Multi-switching adaptive synchronization of two fractional-order chaotic systems with different structure and different order

In this work, we combine the active and adaptive control theories, and propose a novel synchronization scheme for a class of fractional-order chaotic systems with different structure and different order. Based on the new version of fractional-order Lyapunov stability theory, we design the adaptive controllers and updating laws of different switching. We use the fractional-order Lorenz chaotic system and the fractional-order Chen chaotic system as examples to analyze the multi-switching synchronization process for fractional-order chaotic systems with different structures and different orders. Finally, numerical simulations are also given to illustrate the effectiveness and validation of the proposed method, and the model uncertainties and external disturbances are added to the considered systems to verify the robustness of the proposed controllers.     

Robust synchronization of fractional-order unified chaotic systems via linear control

A new scheme for accomplishing synchronization between two fractional-order unified chaotic systems is proposed in this paper. The scheme does not require that the nonlinear dynamics of the synchronization error system must be eliminated. Moreover, the parameter of the systems does not have to be known. A controller is a linear feedback controller, which is simple in implementation. It is designed based on an LMI condition. The LMI condition guarantees that the synchronization between the slave system and the master system is achieved. Numerical simulations are performed to demonstrate the effectiveness of the proposed scheme.     

Stable indirect adaptive interval type-2 fuzzy sliding-based control and synchronization of two different chaotic systems

An indirect approach to adaptive interval type-2 fuzzy sliding mode control is proposed for the stable synchronization of two different chaotic nonlinear systems with different initial conditions under the presence of uncertainties involving process noises and external disturbances. The indirect model-based approach to adaptation is promoted here as a more suitable strategy for the fast changes that occurs in chaotic systems. In other words, the usual direct adaptive strategies may be too slow to respond to the inherently fast changing dynamics of chaotic systems. Using Lyapunov analysis, the sliding mode approach illustrates the asymptotic convergence of synchronization error to zero as well as good robustness against external disturbances. The interval type-2 structure aims to remedy the undesirable chattering phenomenon that is common in most conventional sliding mode control applications. It also provides a more effective equivalent model in the indirect approach, which leads to improved handling of the chaotic variations and uncertainties. Two numerical pairs of chaotic systems, i.e. the Lorenz and Chen’s systems and the Rössler system and modified Chua’s circuit are considered. In particular, in comparison with its type-1 fuzzy counterpart, the control effort is reduced by an average of 26.25% and 17.4% for the synchronization of the two corresponding systems, respectively. Furthermore, the integral of squared error is also improved by an average of 27.2% and 25.33%. This is while convergence time is reduced to less than 0.5 s and 1.5 s.     

基于自适应模糊滑模控制的分数阶混沌系统的投影同步

基于模糊控制理论和滑模控制理论以及自适应控制理论,研究了一类含有外部扰动的不确定分数阶混沌系统的混合投影同步问题.提出了一种自适应模糊滑模控制的分数阶混沌系统投影同步方法.模糊逻辑系统用来逼近未知的非线性函数和外部扰动,并且对逼近误差采用了自适应控制,同时构造了一种具有较强鲁棒性的分数阶积分滑模面.应用分数阶Barbalat引理设计了自适应模糊滑模控制器和参数自适应律.最后数值仿真结果验证了所提控制方法的有效性.     

基于非线性牵制控制的分数阶混沌网络聚同步

针对分数阶混沌复杂网络,提出一种非线性牵制控制策略实现网络聚同步.根据网络结点的不同属性,只对群间点施加非线性控制,然后基于分数阶系统稳定性理论,给出了实现聚同步的充分条件.数值仿真验证了该聚同步方案的有效性和正确性,同时深入讨论了控制增益和耦合强度等对聚同步的影响.     

基于自适应神经网络的分数阶混沌系统滑模同步

针对一类异结构不确定分数阶混沌系统的同步问题,基于Lyapunov稳定性理论和分数阶系统稳定性理论,提出一种神经网络结合干扰观测器的主动反馈控制方法. 设计一种非线性干扰观测器对干扰进行观测,通过滑模控制对未观测出的部分干扰进行补偿,最终实现分数阶混沌系统的同步.与现有方法相比,采用的模型更符合工程应用实际,且不需要已知不确定项上界.数值仿真验证了所提出方法的有效性和正确性.     

分数阶混沌系统同结构与异结构广义同步

基于分数阶拉普拉斯交换理论,提出设计合适的新型非线性反馈控制器,分别实现分数阶混沌系统的同结构广义同步和异结构广义同步.以分数阶Liu混沌系统和分数阶Lü混沌系统为例进行数值仿真,仿真结果表明了该方法的有效性.该方法灵活且适用范围广,具有潜在的应用前景.     

Robust adaptive fuzzy control of unknown chaotic systems

This paper presents a robust adaptive fuzzy control algorithm for controlling unknown chaotic systems. The control approach encompasses a fuzzy system and a robust controller. The fuzzy system is designed to mimic an ideal controller, based on sliding-mode control. The robust controller is designed to compensate for the difference between the fuzzy controller and the ideal controller. The parameters of the fuzzy system, as well as uncertainty bound of the robust controller, are tuned adaptively. The adaptive laws are derived in the Lyapunov sense to guarantee the stability of the controlled system. Numerical simulations show the effectiveness of the proposed approach.     

Intelligent fuzzy controller for chaos synchronization of uncertain fractional-order chaotic systems with input nonlinearities

In this research work, a novel fuzzy adaptive control is proposed to achieve a projective synchronization for a class of fractional-order chaotic systems with input nonlinearities (dead-zone together with sector nonlinearities). These master-slave systems under consideration are supposed to be with distinct models, different fractional-orders, unknown models, and dynamic external disturbances. The proposed control law consists of two main terms, namely: a fuzzy adaptive control term for appropriately approximating the uncertainties and a fractional-order variable-structure control term for robustly dealing with these inherent input nonlinearities. A Lyapunov approach is used to derive the updated laws and to prove the stability of the closed-loop control system. At last, a set of computer simulation results is carried out to illustrate and further validate the theoretical findings.     

Self-organizing adaptive fuzzy neural control for the synchronization of uncertain chaotic systems with random-varying parameters

This paper proposes a self-organizing adaptive fuzzy neural control (SAFNC) for the synchronization of uncertain chaotic systems with random-varying parameters. The proposed SAFNC system is composed of a computation controller and a robust controller. The computation controller containing a self-organizing fuzzy neural network (SOFNN) identifier is the principle controller. The SOFNN identifier is used to online estimate the compound uncertainties with the structure and parameter learning phases of fuzzy neural network (FNN), simultaneously. The structure-learning phase consists of the growing of membership functions, the splitting of fuzzy rules and the pruning of fuzzy rules, and thus the SOFNN identifier can avoid the time-consuming trial-and-error tuning procedure for determining the network structure of fuzzy neural network. The robust controller is used to attenuate the effects of the approximation error so that the synchronization of chaotic systems is achieved.All the parameter learning algorithms are derived based on the Lyapunov stability theorem to ensure network convergence as well as stable synchronization performance. To demonstrate the effectiveness of the proposed method, simulation results are illustrated in this paper.     

Projective synchronization of Chua's chaotic systems with dead-zone in the control input

This paper investigates the chaos synchronization problem for drive–response Chua's systems coupled with dead-zone nonlinear input. Using the sliding mode control technique, an adaptive control law is established which guarantees projective synchronization even when the dead-zone nonlinearity is present. Computer simulations are provided to demonstrate the effectiveness of the proposed synchronization scheme.     

两个不同Sprott混沌系统的控制与同步研究

首先采用线性反馈方法来控制混沌的SprottC系统和混沌的SprottF系统,使这两个混沌系统的轨道被控制到他们各自的每一个平衡点.然后使用主动控制方法来同步这两个不同的混沌系统,使混沌的SprottC系统和SprottF系统的轨道重合.并用数值模拟证实了理论的正确性.     

Leader-following consensus of fractional-order multi-agent systems via adaptive pinning control

In this paper, the leader-following consensus problem of fractional-order multi-agent systems is considered via adaptive pinning control. The dynamics of leader and all followers with linear and nonlinear functions are investigated, respectively. We assume that the node should be pinned if its in-degree is less than its out-degree in the paper. Under this assumption and based on the stability theory of fractional-order differential systems, some leader-following consensus criteria are derived, which are easily obtained by matrix inequalities. The control of each agent using local information is designed and detailed analysis of the leader-following consensus is presented. The design technique is based on algebraic graph theory and the Riccati inequality. Several simulation examples are presented to demonstrate the effectiveness of the proposed method.     

基于状态观测器的一类混沌系统的投影同步

研究了基于状态观测器的一类混沌系统的投影同步问题.基于状态观测器方法和极点配置技术,设计出一种投影同步方案,使得一类混沌系统达到了投影同步.与以往的投影同步方法相比,该方法简便,易于实现,达到投影同步的时间短,并且在同步控制过程中可任意调整缩放比例因子.最后,用Lu系统进行了数值仿真,仿真结果表明了该方法的有效性.     

Quadratic optimal neural fuzzy control for synchronization of uncertain chaotic systems

This paper presents a novel quadratic optimal neural fuzzy control for synchronization of uncertain chaotic systems via H^∞ approach. In the proposed algorithm, a self-constructing neural fuzzy network (SCNFN) is developed with both structure and parameter learning phases, so that the number of fuzzy rules and network parameters can be adaptively determined. Based on the SCNFN, an uncertainty observer is first introduced to watch compound system uncertainties. Subsequently, an optimal NFN-based controller is designed to overcome the effects of unstructured uncertainty and approximation error by integrating the NFN identifier, linear optimal control and H^∞ approach as a whole. The adaptive tuning laws of network parameters are derived in the sense of quadratic stability technique and Lyapunov synthesis approach to ensure the network convergence and H^∞ synchronization performance. The merits of the proposed control scheme are not only that the conservative estimation of NFN approximation error bound is avoided but also that a suitable-sized neural structure is found to sufficiently approximate the system uncertainties. Simulation results are provided to verify the effectiveness and robustness of the proposed control method.     

具有控制约束的分数阶混沌系统柔性同步控制

研究具有控制约束的两个相同分数阶混沌系统的同步问题.首先,在不消除非线性项的情况下,基于比例控制与自适应控制理论,设计线性自适应切换控制器,实现分数阶混沌系统的同步;其次,考虑到控制器存在约束,利用能够提供无限子控制器的柔性变结构控制策略对线性控制器进行改进,设计柔性变结构控制器,以应对控制的约束,并对线性控制器进行优化;同时,基于分数阶系统Mittag-Leffler稳定判定定理对误差系统的稳定性进行证明.在兼顾系统稳定性与鲁棒性的情况下,可以缩短系统的调整时间,并有效抑制抖振.最后,利用所设计的自适应柔性控制器实现分数阶Chen系统的混沌同步,并通过仿真对比两控制器控制效果,从而验证柔性变结构方法在具有约束的分数阶混沌系统同步控制中的优越性.     

基于自适应控制的八个混沌系统的多级组合同步

针对传统的混沌系统结构样式单一和系统变量少的问题,设计了一种混沌电路系统,该电路有较为复杂的动力学行为、较高的敏感性和较强的抗干扰性。随着电路参数的变化,结合自适应稳定性判据和混沌运动理论详细分析了该系统的不同动力学行为;此外,根据电路图搭建了相应的电路并利用示波器观察该电路的动力学行为,其行为与MATLAB的仿真结果相一致,进一步证明了电路的可行性和灵活性。在此基础上,重点提出并研究了基于本系统的多级组合同步,通过构造不同的控制器实现了八个系统之间的多级组合同步。仿真结果表明,该同步方案在收敛速度和精度上具有很好的效果。     

具有死区输入的分数阶混沌系统的有限时间同步

本文提出一种新型分数阶滑模控制方案来实现两个不同分数阶混沌系统的有限时间同步. 首先, 根据实际情况, 在研究系统同步过程中, 充分考虑死区非线性输入、参数不确定性、模型不确定性以及外界扰动对系统的影 响, 然后, 采用Lyapunov稳定理论证明滑模阶段和趋近阶段均是有限时间收敛的, 最后, 给出一个仿真实例充分验证本文所提出控制策略的有效性和可行性.     

分数阶异结构超混沌系统完全同步与反相同步控制

以分数阶Lü混沌系统和分数阶Chen超混沌系统为例,研究了维数不同、分数阶次不相等的异结构的混沌系统和超混沌系统的完全同步和反相同步.首先,基于分数阶系统稳定性理论和非线性动力学理论,构造出相应的非线性控制器,实现了两个维数不同,分数阶次不相等异结构混沌系统与超混沌系统的完全同步和反相同步;其次,基于分数阶稳定性理论,对上述两类同步给出了严格的数学证明;最后,借助于预估-校正算法,利用数值模拟验证了所提方法的有效性.