分数阶双指数混沌系统的自适应滑模同步

研究了分数阶双指数混沌系统的自适应滑模同步问题.通过设计滑模函数和控制器,构造了平方Lyapunov函数进行稳定性分析.利用Barbalat引理证明了同步误差渐近趋于零,获得了系统取得自适应滑模同步的充分条件.数值仿真结果表明:选取适当的控制器及与滑模函数,分数阶双指数混沌系统取得自适应滑模同步.     

一类分数阶超混沌系统修正函数投影同步的滑模控制

对一类具有未知参数的分数阶超混沌系统的修正函数投影同步进行研究.通过设计响应系统的补偿器,进而得到修正函数投影同步的误差系统.基于自适应滑模控制理论和分数阶微分系统的稳定性理论,设计了一种自适应同步的控制方案.通过选取自适应滑模控制器以及参数自适应控制率,最终实现了驱动系统和响应系统修正函数投影同步,并可以对不确定参数进行估计.最后针对结论,以分数阶超混沌L(u|¨)系统为例,利用Adams-Bashfortlh-Moultom算法进行数值仿真,其结果说明了该方法的有效性和可行性.     

超混沌分数阶Bao系统的自适应滑模同步控制

研究超混沌分数阶Bao系统自适应滑模同步,设计出分数阶滑模函数、适应规则和控制器,取得超混沌分数阶Bao系统自适应滑模同步的充分条件,文末用MATLAB数值仿真验证了所得结论.     

分数阶四维忆阻超混沌系统的滑模同步

研究了分数阶四维忆阻超混沌系统滑模同步的两种方法,设计分数阶控制器与滑模函数,获得分数阶忆阻超混沌系统滑模同步两个充分条件,研究表明:在设计适当的滑模面与控制律下,不确定分数阶忆阻超混沌系统可取得滑模同步.     

分数阶高阶不确定系统的自适应反演滑模同步

基于自适应反演滑模同步方法研究分数阶不确定高阶非线性混沌系统的同步问题,给出子系统的Lyapunov函数和虚拟控制,在反演设计中引入滑模函数和控制器及自适应规则得到分数阶不确定非线性混沌系统取得自适应反演滑模同步的充分条件,并把该结论平推到整数阶系统.     

超混沌系统的函数投影同步与参数辨识

研究了一参数未知超混沌系统的函数投影同步问题．基于李雅谱诺夫稳定性理论,设计了实现混沌系统函数投影同步的有效非线性控制器,可以快速实现超混沌系统的加速函数投影同步,同时设计了参数控制律,有效的辨识了系统的未知参数,数值仿真验证了理论分析和数值计算的正确性．     

基于积分滑模方法的一个新型分数阶指数混沌系统的同步

研究一类分数阶新指数混沌系统的积分滑模同步,给出滑模面和控制器的设计,获得系统取得积分滑模同步的充分条件,研究表明:选择适当的控制器与滑模面,整数阶分数阶新指数混沌系统的驱动-响应系统取得积分滑模同步.     

受扰不确定混沌系统的双路组合函数投影同步

研究了具有未知参数和外界扰动的多个混沌系统之间的双路组合函数投影同步问题.首先给出了由四个混沌驱动系统和两个混沌响应系统组成的双路组合函数投影同步系统的定义,然后以Lyapunov稳定性理论和不等式变换方法为分析依据,设计了鲁棒自适应控制器和参数自适应律,使得两路同步系统中的响应系统和驱动系统按照相应的函数比例因子矩阵实现同步,并有效克服未知有界干扰和未知参数的影响.相应的理论分析和数值仿真证明了该同步方案的可行性和有效性.     

分数阶不确定多混沌系统的自适应滑模同步

研究分数阶不确定多混沌系统的自适应滑模同步,通过构造滑模面,设计控制器和适应规则,能够满足滑模面的稳定性与到达性,进而得到分数阶不确定多混沌系统取得自适应滑模同步的充分性条件,研究表明:分数阶不确定多混沌系统满足在一定条件下能够取得自适应滑模同步.     

一类不确定分数阶多混沌系统的终端滑模同步控制

根据分数阶系统理论利用终端滑模方法研究了分数阶不确定多混沌系统同步问题,获得了整数阶分数阶两种情形下多混沌系统取得滑模同步的充分性条件,最终结论说明设计合适的控制律和切换函数,分数阶多混沌系统取得滑模同步.     

Modified projective synchronization of chaotic systems with disturbances via active sliding mode control

We apply the active sliding mode control technique to realize the modified projective synchronization of the chaotic systems. The disturbances are considered both in the drive system and the response system. The sufficient conditions for the modified projective synchronization both the non-identical and identical chaotic systems are presented. The corresponding numerical simulations are provided to illuminate the effectiveness of the proposed active sliding mode controllers.     

Projective lag synchronization of spatiotemporal chaos via active sliding mode control

This paper investigates projective lag synchronization of spatiotemporal chaos with disturbances. A control scheme is designed via active sliding mode control. The synchronization of spatiotemporal chaos between a drive system and a response system with disturbances and time-delay is implemented by adding the active sliding mode controllers. The control law is applied to two identical spatiotemporal Gray-Scott systems. Numerical results demonstrate the feasibility and the effectiveness of the proposed approach.     

Projective synchronization of Chua’s chaotic system 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. An estimator of unknown nonlinear term is proposed. Using the sliding mode control technique and the estimate of unknown nonlinear term, a novel variable structure controller 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.     

Synchronization of fractional‐order chaotic systems with disturbances via novel fractional‐integer integral sliding mode control and application to neuron models

In this paper, a novel fractional‐integer integral type sliding mode technique for control and generalized function projective synchronization of different fractional‐order chaotic systems with different dimensions in the presence of disturbances is presented. When the upper bounds of the disturbances are known, a sliding mode control rule is proposed to insure the existence of the sliding motion in finite time. Furthermore, an adaptive sliding mode control is designed when the upper bounds of the disturbances are unknown. The stability analysis of sliding mode surface is given using the Lyapunov stability theory. Finally, the results performed for synchronization of three‐dimensional fractional‐order chaotic Hindmarsh‐Rose (HR) neuron model and two‐dimensional fractional‐order chaotic FitzHugh‐Nagumo (FHN) neuron model.     

Projective synchronization of different chaotic time-delayed neural networks based on integral sliding mode controller

In this paper, an integral sliding mode control approach is presented to study the projective synchronization for different chaotic time-delayed neural networks. A sliding mode surface is appropriately constructed and a sliding mode controller is synthesized to guarantee the reachability of the specified sliding surface. The global asymptotic stability of the error dynamical system in the specified switching surface is investigated with the Lyapunov–Krasovskii (L–K) functional method. A delay-dependent sufficient condition is derived and the maximum time-delay value is obtained by means of the linear matrix inequality (LMI) technique. A simulation example is finally exploited to illustrate the feasibility and effectiveness of the proposed approach, verify the conservativeness of L–K method and LMI technique, and exhibit the relationship between the convergence velocity of error system and the gain matrix.     

Unidirectional synchronization for Hindmarsh–Rose neurons via robust adaptive sliding mode control

This paper presents an adaptive neural network (NN) based sliding mode control for unidirectional synchronization of Hindmarsh–Rose (HR) neurons in a master–slave configuration. We first give the dynamics of single HR neuron which may exhibit spike-burst chaotic behaviors. Then we formulate the problem of unidirectional synchronization control of two HR neurons and propose a NN based sliding mode controller. The controller consists of two simple radial basis function (RBF) NNs which are used to approximate the desired sliding mode controller and the uncertain nonlinear part of the error dynamical system, respectively. The control scheme is robust to the uncertainties such as approximate errors, ionic channel noise and external disturbances. The simulation results demonstrate the validity of the proposed control method.     

Synchronization and anti-synchronization coexist in two-degree-of-freedom dissipative gyroscope with nonlinear inputs

This study demonstrates that synchronization and anti-synchronization can coexist in two-degree-of-freedom dissipative gyroscope system with input nonlinearity. Because of the nonlinear terms of the gyroscope system, the system exhibits complex motions containing regular and chaotic motions. Using the variable structure control technique, a novel control law is established which guarantees the hybrid projective synchronization including synchronization, anti-synchronization and projective synchronization even when the control input nonlinearity is present. By Lyapunov stability theory with control terms, two suitable sliding surfaces are proposed to ensure the stability of the controlled closed-loop system in sliding mode, and two variable structure controllers (VSC) are designed to guarantee the hitting of the sliding surfaces. Numerical simulations are presented to verify the proposed synchronization approach.     

Robust adaptive synchronization of different uncertain chaotic systems subject to input nonlinearity

In this paper, an adaptive controller is designed to ensure robust synchronization of two different chaotic systems with input nonlinearities. For this purpose, a stable sliding surface is defined and an adaptive sliding mode controller is designed to achieve robust synchronization of the systems when the control input is influenced through nonlinearities produced by actuator or external uncertainty recourses. The adaptation law guarantees the synchronization assuming of unknown model uncertainty. Furthermore by adding an integrator and incorporating a saturation function in the control law, the chattering phenomenon caused by the sign function is avoided. The simulation results for synchronization of Chua’s circuit and Genesio systems show the efficiency of the proposed technique.