Control and synchronization of chaotic systems using a novel indirect model reference fuzzy controller

This paper presents a robust indirect model reference fuzzy control scheme for control and synchronization of chaotic nonlinear systems subject to uncertainties and external disturbances. The chaotic system with disturbance is modeled as a Takagi–Sugeno fuzzy system. Using a Lyapunov function, stable adaptation laws for the estimation of the parameters of the Takagi–Sugeno fuzzy model are derived as well as what the control signal should be to compensate for the uncertainties. The synchronization of chaotic systems is also considered in the paper. It is shown that by the use of an appropriate reference signal, it is possible to make the reference model follow the master chaotic system. Then, using the proposed model reference fuzzy controller, it is possible to force the slave to act as the reference system. In this way, the chaotic master and the slave systems are synchronized. It is shown that not only can the initial values of the master and the slave be different, but also there can be parametric differences between them. The proposed control scheme is simulated on the control and the synchronization of Duffing oscillators and Genesio–Tesi systems.     

调整一类部分线性混沌系统输出的实用方案

利用部分线性混沌系统耦合后内在的投影同步性质对耦合响应系统的状态输出进行反馈控制，得到与驱动系统相位一致(或反相)，振幅成比例的混沌输出信号。该方案所需控制代价较小，为设计任意功率输出的混沌信号源提供了理论依据，在利用混沌电路系统进行保密通信方面有着极大的应用前景；仿真实例进一步表明了控制方案的有效性。     

An Adaptive Control Technique for Motion Synchronization by On-line Estimation of a Recursive Least Square Method

This article presents an adaptive technique to tune controller gains for the motion synchronization of two gimbal systems by using a recursive least square method in the real-time fashion. In the master-slave configuration, the slave gimbal system follows the master’s motion while the master tracks the reference. In order for the slave gimbal system to synchronize with the motion of the master gimbal system, the dynamic difference between two systems is compensated by the controller gains. The controller gains of the slave are adaptively adjusted by the recursive least square method to cope with the deviation. The performances of three control schemes such as an independent PD control, a dependent torque control, and an RLS torque control scheme are evaluated by the experimental studies for the low cost gimbal systems. Experimental studies confirm that the RLS-based adaptive scheme actually outperforms by adjusting controller gains for the motion synchronization of the master and slave configuration.     

Position-Based Fuzzy Force Control for Dual Industrial Robots

In this paper, a fuzzy force control framework is proposed for dual-industrial robot systems. The master/slave control method is used in dual-robot systems. Two MITSUBISHI MELFA RV-M1 industrial robots, one is equipped with an BL Force/Torque sensor and the other is not, are utilized for implementing the dual-arm system. In order to adapt various stiffness of the holding object, an adaptable fuzzy force control scheme has been proposed to improve the performance. The ability of the adaptable force control system is achieved by tuning the scaling factor of the fuzzy logic controller. Successful experiments are carried out for the dual-robot system handling an object.     

不确定Van der Pol混沌系统的模糊同步控制

本文研究了不确定Van der Pol混沌系统的同步问题,并进行了基于规则的模糊逻辑控制器(FLC)的控制。首先寻找主从Van der Pol混沌系统满足Lyapunov稳定性理论的条件,在此基础上建立模糊规则,设计模糊控制器,实现不确定混沌系统的同步。通过不确定VanderPol混沌系统的两组仿真结果,验证了模糊同步控制方法具有很好的鲁棒性。最后为了进一步验证该方法的有效性,本文在相同条件下,利用反馈控制的方法实现不确定主从VanderPol混沌系统的同步,然后再将此方法的仿真结果与本文的模糊同步控制方法的仿真结果在稳态误差及同步所需时间这两个方面进行对比分析。分析结果验证了本文同步方法的可行性及有效性。     

基于模糊观测器混沌系统的广义投影同步

基于混沌系统的T-S模糊模型，提出了混沌系统广义投影同步问题的控制方法。该方法利用线性矩阵不等式技术，把混沌系统的广义投影同步问题设计为模糊状态观测器设计问题，用Matlab软件包可以很容易对线性矩阵不等式求解。该方法可以通过适当选取控制增益对响应系统的动力学比例尺度任意拉伸或压缩。通过对Lorenz系统的数值模拟，表明了该方法的有效性。     

Neural network-based Smith predictor design for the time-delay in a tele-operated control system

This article presents a methodology for compensating for the time-delay effects in tele-operated control systems. Compensation can be carried out by a neural network. A tele-operated system consists of a master robot to give commands, and a slave robot to work with the environment. The positional command by the master robot is transferred to the slave robot, and the contact force from the environment is transferred back to the master robot. The structure of the Smith predictor is modified by replacing the linear estimator with a neural network whose structure is based on the radial basis function (RBF). The RBF network identifies the slave model to deal with the nonlinearities in the system. Simulation studies have been conducted, and experimental studies of one-directional force control were performed to confirm the simulation results.     

Robust synchronization of chaotic systems using slidingmode and feedback control

We propose a robust scheme to achieve the synchronization of chaotic systems with modeling mismatches and parametric variations. The proposed algorithm combines high-order sliding mode and feedback control. The sliding mode is used to estimate the synchronization error between the master and the slave as well as its time derivatives, while feedback control is used to drive the slave track the master. The stability of the proposed design is proved theoretically, and its performance is verified by some numerical simulations. Compared with some existing synchronization algorithms, the proposed algorithm shows faster convergence and stronger robustness to system uncertainties.     

Integrated adaptive robust control for multilateral teleoperation systems under arbitrary time delays

With the increasing industrial requirements such as bigger size object, stable operation, and complex task, multilateral teleoperation systems extended from traditional bilateral teleoperation are widely developed. In this paper, the integrated control design is developed for multilateral teleoperation systems, where n master manipulators are operated by human to remotely control n slave manipulators cooperatively handling a target object. For the first time, the control objectives of multilateral teleoperation including stability, synchronization, transparency, and internal force distribution are clarified systematically. A novel communication architecture is proposed to cope with communication delays, where the estimated environmental parameters are transmitted from the slave side to the master, to replace the traditional environmental force measurement in the communication channel. A kind of nonlinear adaptive robust control technique is used to deal with nonlinearities, unknown parameters, and modeling uncertainties existing in the master, slave, and environmental dynamics, so that the excellent tracking performance is achieved in both master and slave sides. The coordinated motion/force control is designed in the slave side by the optimal internal force distribution among n slave manipulators, and the impedance control is designed in the master side to realize the target transparency behavior. In summary, the proposed control algorithm can achieve the guaranteed robust stability, the excellent synchronization and transparency performance, and the optimal internal force distribution simultaneously for multilateral teleoperation systems under arbitrary time delays and various modeling uncertainties. The simulation is carried out on a 2‐master/2‐slave teleoperation system, and the results show the effectiveness of the proposed control design. Copyright © 2015 John Wiley & Sons, Ltd.     

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.     

Intelligent fuzzy controller for chaos synchronization of uncertain fractional-order chaotic systems with input nonlinearities

In this research work, a novel fuzzy adaptive control is proposed to achieve a projective synchronization for a class of fractional-order chaotic systems with input nonlinearities (dead-zone together with sector nonlinearities). These master-slave systems under consideration are supposed to be with distinct models, different fractional-orders, unknown models, and dynamic external disturbances. The proposed control law consists of two main terms, namely: a fuzzy adaptive control term for appropriately approximating the uncertainties and a fractional-order variable-structure control term for robustly dealing with these inherent input nonlinearities. A Lyapunov approach is used to derive the updated laws and to prove the stability of the closed-loop control system. At last, a set of computer simulation results is carried out to illustrate and further validate the theoretical findings.     

Adaptive sliding mode observer‐based synchronization for uncertain chaotic systems

This paper investigates the synchronization problem for a class of uncertain chaotic systems. Only partial information of the system states is known. An adaptive sliding mode observer‐based slave system is designed to synchronize a given chaotic master system with unknown parameters and external disturbances. Based on the Lyapunov stability theorem, the global synchronization between the master and slave systems is ensured. Furthermore, the structure of the slave system is simple and the proposed adaptive sliding mode observer‐based synchronization scheme can be implemented without requiring a priori knowledge of upper bounds on the norm of the uncertainties and external disturbances. Simulation results demonstrate the effectiveness and robustness of the proposed scheme. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Generalized projective synchronization of uncertain chaotic systems with external disturbance

This paper proposes the generalized projective synchronization (GPS) of uncertain chaotic systems with external disturbance via Gaussian radial basis adaptive sliding mode control (GRBASMC). A sliding surface is adopted to ensure the stability of the error dynamics in sliding mode control. In the neural sliding mode controller, a Gaussian radial basis function is utilized to online estimate the system dynamic function. The adaptation law of the control system is derived in the sense of Lyapunov function, thus the system can be guaranteed to be asymptotically stable.The proposed method allows us to arbitrarily adjust the desired scaling by controlling the slave system. It is not necessary to calculate the Lyapunov exponents and the eigen values of the Jacobian matrix, which makes it simple and convenient. Also, it is a systematic procedure for GPS of chaotic systems and it can be applied to a variety of chaotic systems no matter whether it contains external excitation or not. Note that it needs only one controller to realize GPS no matter how much dimensions the chaotic system contains and the controller is easy to be implemented.The proposed method is applied to three chaotic systems: Genesio system, Lur’e like system and Duffing system.     

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.     

不同阶混沌系统广义混合错位函数投影同步及在保密通信中的应用

为进一步提高保密通信的安全性,应用Lyapunov稳定性理论以及自适应控制方法,在广义混合错位投影同步与函数投影同步的基础上提出了广义混合错位函数投影同步(GHDFPS),给出了不同阶参数不确定混沌系统的广义混合错位函数投影同步与参数辨识的控制方法,并研究该同步类型在保密通信中的应用。通过严格的数学证明和数值仿真,不同阶参数不确定混沌系统实现了广义混合错位函数投影同步,辨识出了不确定参数。由于广义混合错位函数投影同步中的函数比例因子矩阵的多样性,使该同步类型应用在保密通信中更具有安全性;同时,将此同步类型和实现该同步的控制方法用于混沌掩饰调制保密通信中,将能解调出多个信号,并能检验信号的真实性。     

Synchronization of A Class of Uncertain Chaotic Systems with Lipschitz Nonlinearities Using State‐Feedback Control Design: A Matrix Inequality Approach

This paper proposes a new state‐feedback stabilization control technique for a class of uncertain chaotic systems with Lipschitz nonlinearity conditions. Based on Lyapunov stabilization theory and the linear matrix inequality (LMI) scheme, a new sufficient condition formulated in the form of LMIs is created for the chaos synchronization of chaotic systems with parametric uncertainties and external disturbances on the slave system. Using Barbalat's lemma, the suggested approach guarantees that the slave system synchronizes to the master system at an asymptotical convergence rate. Meanwhile, a criterion to find the proper feedback gain vector F is also provided. A new continuous‐bounded nonlinear function is introduced to cope with the disturbances and uncertainties and obtain a desired control performance, i.e. small steady‐state error and fast settling time. Several criteria are derived to guarantee the asymptotic and robust stability of the uncertain master–slave systems. Furthermore, the proposed controller is independent of the order of the system's model. Numerical simulation results are displayed with an expected satisfactory performance compared to the available methods.     

Exponential Lag Synchronization of Memristive Neural Networks with Reaction Diffusion Terms via Neural Activation Function Control and Fuzzy Model

This paper is concerned with the problem of exponential lag synchronization of memristive neural networks with reaction diffusion terms via neural activation function control and fuzzy model. An memristor‐based circuit which exhibits the feature of pinched hysteresis is introduced and further, the memristive neural networks with reaction diffusion terms and such system containing fuzzy model are described at length, respectively. By utilizing the Lyapunov functional method and the neural activation function controller depending on the output of the system in the case of packed circuits, some concise conditions are acquired to guarantee the slave systems exponential lag synchronized with the master systems. Finally, several simulated examples are also presented to demonstrate the correctness of the theoretical results.     

Projective synchronization of two different fractional-order chaotic systems via adaptive fuzzy control

In this paper, the projective synchronization problem of two fractional-order different chaotic (or hyperchaotic) systems with both uncertain dynamics and external disturbances is considered. More particularly, a fuzzy adaptive control system is investigated for achieving an appropriate projective synchronization of unknown fractional-order chaotic systems. The adaptive fuzzy logic systems are used to approximate some uncertain nonlinear functions appearing in the system model. These latter are augmented by a robust control term to compensate for the unavoidable fuzzy approximation errors and external disturbances as well as residual error due to the use of the so-called e-modification in the adaptive laws. A Lyapunov approach is adopted for the design of the parameter adaptation laws and the proof of the corresponding stability as well as the asymptotic convergence of the underlying synchronization errors towards zero. The effectiveness of the proposed synchronization system is illustrated through numerical experiment results.     

预估控制下的实时网络遥操作移动机器人

构建了能使操作者通过Internet远程实时控制的移动机器人系统．为了补偿网络时延和抵消其对遥操作系统的影响，基于我们以前提出的改进型Smith预估器原理，采用了预估控制策略．为了保证系统稳定性和透明性，基于主从端的传感器信息交换，设计了一个动态模型管理器，其中模型和力反馈误差调节通过模糊控制实现．除了力反馈外，为了增强遥操作的实时性，引入了预估的虚拟显示．为了精确地预测网络时延，提出了一个新颖的时钟同步算法．为了降低时延抖动，结合我们提出的两个算法，实现了数据缓冲策略．最后，通过长距离的网络遥操作实验验证了系统和控制策略的实用性和有效性．     

Synchronization of two different chaotic systems using Legendre polynomials with applications in secure communications

In this study, a new controller for chaos synchronization is proposed. It consists of a state feedback controller and a robust control term using Legendre polynomials to compensate for uncertainties. The truncation error is also considered. Due to the orthogonal functions theorem, Legendre polynomials can approximate nonlinear functions with arbitrarily small approximation errors. As a result, they can replace fuzzy systems and neural networks to estimate and compensate for uncertainties in control systems. Legendre polynomials have fewer tuning parameters than fuzzy systems and neural networks. Thus, their tuning process is simpler. Similar to the parameters of fuzzy systems, Legendre coefficients are estimated online using the adaptation rule obtained from the stability analysis. It is assumed that the master and slave systems are the Lorenz and Chen chaotic systems, respectively. In secure communication systems, observer-based synchronization is required since only one state variable of the master system is sent through the channel. The use of observer-based synchronization to obtain other state variables is discussed. Simulation results reveal the effectiveness of the proposed approach. A comparison with a fuzzy sliding mode controller shows that the proposed controller provides a superior transient response. The problem of secure communications is explained and the controller performance in secure communications is examined.