基于新型滑模面分数阶Like-Bao系统自适应滑模同步

基于新型滑模面研究分数阶Like-Bao系统的自适应滑模同步,设计了一种新型滑模面,满足滑模稳定性条件,能够到达滑模面上时误差趋近于零,从而获得分数阶Like-Bao系统取得自适应滑模同步的充分条件,结论表明:一定条件下不确定分数阶Like-Bao系统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.     

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.     

整数阶分数阶Rucklidge混沌系统的自适应滑模同步

基于分数阶自适应滑模同步理论研究不确定Rucklidge混沌系统的同步,得到了不确定分数阶Rucklidge混沌系统取得自适应滑模同步的充分条件,研究表明:构造适当的控制律与滑模函数,整数阶分数阶不确定Rucklidge系统取得自适应滑模同步.     

参数未知的分数阶不确定R?ssler混沌系统的自适应滑模同步

根据自适应滑模方法研究具有未知参数的分数阶不确定R?ssler系统的滑模同步,给出分数阶控制器与滑模函数的设计与构造,得到分数阶不确定R?ssler系统取得同步的两个充分条件,结论表明:选取合适的滑模函数与控制律,分数阶不确定R?ssler系统的主从系统能够取得滑模同步.     

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.     

分数阶多涡卷混沌系统滑模同步的两种控制方案

研究了分数阶多涡卷混沌系统滑模同步的两种控制方案,根据分数阶微积分的相关理论给出了系统取得同步的充分性条件,结果表明:选取适当的控制律以及滑模面,分数阶多涡卷误差系统将取得混沌同步.     

一类不确定分数阶混沌系统的参数辨识

研究了一类不确定分数阶混沌系统的参数辨识问题,基于Lyapunov稳定性理论和分数阶微积分给出了系统取得混沌同步的两个充分条件,并把该结论应用到特殊情形,研究表明选取适当的滑模面和控制律,不确定分数阶混沌系统可以取得混沌同步.     

Adaptive fuzzy sliding mode control for synchronization of uncertain fractional order chaotic systems

This paper deals with chaos synchronization between two different uncertain fractional order chaotic systems based on adaptive fuzzy sliding mode control (AFSMC). With the definition of fractional derivatives and integrals, a fuzzy Lyapunov synthesis approach is proposed to tune free parameters of the adaptive fuzzy controller on line by output feedback control law and adaptive law. Moreover, chattering phenomena in the control efforts can be reduced. The sliding mode design procedure not only guarantees the stability and robustness of the proposed AFSMC, but also the external disturbance on the synchronization error can be attenuated. The simulation example is included to confirm validity and synchronization performance of the advocated design methodology.     

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.     

Robust synchronization of drive–response chaotic systems via adaptive sliding mode control

A robust adaptive sliding control scheme is developed in this study to achieve synchronization for two identical chaotic systems in the presence of uncertain system parameters, external disturbances and nonlinear control inputs. An adaptation algorithm is given based on the Lyapunov stability theory. Using this adaptation technique to estimate the upper-bounds of parameter variation and external disturbance uncertainties, an adaptive sliding mode controller is then constructed without requiring the bounds of parameter and disturbance uncertainties to be known in advance. It is proven that the proposed adaptive sliding mode controller can maintain the existence of sliding mode in finite time in uncertain chaotic systems. Finally, numerical simulations are presented to show the effectiveness of the proposed control scheme.     

Suppression of chaotic behavior in horizontal platform systems based on an adaptive sliding mode control scheme

This work presents an adaptive sliding mode control scheme to elucidate the robust chaos suppression control of non-autonomous chaotic systems. The proposed control scheme utilizes extended systems to ensure that continuous control input is obtained in order to avoid chattering phenomenon as frequently in conventional sliding mode control systems. A switching surface is adopted to ensure the relative ease in stabilizing the extended error dynamics in the sliding mode. An adaptive sliding mode controller (ASMC) is then derived to guarantee the occurrence of the sliding motion, even when the chaotic horizontal platform system (HPS) is undergoing parametric uncertainties. Based on Lyapunov stability theorem, control laws are derived. In addition to guaranteeing that uncertain horizontal platform chaotic systems can be stabilized to a steady state, the proposed control scheme ensures asymptotically tracking of any desired trajectory. Furthermore, the numerical simulations verify the accuracy of the proposed control scheme, which is applicable to another chaotic system based on the same design scheme.     

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.     

A note on phase synchronization in coupled chaotic fractional order systems

The dynamic behaviors of fractional order systems have received increasing attention in recent years. This paper addresses the reliable phase synchronization problem between two coupled chaotic fractional order systems. An active nonlinear feedback control scheme is constructed to achieve phase synchronization between two coupled chaotic fractional order systems. We investigated the necessary conditions for fractional order Lorenz, Lü and Rössler systems to exhibit chaotic attractor similar to their integer order counterpart. Then, based on the stability results of fractional order systems, sufficient conditions for phase synchronization of the fractional models of Lorenz, Lü and Rössler systems are derived. The synchronization scheme that is simple and global enables synchronization of fractional order chaotic systems to be achieved without the computation of the conditional Lyapunov exponents. Numerical simulations are performed to assess the performance of the presented analysis.     

Multi‐switching combination–combination synchronization of non‐identical fractional‐order chaotic systems

In this paper, multi‐switching combination–combination synchronization scheme has been investigated between a class of four non‐identical fractional‐order chaotic systems. The fractional‐order Lorenz and Chen's systems are taken as drive systems. The combination–combination of multi drive systems is then synchronized with the combination of fractional‐order Lü and Rössler chaotic systems. In multi‐switching combination–combination synchronization, the state variables of two drive systems synchronize with different state variables of two response systems simultaneously. Based on the stability of fractional‐order chaotic systems, the multi‐switching combination–combination synchronization of four fractional‐order non‐identical systems has been investigated. For the synchronization of four non‐identical fractional‐order chaotic systems, suitable controllers have been designed. Theoretical analysis and numerical results are presented to demonstrate the validity and feasibility of the applied method. Copyright © 2017 John Wiley & Sons, Ltd.     

Adaptive sliding mode control in a novel class of chaotic systems

This paper proposes a robust adaptive sliding mode control strategy for an introduced class of uncertain chaotic systems. Using the sliding mode control technique and based on Lyapunov stability theory, a time varying sliding surface is determined and an adaptive gain of the robust control law will be tuned to stabilize the new chaotic class. Unlike many well-known methods of the sliding mode control, no knowledge on the bound of uncertainty and disturbance is required. Simulation results are demonstrated for several chaotic examples to illustrate the effectiveness of the proposed adaptive sliding mode control scheme.     

Chaos synchronization between two different chaotic systems with uncertainties, external disturbances, unknown parameters and input nonlinearities

In this paper, the problem of chaos synchronization between two different uncertain chaotic systems with input nonlinearities is investigated. Both master and slave systems are perturbed by model uncertainties, external disturbances and unknown parameters. The bounds of the model uncertainties and external disturbances are assumed to be unknown in advance. First, a simple linear sliding surface is selected. Then, appropriate adaptive laws are derived to tackle the model uncertainties, external disturbances and unknown parameters. Subsequently, based on the adaptive laws and Lyapunov stability theory, a robust adaptive sliding mode control law is designed to guarantee the existence of the sliding motion. Two illustrative examples are presented to verify the usefulness and applicability of the proposed technique.