Controlling and synchronizing spatiotemporal chaos of the coupled Bragg acousto-optical bistable map system using nonlinear feedback

In this paper we present the control and synchronization of a coupled Bragg acousto-optic bistable map system using nonlinear feedback technology. This nonlinear feedback technology is useful to control a temporally chaotic system as well as a spatiotemporally chaotic system. It can be extended to synchronize the spatiotemporal chaos. It can work in a wide range of the controlled and synchronized signals, so it can decrease the sensitivity down to a noise level. The synchronization can be obtained by the analysis of the largest conditional Lyapunov exponent spectrum, and easily implemented in practical systems just by adjusting the coupled strength without any pre-knowledge of the dynamic system required.

Synchronizing spatiotemporal chaos in the coupled map lattices using nonlinear feedback functions

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Controlof Orbitand Controlof Chaosina Class of Dynamic System

The problem of control of orbit for the dynamic system x ¨+x(1-x)(x-a)=0 is discussed. Any unbounded orbit of the dynamic system can be controlled to become a bounded periodic orbit by adding a periodic step excitation to the system. By using a nonlinear feedback control law presented in this paper the chaos of the dynamic system with excitation and damping is stabilized. This method is more effectual than the linear feedback control.

Control Chaos in System with Fractional Order

In this paper, by utilizing the fractional calculus theory and computer simulations, dynamics of the fractional order system is studied. Further, we have extended the nonlinear feedback control in ODE systems to fractional order systems, in order to eliminate the chaotic behavior. The results are proved analytically by stability condition for fractional order system. Moreover numerical simulations are shown to verify the effectiveness of the proposed control scheme.

Chaos synchronization between two different 4D hyperchaotic Chen systems

This paper presents chaos synchronization between two different four-dimensional （4D） hyperchaotic Chen systems by nonlinear feedback control laws. A modified 4D hyperchaotic Chen system is obtained by changing the nonlinear function of the 4D hyperchaotic Chen system, furthermore, an electronic circuit to realize two different 4D hyperchaotic Chen systems is designed. With nonlinear feedback control method, chaos synchronization between two different 4D hyperchaotic Chen systems is achieved. Based on the stability theory~ the functions of the nonlinear feedback control for synchronization of two different 4D hyperchaotic Chen systems is derived, the range of feedback gains is determined. Numerical simulations are shown to verify the theoretical results.

Chaos and Nonlinear Feedback Control of the Arch Micro-Electro-Mechanical System

This paper addresses a nonlinear feedback control problem for the chaotic arch micro- electro-mechanical system with unknown parameters,immeasurable states and partial state-constraint subjected to the distributed electrostatic actuation.To reflect inherent properties and design controller, the phase diagrams,bifurcation diagram and Poincare section are presented to investigate the nonlinear dynamics.The authors employ a symmetric barrier Lyapunov function to prevent violation of constraint when the arch micro-electro-mechanical system faces some limits.An RBF neural network system integrating with an update law is adopted to estimate unknown function with arbitrarily small error. To eliminate chaotic oscillation,a neuro-adaptive backstepping control scheme fused with an extended state tracking differentiator and an observer is constructed to lower requirements on measured states and precise system model.Besides,introducing an extended state tracking differentiator avoids repeated derivative for the virtual control signal associated with conventional backstepping.Finally,simulation results are presented to illustrate feasibility of the proposed scheme.

Nonlinear feedback control of a novel hyperchaotic system and its circuit implementation

This paper reports a new hyperchaotic system by adding an additional state variable into a three-dimensional chaotic dynamical system. Some of its basic dynamical properties, such as the hyperchaotic attractor, Lyapunov expo- nents, bifurcation diagram and the hyperchaotic attractor evolving into periodic, quasi-periodic dynamical behaviours by varying parameter k are studied. An effective nonlinear feedback control method is used to suppress hyperchaos to unstable equilibrium. Furthermore, a circuit is designed to realize this new hyperchaotic system by electronic workbench （EWB）. Numerical simulations are presented to show these results.

Nonlinear feedback synchronisation control between fractional-order and integer-order chaotic systems

This paper focuses on the synchronisation between fractional-order and integer-order chaotic systems. Based on Lyapunov stability theory and numerical differentiation, a nonlinear feedback controller is obtained to achieve the synchronisation between fractional-order and integer-order chaotic systems. Numerical simulation results are presented to illustrate the effectiveness of this method.

CONTROLLING CHAOTIC OSCILLATIONS OF VISCO-ELASTIC PLATESBY THE LINEARIZATION VIA OUTPUTFEEDBACK

Controlling chaotic oscillations of viscoelastic plates are investigated in this paper. Based on the exact linearization method in nonlinear system control theory, a nonlinear feedback control law is presented for a class of non_affine control systems. The mathematical model describing motion of nonlinear viscoelastic plates is established, and it is simplified by the Galerkin method. The phase space portrait and the power spectrum are employed to demonstrate chaos in the system. The deflection is treated as an output, and is controlled to given periodic goals.

Robust Output Feedback Control for Fractional Order Nonlinear Systems with Time-varying Delays

Robust controller design problem is investigated for a class of fractional order nonlinear systems with time varying delays. Firstly, a reduced-order observer is designed. Then, an output feedback controller is designed. Both the designed observer and controller are independent of time delays. By choosing appropriate Lyapunov functions, we prove the designed controller can render the fractional order system asymptotically stable. A simulation example is given to verify the effectiveness of the proposed approach. © 2014 Chinese Association of Automation.

State Feedback Control for a Class of Fractional Order Nonlinear Systems

Using the Lyapunov function method, this paper investigates the design of state feedback stabilization controllers for fractional order nonlinear systems in triangular form, and presents a number of new results. First, some new properties of Caputo fractional derivative are presented, and a sufficient condition of asymptotical stability for fractional order nonlinear systems is obtained based on the new properties. Then, by introducing appropriate transformations of coordinates, the problem of controller design is converted into the problem of finding some parameters, which can be certainly obtained by solving the Lyapunov equation and relevant matrix inequalities. Finally, based on the Lyapunov function method, state feedback stabilization controllers making the closed-loop system asymptotically stable are explicitly constructed. A simulation example is given to demonstrate the effectiveness of the proposed design procedure. © 2014 Chinese Association of Automation.

Fuzzy Adaptive Control of a Fractional Order Chaotic System With Unknown Control Gain Sign Using a Fractional Order Nussbaum Gain

In this paper we propose an improved fuzzy adaptive control strategy, for a class of nonlinear chaotic fractional order(SISO) systems with unknown control gain sign. The online control algorithm uses fuzzy logic sets for the identification of the fractional order chaotic system, whereas the lack of a priori knowledge on the control directions is solved by introducing a fractional order Nussbaum gain. Based on Lyapunov stability theorem, stability analysis is performed for the proposed control method for an acceptable synchronization error level. In this work, the Gr ¨unwald-Letnikov method is used for numerical approximation of the fractional order systems. A simulation example is given to illustrate the effectiveness of the proposed control scheme.

Robust H_∞ control of piecewise-linear chaotic systems with random data loss

This paper studies the problem of robust H∞ control of piecewise-linear chaotic systems with random data loss. The communication links between the plant and the controller are assumed to be imperfect （that is, data loss occurs intermittently, which appears typically in a network environment）. The data loss is modelled as a random process which obeys a Bernoulli distribution. In the face of random data loss, a piecewise controller is designed to robustly stabilize the networked system in the sense of mean square and also achieve a prescribed H∞ disturbance attenuation performance based on a piecewise-quadratic Lyapunov function. The required H∞ controllers can be designed by solving a set of linear matrix inequalities （LMIs）. Chua＇s system is provided to illustrate the usefulness and applicability of the developed theoretical results.

Robust output-feedback stabilization of a class of nonlinear systems with the nonlinearities of varied form

The back-stepping designs based on confine functions are suggested for the robust output-feedback global stabilization of a class of nonlinear continuous systems; the proposed stabilizer is efficient for the nonlinear continuous systems confined by a bound function, the nonlinearities of the systems may be of varied forms or uncertain; the designed stabilizer is robust means that a class of nonlinear continuous systems can be stabilized by the same output feedback stabilization schemes; numerical simulation examples are given.

LMI Based Synchronization Control of Nonlinear Affine Fractional Order Chaotic Systems Considering Input Constraint

The current paper deals with synchronization problem among chaotic nonlinear fractional order systems considering input saturation constraint.To develop the idea,at first a generalized sector condition and a memory-less nonlinear function are employed to deal with the saturation problem.Then a new state feedback controller is designed to achieve synchronization in master-slave chaotic fractional order nonlinear systems with input saturation.Using the state feedback controller,the asymptotic stability of whole dynamic error model between master and slave is achieved.The stability of the closed-loop system is guaranteed using Lyapunov theory and sufficient stability conditions are formulated in terms of caputo fractional derivative of a quadratic Lyapunov function and Linear Matrix Inequalities(LMI).Finally,to verify the effectiveness of the proposed control scheme,some simulation results are employed to show the effectiveness of the proposed methodology.

输入饱和约束下自适应RBF神经网络非线性反馈船舶航向控制

针对输入饱和约束下外界扰动和模型不确定情况下的船舶航向跟踪控制问题,提出一种自适应径向基函数(radial basis function,RBF)神经网络非线性反馈航向跟踪控制方法。利用自适应RBF神经网络对外界扰动和模型不确定项进行估计,并利用最小学习参数法减少计算量;将一个具有误差增益反相关特征的非线性函数嵌入控制律中,设计一种非线性反馈控制方法;利用李雅普诺夫理论证明所有信号在考虑外界扰动和模型不确定的船舶航向跟踪控制系统中都是一致有界的。通过仿真和比较,验证了所设计控制方法的有效性。所做研究可为输入饱和约束下船舶航向跟踪控制提供参考,具有工程实际意义。

基于全驱系统方法的高阶严反馈系统时变输出约束控制

针对输出受不对称时变约束的不确定高阶严反馈系统,提出一种基于全驱系统方法的高阶自适应动态面输出约束控制方法.所研究的高阶严反馈系统,每个子系统都是高阶形式,通过非线性转换函数将原输出约束系统转换为新的无约束系统,从而将原系统输出约束问题转化为新系统输出有界的问题.进一步结合全驱系统方法和自适应动态面控制,直接将每个高阶子系统作为一个整体进行控制器设计,而不需要将其转化为一阶系统形式,有效简化了设计步骤;同时通过引入一系列低通滤波器来获得虚拟控制律的高阶导数,以代替复杂的微分运算.基于Lyapunov稳定性理论证明闭环系统所有信号是一致最终有界的,系统输出在满足约束的条件下能有效跟踪期望的参考信号,且可通过调整参数使得系统跟踪误差收敛到零附近的足够小的邻域内.最后,通过对柔性关节机械臂系统进行仿真,验证了所提出控制方法的有效性.

三相电压型PWM整流器的自抗扰控制研究

三相电压型PWM整流器是一个多输入多输出的强非线性结构,并对三相电压型PWM整流器的数学模型和自抗扰控制器进行了原理分析;为了改善整流系统抗扰性及参数摄动等问题,采用一种改进型的非线性自抗扰控制方案,同时给出了离散形式的表达式;然后,重新构造了常规自抗扰控制器中非线性状态误差反馈控制律(NLSEF)和扩张状态观测器(ESO)的非线性函数,以此来克服非线性函数的不平滑性能,从而减小整流系统输出的高频颤振现象;在MATLAB/Simulink环境下进行仿真和搭建了实验样机来验证,改进型自抗扰控制器与常规自抗扰控制器进行对比分析。结果表明了改进型自抗扰控制策略改善了交流侧电压和负载突变敏感的缺点,并降低了交流侧电流总谐波含量,且直流侧电压具有更好的动静态性和鲁棒性。

基于Cubic映射混合粒子蝴蝶优化算法

针对传统蝴蝶优化算法BOA具有搜索能力强、收敛速度快的特点,以及平衡局部和全局搜索不足、易陷入局部最优和泛化不足等问题,提出基于Cubic映射混合粒子蝴蝶优化算法(Cubic Admix Particle Butterfly Optimization Algorithm,CAPBOA)。先引入Cubic映射用来初始化蝴蝶位置,提高蝴蝶优化算法整体搜索能力,再利用粒子群算法增加算法的局部和全局搜索能力以及收敛速度,最后加入非线性控制策略来优化蝴蝶香味计算公式,用来平衡算法的全局和局部搜索。将CAPBOA算法与普通BOA算法、目前已有的BOA优化算法以及同类智能算法进行仿真对比,在不同测试函数下,通过仿真,进行最优收敛值、平均收敛值、方差、标准差、曲线收敛和摆脱局部极值对比,从而评价算法的性能,仿真证明CAPBOA算法具有快速寻优、收敛快、避免算法陷入局部极值和泛化能力较好的优点。