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.     

参数未知的永磁同步电机混沌系统模糊自适应同步控制

提出了一种参数未知的永磁同步电机(PMSM)系统的模糊自适应同步控制方法.首先通过放射变换和时间尺度变换,将转子磁场定向坐标系下的PMSM模型,变换成无量纲模型.其次通过分析其相图和Lyapunov指数谱,阐述了PMSM的混沌动态行为.接着,在假设PMSM系统参数未知并将PMSM混沌模型及其响应系统模型表示成T-S模糊模型的基础上,利用Lyapunov稳定性理论和自适应控制策略设计了响应系统,并导出了自适应控制律来估计驱动系统参数.此外,设计了响应系统的模糊控制器,对PMSM系统及其响应系统进行同步控制,并证明了同步误差动态是渐近稳定的.最后,仿真结果验证了该方法的有效性.     

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。     

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.     

新混沌系统及其分数阶系统的自适应同步控制

研究一个存在共存吸引子的混沌系统及相应的分数阶系统的自适应同步问题.首先,提出了一个新的具有双翼和四翼吸引子共存的混沌系统,对系统的动力学特性进行了分析,找到了系统的拓扑马蹄和拓扑熵,从而验证了系统具有混沌特性;然后,根据该系统构建了一个亦存在两个孤立的双翼吸引子以及四翼吸引子的分数阶系统.最后,采用分数阶Lyapunov稳定性理论以及自适应控制方法,对分数阶系统的自适应同步问题进行了研究.仿真结果表明,控制参数k越大,系统同步速度越快;控制参数λ越大,系统参数识别的速度越快.     

Robust adaptive fuzzy control of unknown chaotic systems

This paper presents a robust adaptive fuzzy control algorithm for controlling unknown chaotic systems. The control approach encompasses a fuzzy system and a robust controller. The fuzzy system is designed to mimic an ideal controller, based on sliding-mode control. The robust controller is designed to compensate for the difference between the fuzzy controller and the ideal controller. The parameters of the fuzzy system, as well as uncertainty bound of the robust controller, are tuned adaptively. The adaptive laws are derived in the Lyapunov sense to guarantee the stability of the controlled system. Numerical simulations show the effectiveness of the proposed approach.     

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.     

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.     

具有未知参数的不确定分数阶Sprott-C系统的Terminal滑模同步

基于滑模控制的优良性能,探讨了利用Terminal滑模控制实现分数阶混沌系统的有限时间同步问题,给出了滑模控制实现具有未知参数和扰动的分数阶Sprott-C驱动—响应系统(阶数0<α<1)的同步结论。通过构造合适的滑动模态曲面,针对系统未知参数上界已知和未知两种情况,设计了合适的分数阶控制器和参数自适应率,结合分数阶微分方程相关理论和有限时间稳定性定理,证明了实现该系统的同步控制结论,并对未知参数和扰动上界进行了准确估计。最后选取适当参数,通过数值仿真,验证了所给结论的有效性和可行性。     

基于自适应控制的八个混沌系统的多级组合同步

针对传统的混沌系统结构样式单一和系统变量少的问题,设计了一种混沌电路系统,该电路有较为复杂的动力学行为、较高的敏感性和较强的抗干扰性。随着电路参数的变化,结合自适应稳定性判据和混沌运动理论详细分析了该系统的不同动力学行为;此外,根据电路图搭建了相应的电路并利用示波器观察该电路的动力学行为,其行为与MATLAB的仿真结果相一致,进一步证明了电路的可行性和灵活性。在此基础上,重点提出并研究了基于本系统的多级组合同步,通过构造不同的控制器实现了八个系统之间的多级组合同步。仿真结果表明,该同步方案在收敛速度和精度上具有很好的效果。     

一个混沌系统的同步控制研究

研究了一个混沌系统的混沌同步控制问题。分别采用线性反馈控制方法、非线性反馈方法、脉冲控制方法对该混沌系统进行同步控制。基于Lyapunov稳定性理论和脉冲控制技术,对同步的充分条件进行了讨论,并给出了相应的理论证明。数值仿真证明了这三种不同方法的有效性。     

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.     

Distributed adaptive control for synchronization of unknown nonlinear networked systems

This paper is concerned with synchronization of distributed node dynamics to a prescribed target or control node dynamics. A design method is presented for adaptive synchronization controllers for distributed systems having non-identical unknown nonlinear dynamics, and for a target dynamics to be tracked that is also nonlinear and unknown. The development is for strongly connected digraph communication structures. A Lyapunov technique is presented for designing a robust adaptive synchronization control protocol. The proper selection of the Lyapunov function is the key to ensuring that the resulting control laws thus found are implementable in a distributed fashion. Lyapunov functions are defined in terms of a local neighborhood tracking synchronization error and the Frobenius norm. The resulting protocol consists of a linear protocol and a nonlinear control term with adaptive update law at each node. Singular value analysis is used. It is shown that the singular values of certain key matrices are intimately related to structural properties of the graph.     

参数自适应控制的混沌同步研究

在对同步系统特性分析的基础上,利用参数自适应控制混沌原理,提出了一种混沌系统在不同系统参数下的混沌同步方法.在参数自适应控制方程中,采用了分段控制与非线性反馈控制相结合的控制函数.通过选取合适的控制律和控制参数可以实现不同系统参数的两个 logistic映射的混沌同步.基于 Matlab软件的数值仿真的结果表明该方法是控制离散混沌系统同步化的一种快速有效的方法.     

统一混沌系统的自适应控制同步

基于Pecora-Carroll混沌同步原理和参数自适应控制策略,提出一种单参数统一混沌系统的自适应同步控制方法;推导出实现不同参数、不同初值的两统一混沌系统同步的参数自适应控制律和同步条件;研究了确定控制常数边界和范围的方法,并讨论了控制常数对同步性能的影响.理论分析和数值仿真表明,选择合适的控制常数,可实现两统一混沌系统的大范围渐近稳定同步.     

Neural network-based synchronization of uncertain chaotic systems with unknown states

In this paper, synchronization of chaotic systems with unknown parameters and unmeasured states is investigated. Two nonidentical chaotic systems in the framework of a master and a slave are considered for synchronization. It is assumed that both systems have uncertain dynamics, and states of the slave system are not measured. To tackle this challenging synchronization problem, a novel neural network-based adaptive observer and an adaptive controller have been designed. Moreover, a neural network is utilized to approximate the unknown dynamics of the slave system. The proposed method imposes neither restrictive assumption nor constraint on the dynamics of the systems. Furthermore, the stability of the entire closed-loop system in the presence of the observer dynamics has been established. Finally, effectiveness of the proposed scheme is demonstrated via computer simulation.     

Decoupled adaptive neuro-fuzzy (DANF) sliding mode control system for a Lorenz chaotic problem

This paper introduces a decoupled adaptive neuro-fuzzy (DANF) sliding mode control system for the chaos control problem in a system without precise system model information. It has on-line learning ability to deal with the parametric uncertainty and disturbance by adjusting the control parameters and no constrained conditions and prior knowledge of the controlled plant is required in the design process. Also, a decoupled adaptive sliding mode controller is developed to control the chaotic Lorenz system for comparison. Finally, the effectiveness of the proposed decoupled adaptive sliding mode and DANF sliding mode controllers are demonstrated by some simulated results.     

单喷泵无人滑行艇航向的反步自适应滑模控制

针对单泵喷水推进型无人滑行艇航向跟踪的非线性系统控制问题,对无人滑行艇的运动稳定性分析表明,其具有水平面内的自动稳定性.考虑建模误差和外界干扰力影响下的滑行艇运动响应模型,基于backstepping方法和滑模控制理论,提出了一种自适应滑模控制律.利用Lyapunov函数,证明该控制律保证了航向跟踪系统的全局渐近稳定性.仿真对比结果验证了所提出控制器的有效性.     

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.