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.     

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.     

不确定Duffing混沌系统的同步控制

在模糊滑模变结构控制基础上,研究具有不确定性Duffing混沌系统的同步控制问题。选择合适的滑模面,基于Lyapunov稳定性理论设计模糊滑模变结构控制器及自适应更新规则,从理论上证明控制系统的稳定性。由于控制器的设计是基于自适应模糊滑模变结构控制的,与常规方法相比,控制器滑动模态不受干扰的影响,有较好的鲁棒性和快速跟踪能力。通过数值仿真实验验证了该系统的有效性。     

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．     

不确定Willis脑动脉瘤系统的自适应模糊滑模控制

研究了具有不确定项的非线性Willis环上脑动脉瘤系统的混沌控制和同步问题,提出了一种自适应模糊滑模变结构控制方法,设计了模糊滑模变结构控制器及自适应控制律,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,受控Willis脑动脉瘤系统能够达到任意目标轨道,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了控制器的有效性。     

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.     

不同维分数阶混沌预设时间有限时间投影同步

对于不同维分数阶混沌系统的投影同步问题,设计了一种自适应滑模控制器。这使得带有内部不确定量和外部扰动的驱动,响应系统能够在任意预设的时间完成同步,自适应律可以逼近未知量的上界。并针对自适应滑模控制器由于干扰产生抖振的问题,提出了两种解决方案。首先是设计二维滑模控制表,将模糊控制方法加入滑模控制器组成模糊自适应滑模控制器...     

基于输出反馈滑模控制的分数阶超混沌系统同步

以具有更大秘钥空间的分数阶超混沌系统为驱动系统和响应系统,利用具有实际应用意义的输出反馈滑模控制实现两个系统的同步.通过对同步误差系统方程进行结构分解,在辅助系统的基础上设计具有输出反馈特性的滑模控制律.在分数阶系统稳定性理论基础上利用MATLAB YALMIP工具箱对滑模参数进行整定,并利用分数阶Lyapunov稳定性定理证明了滑模控制律和自适应滑模控制律的稳定性.最后,数值仿真表明了本文方法的有效性和可行性.     

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.      

Research on adaptive sliding synchronization of Rikitake chaotic system with single unknown control coefficient

The control of second order system with uncertain parameters and single unknown control coefficient was investigated to solve the synchronization problem of Rikitake chaotic with reduced number of active inputs. In addition, a kind of adaptive strategy was hybrid with sliding mode method, where the adaptive strategy was used to cope with uncertain parameters produced in the process of sliding mode controller design. At last, detailed numerical simulations with both second order systems and synchronous chaotic system were done to testify the rightness of the proposed method and also multi-time random simulations were done to testify the robustness of the controller. In addition, the main conclusion is that the sliding mode control has very good consistency since the strategy formation is almost the same as the controller for system with known control coefficient, and high gain is necessary for system with single uncertain control coefficient.     

Decentralized sliding‐mode control for attitude synchronization in spacecraft formation

This paper addresses attitude synchronization and tracking problems in spacecraft formation in the presence of model uncertainties and external disturbances. A decentralized adaptive sliding mode control law is proposed using undirected interspacecraft communication topology and analyzed based on algebraic graph theory. A multispacecraft sliding manifold is derived, on which each spacecraft approaches desired time‐varying attitude and angular velocity while maintaining attitude synchronization with the other spacecraft in the formation. A control law is then developed to ensure convergence to the sliding manifold. The stability of the resulting closed‐loop system is proved by application of Barbalat's Lemma. Simulation results demonstrate the effectiveness of the proposed attitude synchronization and tracking methodology. Copyright © 2012 John Wiley & Sons, Ltd.     

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.     

不确定混沌系统的自适应滑模变结构同步

针对一类不确定混沌系统,运用自适应滑模变结构控制方法,设计了相应的控制器和自适应律,实现了混沌系统的主从同步控制.通过构造Lyapunov函数在理论上证明了该同步方法的有效性,并且在不确定项上界未知的情况下,对系统未建模部分和噪声干扰具有很强的鲁棒性.最后以Duffing-Holmes系统为例,进行了混沌同步仿真,仿真结果表明该方法的有效性.     

Adaptive synchronization on uncertain dynamics of high-order nonlinear multi-agent systems with partition of unity approach

An adaptive synchronization of uncertain chaotic system is presented using partition of unity method. First, the uncertainties of chaotic systems are approximate by the linear combination of partition of unity. Subsequently, the sliding mode adaptive controllers are proposed for synchronization of the uncertain chaotic systems. The proposed approach offers a systematic design procedure for adaptive synchronization of a class of uncertain chaotic system in the chaos research literature. We also illustrate examples of chaotic systems such as Chen and Lorenz chaotic systems to show the effectiveness of the approach.     

Control for the synchronization of Chen system via a single nonlinear input

This paper addresses control for the synchronization of Chen chaotic systems via sector nonlinear inputs. Feedback control, adaptive control, fast sliding mode and robust control approaches based on single state feedback controller are investigated. In these cases, sufficient conditions for the synchronization are obtained analytically. Numerical simulations verify the control performances.     

Control for the synchronization of Chen system via a single nonlinear input

This paper addresses control for the synchronization of Chen chaotic systems via sector nonlinear inputs. Feedback control, adaptive control, fast sliding mode and robust control approaches based on single state feedback controller are investigated. In these cases, sufficient conditions for the synchronization are obtained analytically. Numerical simulations verify the control performances.     

一类不确定时滞系统的自适应滑模控制

讨论了不确定时滞系统的鲁棒控制器设计问题。利用自适应滑模控制策略,直接克服系统不确定性的影响,保证了从任意初始位置出发的系统在有限时间内到滑模面;基于时滞系统鲁棒稳定控制的结论,导出了时滞依赖滑模控制的新结论。仿真实验证明了所提方法的有效性。     

基于干扰观测器的一类不确定非线性系统自适应二阶动态terminal滑模控制

针对一类不确定非线性系统的跟踪控制问题,在考虑建模误差、参数不确定和外部干扰情况下,以其拥有良好的跟踪性能以及强鲁棒性为目标,提出基于回归扰动模糊神经网络干扰观测器(recurrent perturbation fuzzy neural networks disturbance observer,RPFNNDO)的鲁棒自适应二阶动态terminal滑模控制策略.将回归网络、模糊神经网络和sine-cosine扰动函数各自优势相结合,给出一种回归扰动模糊神经网络结构,提出RPFNNDO设计方法,保证干扰估计准确性;构造基于带有指数函数滑模面的二阶快速terminal滑模面,给出其控制器设计过程,避免了滑模到达阶段、传统滑模的抖振问题,采用具有指数收敛的鲁棒项抑制干扰估计误差对系统跟踪性能的影响,利用Lyapunov理论证明闭环系统的稳定性;将该方法应用于混沌陀螺系统同步控制仿真实验,结果表明所提方法的有效性.     

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.