一类混沌系统的滑动模态同步控制及其应用

利用Lyapunov函数定理,设计滑动模态控制器,研究了两个相同Chen混沌系统的同步控制问题。寻找主-从Chen混沌系统满足Lyapunov稳定性理论的条件,在此基础上构造出合适的滑模控制律实现混沌系统之间的完全同步。通过数值仿真结果,证实了所设计方法的有效性和鲁棒性。结合混沌掩盖技术,将该同步方法应用于保密通信中,可以达到掩盖有用传输信号的目的,在接收端无失真地复原出发送端传送的有用信号。     

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。     

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.      

The neural sliding mode controller design of fan-plate system

This paper proposed a sliding mode angle control with neural network estimator design for a fan-plate system. The neural network estimator is based on radial basis function and it estimates the unknown lumped bounded uncertainty of parameter variations and external disturbances in real-time. The abilities of anti-disturbance and anti-chattering are better than conventional sliding mode controller and adaptive sliding mode controller. The Lyapunov stability theorem is employed to ensure the stability of the proposed controller. The convergence and signal tracking properties are better than the conventional sliding mode controller. Finally, we employed the experiment to validate the proposed method is feasible.     

一类不确定分数阶混沌系统同步的自适应滑模控制方法

针对一类系统不确定及受外界干扰的分数阶混沌系统,本文首先将分数阶微积分应用到滑模控制中,构造了一个具有分数阶积分项的滑模面.针对系统不确定及外界干扰项,基于分数阶Lyapunov稳定性理论与自适应控制方法,设计了一种滑模控制器以及分数阶次的参数自适应律,实现了两不确定分数阶混沌系统的同步控制,并辨识出相应误差系统中不确定项及外界干扰项的边界.在分数阶系统稳定性分析中使用的分数阶Lyapunov稳定性理论及相关函数都可以很好地运用到其它分数阶系统同步控制方法中.最后数值仿真验证了所提控制方法的可行性与有效性.     

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。     

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.     

分数阶混沌系统的主动滑模同步

结合主动控制和滑模控制原理,提出了一个同步分数阶混沌系统的主动滑模控制方法.该方法首先用分数阶积分对所有维状态分量设计一个滑模面,分数阶混沌系统在该滑模面上稳定.然后采用极点配置的方法获得主动滑模控制器中的增益矩阵.应用Lyapunov稳定性理论、分数阶系统稳定理论对所提的控制器的存在性和稳定性分别进行了分析.对分数阶Lorenz系统进行数值仿真,仿真结果验证了该方法的有效性.     

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。     

基于自适应模糊滑模控制的船舶航向控制器设计

针对船舶运动系统中固有的非线性、模型不确定性和风、浪、流等的干扰.提出了自适应模糊滑模控制(AFSMC)策略解决船舶的航向控制问题.通过采用模糊逻辑系统逼近系统未知函数,将滑模控制技术与自适应模糊控制技术相结合,设计了船舶航向AFSMC控制器.在滑模边界层内应用PI (proportional-integral)控制代替滑模控制中的切换项,削弱了滑模控制带来的抖振现象.借助李亚普诺夫函数证明了船舶运动系统中的信号都一致有界并利用Barbalat引理证明了跟踪误差渐近收敛到零.在参数摄动和外界干扰情况下进行了航向保持与改变仿真试验,采用AFSMC控制器得到了与无摄动和无干扰情况下相似的输出响应.实验结果表明,所提控制器能有效地处理系统不确定性和外界干扰,控制性能良好,具有很强的鲁棒性.     

A new multi-stable fractional-order four-dimensional system with self-excited and hidden chaotic attractors: Dynamic analysis and adaptive synchronization using a novel fuzzy adaptive sliding mode control method

Four-dimensional chaotic systems are a very interesting topic for researchers, given their special features. This paper presents a novel fractional-order four-dimensional chaotic system with self-excited and hidden attractors, which includes only one constant term. The proposed system presents the phenomenon of multi-stability, which means that two or more different dynamics are generated from different initial conditions. It is one of few published works in the last five years belonging to the aforementioned category. Using Lyapunov exponents, the chaotic behavior of the dynamical system is characterized, and the sensitivity of the system to initial conditions is determined. Also, systematic studies of the hidden chaotic behavior in the proposed system are performed using phase portraits and bifurcation transition diagrams. Moreover, a design technique of a new fuzzy adaptive sliding mode control (FASMC) for synchronization of the fractional-order systems has been offered. This control technique combines an adaptive regulation scheme and a fuzzy logic controller with conventional sliding mode control for the synchronization of fractional-order systems. Applying Lyapunov stability theorem, the proposed control technique ensures that the master and slave chaotic systems are synchronized in the presence of dynamic uncertainties and external disturbances. The proposed control technique not only provides high performance in the presence of the dynamic uncertainties and external disturbances, but also avoids the phenomenon of chattering. Simulation results have been presented to illustrate the effectiveness of the presented control scheme.     

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.     

Chen混沌系统的滑模同步控制方法

设计一种滑模控制器,用于实现2个相同Chen混沌系统的同步。根据主从Chen混沌系统满足Lyapunov稳定性理论的条件,设计滑模控制器,使用混沌掩盖的方法将其应用于保密通信中,以掩盖和无失真地恢复有用信号。实验结果表明,该方法具有较好的鲁棒性和较高的安全性。     

Gaussian radial basis function neural network controller of a synchronous reluctance motor in electric motorcycle applications

In this article, a sliding mode control (SMC) design based on a Gaussian radial basis function neural network (GRBFNN) is proposed for the synchronous reluctance motor (SynRM) system in electrical motorcycle applications. The conventional SMC assumes that the upper lumped boundaries of parameter variations and external disturbances are known, and the sign function is used. This causes high-frequency chattering and the high-gain phenomenon. In order to avoid these drawbacks, the proposed method utilizes the Lyapunov stability method and the steep descent rule to guarantee the convergence asymptotically, and reduce the magnitude of the chattering or avoid it completely. Finally, numerical simulations are shown to illustrate the good performance of our controller design.     

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.     

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.     

一类不确定系统的自适应非奇异Terminal滑模控制

提出针对一类不确定系统的自适应非奇异Terminal滑模控制。确定含非线性项的滑模面,通过构造李亚普洛夫函数的方式确定控制器结构,设计自适应增益控制律实时估计不确定参数,并考虑外扰动的影响,证明控制系统的稳定性和鲁棒性。仿真结果验证自适应非奇异Terminal滑模控制器能够使不确定系统状态变量快速收敛。     

一种新的模糊滑模控制器设计方法

针对具有较大且不可观测外界干扰的一类不确定系统,提出一种新的模糊滑模控制器设计方法.首先基于模糊滑模控制原理,引入全局快速终端滑模控制,使系统在有限时间内达到稳态;然后构造以李雅普诺夫函数导数的绝对值为补偿的自适应干扰估计项,对外界干扰进行准确估计,进而提出一种双层递阶指数趋近全局快速终端模糊滑模控制器,通过指数趋近率来调节滑模面的动态品质,该控制器能快速收敛到稳定状态,且有效消除控制器的抖振情况;最后通过仿真算例验证所提方法的有效性.     

Hybrid control of synchronization of fractional order nonlinear systems

Under the existence of model uncertainties and external disturbance, finite‐time projective synchronization between two identical complex and two identical real fractional‐order (FO) chaotic systems are achieved by employing FO sliding mode control approach. In this paper, to ensure the occurrence of synchronization and asymptotic stability of the proposed methods, a sliding surface is designed and the Lyapunov direct method is used. By using integer and FO derivatives of a Lyapunov function, three different FO real and complex control laws are derived. A hybrid controller based on a switching law is designed. Its behavior is more efficient that if the individual controllers were designed based on the minimization of an appropriate cost function. Numerical simulations are implemented for verifying the effectiveness of the methods.     

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...