混沌系统的有限时间滑模同步控制

采用滑模控制的方法,研究了两个不同的带有不确定性和外部扰动的混沌系统之间的同步问题。基于Lyapunov稳定性理论和有限时间滑模控制方法,设计了终端滑模控制器来实现两个混沌系统的同步。在设计控制器过程中提出了一个新的非奇异的终端滑模面,并证明它能在有限时间内收敛于零平衡点。通过数值仿真验证了所设计的控制器的有效性。     

Anti-synchronization of four-wing chaotic systems via sliding mode control

Sliding mode control is an important method used in nonlinear control systems. In robust control systems, the sliding mode control is often adopted due to its inherent advantages of easy realization, fast response and good transient performance as well as its insensitivity to parameter uncertainties and disturbances. In this paper, we derive new results based on the sliding mode control for the anti-synchronization of identical Qi three-dimensional (3D) four-wing chaotic systems (2008) and identical Liu 3D four-wing chaotic systems (2009). The stability results for the anti-synchronization schemes derived in this paper using sliding mode control (SMC) are established using Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the SMC method is very effective and convenient to achieve global chaos anti-synchronization of the identical Qi four-wing chaotic systems and identical Liu four-wing chaotic systems. Numerical simulations are shown to illustrate and validate the synchronization schemes derived in this paper.     

基于主动滑模控制的一类不确定混沌系统的同步

讨论了一类不确定混沌系统的同步问题。基于主动控制思想,提出了一种新的主动滑模控制策略,使得从任意初始条件出发的不确定混沌系统在有限时间内趋近滑模面;通过一种新颖的虚拟反馈控制,得到了设计鲁棒滑模面的一个充分条件,较好地实现了响应系统与驱动系统的完全同步,确保了不确定混沌系统同步的鲁棒稳定性。该控制器适用于一般的混沌系统。以Lü混沌系统为例进行了仿真验证,仿真结果表明,该控制方法可以实现较快的混沌同步,且同步的鲁棒稳定性良好。     

具有未知参数的混沌系统的有限时间滑模同步控制

针对带有未知参数和非线性输入的两个不同的混沌系统之间的同步问题进行研究. 提出一个相比于传统滑模面具有更快收敛速度的终端滑模面, 并结合自适应控制理论和滑模控制理论, 设计一个自适应滑模控制律, 使同步误差在有限时间内收敛到滑模面, 并沿滑模面在有限时间内收敛到零点, 最终实现两个不同的混沌系统之间的同步. 最后, 以带有不确定性和外部扰动的Lorenz 系统和Liu 系统为例进行数值仿真, 仿真结果表明, 同步误差在有限时间内收敛到零点, 从而验证了所设计控制律的有效性和可行性.     

Terminal滑模自适应控制实现一类不确定混沌系统的同步

应用Terminal滑模控制技术和选择指数趋近律来综合滑模控制器，实现一类混沌系统的状态同步．在控制器中引入一类简单的自适应律，用以在线估计界参数．该设计方案消除了滑模控制的到达阶段，状态始终保持在滑模面上，并能在有限时间内趋近于原点．与一般滑模控制同步实现相比，具有更小的同步时间和鲁棒性．通过对Duffing—Holmes系统的同步仿真，验证了该方法的可行性．     

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.     

Synchronization of uncertain chaotic systems based on adaptive type-2 fuzzy sliding mode control

A novel direct adaptive interval type-2 fuzzy neural network (FNN) controller in which linguistic fuzzy control rules can be directly incorporated into the controller is developed to synchronize chaotic systems with training data corrupted by noise or rule uncertainties involving external disturbances, in this paper. By incorporating direct adaptive interval type-2 FNN control scheme and sliding mode approach, two non-identical chaotic systems can be synchronized based on Lyapunov stability criterion. Moreover, the chattering phenomena of the control efforts can be reduced and the external disturbance on the synchronization error can be attenuated. The stability of the proposed overall adaptive control scheme will be guaranteed in the sense that all the states and signals are uniformly bounded. From the simulation example, to synchronize two non-identical Chua’s chaotic circuits, it has been shown that type-2 FNN controllers have the potential to overcome the limitations of tpe-1 FNN controllers when training data is corrupted by high levels of uncertainty.     

Adaptive sliding mode control of chaotic dynamical systems with application to synchronization

We address the problem of control and synchronization of a class of uncertain chaotic systems. Our approach follows techniques of sliding mode control and adaptive estimation law. The adaptive algorithm is constructed based on the sliding mode control to ensure perfect tracking and synchronization in presence of system uncertainty and external disturbance. Stability of the closed-loop system is proved using Lyapunov stability theory. Our theoretical findings are supported by simulation results.     

Robust Finite-time Synchronization of Non-identical Fractional-order Hyperchaotic Systems and Its Application in Secure Communication

This paper proposes a novel adaptive sliding mode control (SMC) method for synchronization of non-identical fractional-order (FO) chaotic and hyper-chaotic systems. Under the existence of system uncertainties and external disturbances, finite-time synchronization between two FO chaotic and hyperchaotic systems is achieved by introducing a novel adaptive sliding mode controller (ASMC). Here in this paper, a fractional sliding surface is proposed. A stability criterion for FO nonlinear dynamic systems is introduced. Sufficient conditions to guarantee stable synchronization are given in the sense of the Lyapunov stability theorem. To tackle the uncertainties and external disturbances, appropriate adaptation laws are introduced. Particle swarm optimization (PSO) is used for estimating the controller parameters. Finally, finite-time synchronization of the FO chaotic and hyper-chaotic systems is applied to secure communication.      

Robust synchronization of chaotic systems using slidingmode and feedback control

We propose a robust scheme to achieve the synchronization of chaotic systems with modeling mismatches and parametric variations. The proposed algorithm combines high-order sliding mode and feedback control. The sliding mode is used to estimate the synchronization error between the master and the slave as well as its time derivatives, while feedback control is used to drive the slave track the master. The stability of the proposed design is proved theoretically, and its performance is verified by some numerical simulations. Compared with some existing synchronization algorithms, the proposed algorithm shows faster convergence and stronger robustness to system uncertainties.     

Design of a chatter-free terminal sliding mode controller for nonlinear fractional-order dynamical systems

This paper investigates the problem of robust control of nonlinear fractional-order dynamical systems in the presence of uncertainties. First, a novel switching surface is proposed and its finite-time stability to the origin is proved. Subsequently, using the sliding mode theory, a robust fractional control law is proposed to ensure the existence of the sliding motion in finite time. We use a fractional Lyapunov stability theory to prove the stability of the system in a given finite time. In order to avoid the chattering, which is inherent in conventional sliding mode controllers, we transfer the sign function of the control input into the fractional derivative of the control signal. The proposed chattering-free sliding mode technique is then applied for stabilisation of a broad class of three-dimensional fractional-order chaotic systems via a single variable driving control input. Simulation results reveal that the proposed fractional sliding mode controller works well for chaos control of fractional-order hyperchaotic Chen, chaotic Lorenz and chaotic Arneodo systems with no-chatter control inputs.     

A multitask sliding mode control for mismatched uncertain large-scale systems

A new sliding mode control (SMC) approach, output variables only, single phase only and chattering phenomenon free, is presented for a class of mismatched uncertain large-scale systems. For a new multitask SMC, it is not required that the system states are available. Moreover, the sliding function in this study just depends on output variables. Using an exponential type sliding surface, the system states are always in the sliding mode at the beginning time t = 0. Using a newly appropriate linear matrix inequality stability conditions by the Lyapunov method are derived such that each subsystem in the new sliding mode is completely invariant to matched uncertainties. As a result, robustness of the mismatched uncertain large-scale systems can be assured throughout an entire response of the system starting from the initial time t = 0. In every subsystem, a scheme of decentralised control using only output states is proposed. In addition, a continuous controller is finally designed for chattering removal. Finally, a numerical example is used to demonstrate the efficacy of the proposed method.     

一类不确定混沌系统的模糊滑模控制与同步

针对一类具有不确定项的二阶连续时间混沌系统的定值跟踪控制和自混沌同步及异结构混沌同步问题,提出了一种模糊滑模变结构控制方法,设计了模糊滑模变结构控制器,并从理论上证明了控制系统的稳定性.在该控制器的作用下,可以实现两个相同或不同结构的混沌系统的控制与同步,且不受不确定性的影响,具有很强的鲁棒性.定值跟踪和同步控制的仿真结果表明,该控制器是有效的.     

利用滑模变结构控制的混沌同步控制

利用滑动模态控制研究了含有不确定性的混沌系统的同步控制问题。用极点配置和LMI方法设计的切换函数保证了带有非线性项的滑动模态混沌同步,用指数滑模到达条件给出了鲁棒混沌同步控制器设计。由于控制器的设计是基于滑动模态的不变性和线性矩阵不等式方法给出的,与常规方法相比较,给出的控制器滑动模态不受干扰的影响,系统有很好的鲁棒性和快速跟踪能力;切换函数的参数可用线性矩阵不等式求解得出,计算方便,所得结果保守性小。最后以Chen系统为例,进行了混沌同步仿真,仿真结果表明所给出的方法是有效的。     

Chaos control and hybrid projective synchronization for a class of new chaotic systems

The problems on chaos control and hybrid projective synchronization for a class of new chaotic systems are considered. First, new 4D chaotic systems are proposed by introducing an additional state into a 3D quadratic chaotic system and the states of the systems corresponding to the different ranges of parameter b are exhibited. Second, a single scalar adaptive feedback controller for chaos control of the systems is presented. Third, hybrid projective synchronization (HPS) of two of the chaotic systems with parameters in different conditions are investigated by presenting adaptive feedback control strategies with adaptive parameter update laws and considering controller simplification to achieve complete synchronization. Finally, numerical simulations are demonstrated to verify the effectiveness of the strategies.     

陀螺仪系统同步控制的参数自适应滑模控制

针对带有内部不确定性及外部扰动的陀螺仪混沌系统的同步问题,提出了一种参数自适应滑模控制方法,并给出参数自适应律.该方法不依赖被控混沌系统的数学模型,可以快速跟踪主混沌系统.时域及复频域理论分析表明,由参数自适应滑模控制器组成的闭环控制系统是全局渐近稳定的,而且参数自适应滑模控制器具有良好的抗扰动鲁棒性.仿真结果表明该控制方法计算量小、响应速度快、控制精度高、抗扰动鲁棒性强,在非线性不确定系统控制领域具有广泛的应用价值.     

Robust control for uncertain linear delay systems via sliding mode control

In this paper, a novel discontinuous control strategy for robust stabilization of a class of uncertain multivariable linear time‐delay systems with delays in both the state and control variables is proposed. Two predictors are first designed to compensate the delay effect in the control input, and then an integral sliding mode control technique is applied to compensate partially the effect of the perturbation term. Finally, a nominal delay‐free component of the full control input is designed to stabilize the sliding mode dynamics. Conditions for the stability of the closed‐loop perturbed system are then derived. The proposed framework is then extended to the class of systems modeled in regular form. Some examples illustrate the feasibility of the proposed scheme. Copyright © 2017 John Wiley & Sons, Ltd.     

具有扇区非线性和死区的混沌系统的跟踪控制

研究控制系统优化问题,由于系统具有扇区非线性和死区的混沌系统的跟踪控制,针对系统的稳定性和跟踪响应特性优化问题,首先通过滑模控制的方法,设计了一个时变滑模控制器并提出了控制规律。利用李雅普诺夫稳定性理论,证明了控制器能够有效的实现Duffing混沌系统的状态跟踪给定的充分光滑信号,Duffing混沌系统在时变滑模控制器下不受输入非线性、死区以及外部噪声等因素的影响。实验结果证明在死区原点对称和死区原点非对称情况下,控制器跟踪的有效性能满足系统的要求,为系统设计提供了支持。     

Adaptive sliding mode control of chaotic dynamical systems with application to synchronization

We address the problem of control and synchronization of a class of uncertain chaotic systems. Our approach follows techniques of sliding mode control and adaptive estimation law. The adaptive algorithm is constructed based on the sliding mode control to ensure perfect tracking and synchronization in presence of system uncertainty and external disturbance. Stability of the closed-loop system is proved using Lyapunov stability theory. Our theoretical findings are supported by simulation results.     

基于主动滑模控制实现一类含有非匹配不确定混沌系统的同步

讨论了一类非匹配不确定混沌系统的同步问题.基于主动控制思想,提出了一种主动滑模控制策略,使得从任意初始条件出发的不确定混沌系统在有限时间内到达滑模面.利用线性矩阵不等式(LMI)技术设计了一个鲁棒稳定的滑模面,以降低非匹配不确定对系统的影响.给出了线性矩阵不等式形式的稳定滑模面存在的充分条件.通过对Rssler系统的同步仿真,验证了该方法的可行性.