further, the Fisher–Kolmogorov system with spatiotemporal chaotic behavior is taken as the nodes of drive and response networks to imitate the experiment. It is found that the synchronization performance between two networks is very stable.     

Finite-time combination-combination synchronization of four different chaotic systems with unknown parameters via sliding mode control

In this paper, we apply the nonsingular terminal sliding mode control technique to realize the novel combination-combination synchronization between combination of two chaotic systems as drive system and combination of two chaotic systems as response system with unknown parameters in a finite time. On the basic of the adaptive laws and finite-time stability theory, an adaptive combination sliding mode controller is proposed to ensure the occurrence of the sliding motion in a given finite time for four different chaotic systems. In theory, it is proved that the sliding mode technique can realize fast convergence for four different chaotic systems in the finite time. Some criteria and corollaries are derived for finite-time combination-combination synchronization of four different chaotic systems. Numerical simulation results are shown to verify the effectiveness and correctness of the combination-combination synchronization.     

Analog circuit design and optimal synchronization of a modified Rayleigh system

This paper addresses the problem of optimization of the synchronization of a chaotic modified Rayleigh system. We first introduce a four-dimensional autonomous chaotic system which is obtained by the modification of a two-dimensional Rayleigh system. Some basic dynamical properties and behaviors of this system are investigated. An appropriate electronic circuit (analog simulator) is proposed for the investigation of the dynamical behavior of the proposed system. Correspondences are established between the coefficients of the system model and the components of the electronic circuit. Furthermore, we propose an optimal robust adaptive feedback which accomplishes the synchronization of two modified Rayleigh systems using the controllability functions method. The advantage of the proposed scheme is that it takes into account the energy wasted by feedback coupling and the closed loop performance on synchronization. Also, a finite horizon is explicitly computed such that the chaos synchronization is achieved at an established time. Numerical simulations are presented to verify the effectiveness of the proposed synchronization strategy. Pspice analog circuit implementation of the complete master–slave controller system is also presented to show the feasibility of the proposed scheme.     

Finite-time synchronization of complex networks with nonidentical discontinuous nodes

In this paper, we study the finite-time synchronization problem for linearly coupled complex networks with discontinuous nonidentical nodes. Firstly, new conditions for general discontinuous chaotic systems is proposed, which is easy to be verified. Secondly, a set of new controllers are designed such that the considered model can be finite-timely synchronized onto any target node with discontinuous functions. Based on a finite-time stability theorem for equations with discontinuous right-hand and inequality techniques, several sufficient conditions are obtained to ensure the synchronization goal. Results of this paper are general, and they extend and improve existing results on both continuous and discontinuous complex networks. Finally, numerical example, in which a BA scale-free network with discontinuous Sprott and Chua circuits is finite-timely synchronized onto discontinuous Chen system, is given to show the effectiveness of our new results.     

Finite-time synchronization control for uncertain Markov jump neural networks with input constraints

This paper is concerned with the problem of finite-time synchronization control for uncertain Markov jump neural networks in the presence of constraints on the control input amplitude. The parameter uncertainties under consideration are assumed to belong to a fixed convex polytope. By using a parameter-dependent Lyapunov functional and a simple matrix decoupling method, a sufficient condition is proposed to ensure that the considered networks are stochastically synchronized over a finite-time interval. The desired mode-independent controller parameters can be computed via solving a convex optimization problem. Finally, two chaos neural networks are employed to demonstrate the effectiveness of our proposed approach.     

航天器有限时间饱和姿态跟踪控制

针对刚体航天器系统,对存在模型不确定性、外界干扰力矩和控制器饱和等条件下的姿态跟踪控制问题进行了研究。首先,考虑未知模型不确定性和外界干扰,且总干扰上界为未知常数,结合快速非奇异终端滑模、快速终端滑模趋近律以及辅助系统构造了基本的鲁棒有限时间饱和控制器,并通过辅助系统直接补偿了控制器饱和;其次,针对系统总干扰具有多项式上界的情形,进一步结合自适应控制算法,对其上界函数中的未知参数进行在线估计,并设计了自适应有限时间饱和控制器。同时,基于Lyapunov稳定性理论证明了所提出控制算法的有限时间收敛特性。最后,通过数值仿真验证所提出控制算法的控制效果,在两种控制器作用下姿态的跟踪精度分别为5×10-5和1×10-5,证明了所提出控制算法的有效性。     

Robust chaos synchronization of four-dimensional energy resource system via adaptive feedback control

This paper investigates the robust chaos synchronization problem for the four-dimensional energy resource systems with mismatched parameters. Based on the Lyapunov stability theory, the sufficient conditions for the synchronization are obtained analytically and an adaptive feedback control law is derived to make the states of two slightly mismatched chaotic systems asymptotically synchronized. Finally, some numerical simulations are performed to verify the proposed results.     

Finite-time real combination synchronization of three complex-variable chaotic systems with unknown parameters via sliding mode control

The problem of real combination synchronization between three complex-variable chaotic systems with unknown parameters is investigated by nonsingular terminal sliding mode control in a finite time. Based on the adaptive laws and finite-time stability theory, a nonsingular terminal sliding mode control is designed to ensure the real combination synchronization of three complex-variable chaotic systems in a given finite time. It is theoretically gained that the introduced sliding mode technique has finite-time convergence and stability in both arriving and sliding mode phases. Numerical simulation results are given to show the effectiveness and reliability of the finite-time real combination synchronization.     

Projective synchronization of the small-world delayed network with uncertainty

Spatiotemporal chaotic systems are taken as nodes to constitute the small-world delayed network with uncertainty, and projective synchronization of the network is researched. The control input of the network and the adaptive law of adjustment parameters are designed based on Lyapunov theorem. Concretely, the Burgers systems with spatiotemporal chaotic behavior in physics domain are taken as nodes to constitute the complex network, and the Fisher–Kolmogorov system is taken as the target system. The simulation results show that the synchronization performance of the network is very stable.     

Finite-time chaos control and synchronization of fractional-order nonautonomous chaotic (hyperchaotic) systems using fractional nonsingular terminal sliding mode technique

In this paper, a novel fractional-order terminal sliding mode control approach is introduced to control/synchronize chaos of fractional-order nonautonomous chaotic/hyperchaotic systems in a given finite time. The effects of model uncertainties and external disturbances are fully taken into account. First, a novel fractional nonsingular terminal sliding surface is proposed and its finite-time convergence to zero is analytically proved. Then an appropriate robust fractional sliding mode control law is proposed to ensure the occurrence of the sliding motion in a given finite time. The fractional version of the Lyapunov stability is used to prove the finite-time existence of the sliding motion. The proposed control scheme is applied to control/synchronize chaos of autonomous/nonautonomous fractional-order chaotic/hyperchaotic systems in the presence of both model uncertainties and external disturbances. Two illustrative examples are presented to show the efficiency and applicability of the proposed finite-time control strategy. It is worth to notice that the proposed fractional nonsingular terminal sliding mode control approach can be applied to control a broad range of nonlinear autonomous/nonautonomous fractional-order dynamical systems in finite time.     

脑科学中若干非线性动力学问题

对近年发展起来的脑科学中的非线性问题作一介绍.这些问题得到脑科学界的广泛注意.它们是同步, 混沌与混沌周游, 噪声与随机共振.在很多不同背景下的神经生理实验表明脑皮层的振荡活动都存在同步与去同步现象.混沌在人与动物的脑中扮演着重要的角色, 混沌周游与Freeman模型被认为与联想记忆或记忆的动态连接有关.适当噪声强度导致信噪比的极大提高------随机共振是脑神经系统能检测到极其微弱信号的工作机制.噪声也导致同步态并使之稳定.此外,噪声的一些其他作用也在本文中提及.      

Adaptive synchronization of chaotic systems with unknown bounded uncertainties via backstepping approach

Backstepping design is proposed for adaptive synchronization of a class of chaotic systems with unknown bounded uncertainties. An adaptive backstepping control law is derived to make the error signals between the master and slave systems asymptotically synchronized without knowing the upper-bounds of the uncertainties in advance. The stability analysis is proved by using a well-known Lyapunov stability. Two illustrative examples are presented to show the effectiveness of the proposed adaptive chaos synchronization.     

Generalized synchronization of the fractional-order chaos in weighted complex dynamical networks with nonidentical nodes

A fractional-order weighted complex network consists of a number of nodes, which are the fractional-order chaotic systems, and weighted connections between the nodes. In this paper, we investigate generalized chaotic synchronization of the general fractional-order weighted complex dynamical networks with nonidentical nodes. The well-studied integer-order complex networks are the special cases of the fractional-order ones. Based on the stability theory of linear fraction-order systems, the nonlinear controllers are designed to make the fractional-order complex dynamical networks with distinct nodes asymptotically synchronize onto any smooth goal dynamics. Numerical simulations are provided to verify the theoretical results. It is worth noting that the synchronization effect sensitively depends on both the fractional order ?? and the feedback gain k _i . Moreover, generalized synchronization of the fractional-order weighted networks can still be achieved effectively with the existence of noise perturbation.