Decentralized adaptive controller for synchronization of nonlinear dynamical heterogeneous networks

For a network of interconnected nonlinear dynamical systems, an adaptive leader–follower output feedback synchronization problem is considered. The proposed structure of decentralized controller and adaptation algorithm is based on speed gradient and passivity. Sufficient conditions of synchronization for one class of heterogeneous networks are established. An example of synchronization of the network of nonidentical Chua systems is analyzed. The main contribution of the paper is adaptive controller design and analysis under conditions of incomplete measurements, incomplete control, and uncertainty. Copyright © 2012 John Wiley & Sons, Ltd.     

Impulsive adaptive pinning synchronization of Lur'e networks with cluster-tree topology via parameters variation protocols

This article is devoted to studying the problem of globally and exponentially adaptive cluster synchronization for a class of Lur'e dynamical networks with multiple time-varying delays and hybrid couplings. A novel impulsive adaptive pinning feedback control protocol is proposed with fully considering the cluster-tree topology structures of the networks and only imposed on the Lur'e systems in current cluster which exist directed paths with those Lur'e systems in the other clusters. In view of the concept of average impulsive interval, the comparison principle, the extended parameter variation methods, and the reductio ad absurdum, sufficient conditions are acquired for achieving the cluster synchronization of the derivative coupled Lur'e networks with considering different functions of the impulsive effects, respectively. Furthermore, according to the designed adaptive updating law, suitable feedback control strengths are obtained, which largely save the control costs. Finally, the effectiveness of the control schemes and the theoretical results have been proved by executing two numerical simulation examples.     

Adaptive function Q‐S synchronization of chaotic systems with unknown parameters

This work investigates the adaptive function Q‐S synchronization of non‐identical chaotic systems with unknown parameters. The sufficient conditions for achieving Q‐S synchronization with a desired scaling function of two different chaotic systems (including different dimensional systems) are derived based on the Lyapunov stability theory. By the adaptive control technique, the control laws and the corresponding parameter update laws are proposed such that the Q‐S synchronization of non‐identical chaotic systems is to be achieved. Finally, four illustrative numerical simulations are also given to demonstrate the effectiveness of the proposed scheme. Copyright © 2009 John Wiley & Sons, Ltd.     

Adaptive synchronization of GLHS with unknown parameters

In this paper, an adaptive controller for the synchronization of two generalized Lorenz hyperchaos systems (GLHSs) is designed by using the Lyapunov method. In the synchronization schema, the parameters of the drive system are unknown and different from those of the response system. By introducing update laws for both the control coefficients and the parameters of the response system, the adaptive controller proposed in this paper is brand new compared with the former relative works. The proposed adaptive controller is feasible for any possible parameters of GLHS. Numerical simulation is carried out to verify and illustrate the analytical result. Copyright © 2008 John Wiley & Sons, Ltd.     

Fixed-time synchronization for discontinuous delayed complex-valued networks with semi-Markovian switching and hybrid couplings via adaptive control

In this article, the global fixed-time synchronization issue is considered for semi-Markovian switching discontinuous complex-valued dynamical networks (CVDNs) with hybrid couplings and time-varying delays, in which CVDNs are not divided into two real value systems, contrary to existing literature. First, a new fixed-time convergence principle for complex-valued nonlinear system with semi-Markovian switching is developed. Second, to realize the fixed-time synchronization, the state feedback controller with integral term and adaptive controller are designed, respectively. Under the complex-valued differential inclusions framework, by utilizing Lyapunov-Krasovskii functional method and inequality analysis technique, the global fixed-time synchronization conditions are addressed in terms of linear matrix inequalities. Finally, two numerical simulations are given to illustrate the validity of the presented theoretical results.     

Fixed time synchronization of delayed chaotic neural networks by using active adaptive control

This article aims to investigate the fixed time synchronization of a class of chaotic neural systems by way of adaptive control method. Using Lyapunov stability theory, a new fixed time stability theorem which plays an important role on the synchronization scheme is presented at first. Then, combining the fixed time stability theorem and adaptive control technique, an adaptive control scheme has been developed to achieve the fixed time synchronization of chaotic neural systems. The proposed controllers assure the global convergence of the error dynamics in fixed-time based on the Lyapunov stability theory. Furthermore, the proposed control strategy cannot only provide a fast convergence rate, but also afford a bounded convergence time which is unrelated to the initial values and easy to work out by using the simple time calculation formula. Finally, numerical simulations are presented by taking a typical two-order chaotic neural system as an example to verify and demonstrate the effectiveness of the proposed scheme.     

Pinning synchronization of complex networks with delayed nodes

This paper reveals the dynamical mechanism of synchronization in general complex networks with delayed nodes. It considers, in particular, the global synchronization of complex networks without assuming any symmetry in the coupling matrix by using pinning controllers. Sufficient conditions for global synchronization are obtained by suitably adding linear and adaptive feedback controllers to a certain sub‐collection of the nodes and numerical examples that are provided to demonstrate the effectiveness of the theory. Copyright © 2014 John Wiley & Sons, Ltd.     

存在扰动的永磁同步电机混沌运动模糊自适应同步

电机的混沌运动并不总是有害的,在某种特殊应用场合中永磁同步电机的混沌运动是有益的,因此需要对永磁同步电机的混沌运动进行反控制。提出了一种存在扰动的永磁同步电机（PMSM）混沌运动的模糊自适应同步控制方法。分析了PMSM混沌运动的吸引子和lyapunov指数谱,使模糊控制规则满足系统的lyapunov稳定条件,设计模糊自适应控制器对存在扰动的PMSM混沌系统进行同步控制,仿真结果表明该方法可实现PMSM混沌运动的同步控制,具有较好的控制效果。     

采用模糊控制实现混沌系统的广义投影同步

研究了离散混沌系统的广义投影同步问题.基于Takagi-Sugeno(TS)模糊动态模型和Lyapunov稳定性理论,导出了离散混沌系统广义投影同步的一个充分条件.通过一些矩阵操作技巧,这个准则被转化为一组线性矩阵不等式形式.然后,这些线性矩阵不等式的求解可以用Matlab工具箱方便地解决.对Henon映射的数值模拟,仿真结果表明该方法的有效性.     

Hybrid adaptive control for non‐linear uncertain impulsive dynamical systems

A direct hybrid adaptive control framework for non‐linear uncertain hybrid dynamical systems is developed. The proposed hybrid adaptive control framework is Lyapunov‐based and guarantees partial asymptotic stability of the closed‐loop hybrid system; that is, asymptotic stability with respect to part of the closed‐loop system states associated with the hybrid plant states. Furthermore, hybrid adaptive controllers guaranteeing attraction of the closed‐loop system plant states are also developed. Finally, two numerical examples are provided to demonstrate the efficacy of the proposed hybrid adaptive stabilization approach. Copyright © 2004 John Wiley & Sons, Ltd.     

A new command governor architecture for transient response shaping

In this paper, we develop a control framework for stabilization and command following of nonlinear uncertain dynamical systems. The proposed methodology consists of a new command governor architecture and an adaptive controller. The command governor is a dynamical system that adjusts the trajectory of a given command to follow an ideal reference system capturing a desired closed‐loop dynamical system behavior in transient time. Specifically, we show that the controlled nonlinear uncertain dynamical system can approach the ideal reference system by choosing the design parameter of the command governor. In addition, an adaptive element is used to asymptotically assure that the error between the controlled nonlinear uncertain dynamical system and the ideal reference system is reduced in long term. Therefore, the proposed methodology not only has closed‐loop transient and steady‐state performance guarantees but can also shape the transient response by adjusting the trajectory of the given command with the command governor. We highlight that there exists a trade‐off between the adaptive controller's learning rate and the command governor's design parameter. This key feature of our framework allows rapid suppression of system uncertainties without resorting to a high learning rate in the adaptive controller. Furthermore, we discuss the robustness properties of the proposed approach with respect to high‐frequency dynamical system content such as measurement noise and ∕ or unmodeled dynamics. A numerical example is provided to demonstrate the efficacy of the proposed architecture. Copyright © 2012 John Wiley & Sons, Ltd.     

不确定混沌系统的鲁棒自适应容错同步控制

针对一类带有执行器故障、非线性不确定性以及外界干扰的混沌系统,设计一个鲁棒自适应容错控制器,来实现主从混沌系统之间的同步容错控制。不需要知晓准确的故障信息以及外界干扰的上界,根据自适应律在线估计未知量。结合自适应控制技术,设计鲁棒自适应容错控制器,使得无论执行器是否有故障发生,主从两个混沌系统都能够实现同步。以经典的蔡氏混沌电路系统为例进行数值仿真,仿真结果验证了所设计控制器的有效性和可行性。     

Adaptive observer design for nonlinear interconnected systems by the application of LaSalle's theorem

In this article, a class of nonlinear interconnected systems with uncertain time varying parameters (TVPs) is considered. Both the interconnections and the isolated subsystems are nonlinear. The differences between the unknown TVPs and their corresponding nominal values are assumed to be bounded where the nominal value is not required to be known. A dynamical system is proposed and then, the error systems between the original interconnected system and the designed dynamical system are analysed. A set of conditions is developed such that the augmented systems formed by the error dynamical systems and the designed adaptive laws are uniformly ultimately bounded. Specifically, the state observation errors are asymptotically convergent to zero based on the LaSalle's Theorem while the parameter estimation errors are uniformly ultimately bounded, and the classical condition of persistent excitation is not required. A case study on a coupled inverted pendulum system is presented to demonstrate the developed methodology, and simulation shows that the proposed approach is effective and practicable.     

A method for synchronization of power electronic converters in polluted and variable-frequency environments

This paper presents a new synchronization method which employs an enhanced phase-locked loop (EPLL) system. The operational concept of the EPLL is novel and based on a nonlinear dynamical system. As compared with the existing synchronization methods, the introduced EPLL-based synchronization method provides higher degree of immunity and insensitivity to noise, harmonics and other types of pollutions that exist in the signal used as the basis of synchronization. The salient feature of the EPLL-based synchronization method over conventional synchronization methods is its frequency adaptivity which permits satisfactory operation when the centre frequency of the base signal varies. The proposed EPLL-based method of synchronization is also capable of coping with the unbalanced system scenarios. Structural simplicity of the EPLL-based method greatly simplifies its implementation in digital software and/or hardware environments as an integral part of a digital control platform for power electronic converters. The primary application of the proposed synchronization method is for the distributed generation units, e.g., wind generation systems, which utilize power electronic converters as an integral part of their systems.     

Avoiding singularities in recurrent neural control for induction motors

In this paper, a master–slave synchronization scheme based on parameter identification is proposed to overcome the controller singularity problem that appears when linearization‐like techniques are applied in indirect adaptive neural control, like Neural Block Control (NBC). Such a synchronization strategy requires an identifier‐like recurrent neural network and an adaptive law to update the neural weights. The proposed adaptive law prevents both, specific adaptive weights zero‐crossing and the ‘parameter drift’ phenomenon. NBC consists of two tasks; synchronizing an identifier‐like recurrent neural network (slave) with the plant (master) and controlling the system based on the slave model. The effectiveness of the synchronization law is tested using NBC for controlling the angular speed and magnetic flux magnitude of an induction motor. Usingit a priori knowledge about the real plant, a high‐order recurrent neural network is proposed as the slave system. Based on the slave neural model, a discontinuous control law is derived, which combines Block Control and Sliding Modes. NBC with the proposed synchronization strategy is tested via simulations, comparing results with a standard parameters adaptive law. Copyright © 2011 John Wiley & Sons, Ltd.     

Stability analysis and robust synchronization of fractional‐order competitive neural networks with different time scales and impulsive perturbations

This article mainly examine a class of robust synchronization, global stability criterion, and boundedness analysis for delayed fractional‐order competitive type‐neural networks with impulsive effects and different time scales. Firstly, by endowing the robust analysis skills and a new class of Lyapunov‐Krasovskii functional approach, the error dynamical system is furnished to be a robust adaptive synchronization in the voice of linear matrix inequality (LMI) technique. Secondly, by ignoring the uncertain parameter terms, the existence of equilibrium points are established by means of topological degree properties, and the solution representation of the considered network model are provided. Thirdly, a novel global asymptotic stability condition is proposed in the voice of LMIs, which is less conservative. Finally, our analytical results are justified with two numerical examples with simulations.     

Chaotification of unknown linear and nonlinear systems with applications

A new chaotification method (chaos anti-control) of dynamical systems, which have unknown parameters, is proposed in this paper. The method is based on tracking reference models, through a control law that chaotifies a class of non-linear systems, linear in the control and fully state feedback linearizable. Besides, adaptive laws for control parameters are derived that guarantee the stability of the resulting adaptive system and the convergence of the tracking error to zero. The proposed method has two possible approaches: indirect and direct. Finally, the proposed scheme is applied to secure communications, by means of encrypted information transmission and reception of a message in a chaotic system.     

Adaptive synchronization for nonlinear FitzHugh–Nagumo neurons in external electrical stimulation

This paper investigates the synchronization problem for FitzHugh–Nagumo (FHN) neurons in external electrical stimulations. Using the sliding mode control technique, an adaptive control law is established that guarantees synchronization even when the parameters of the master and slave FHN neurons are fully unknown. A proportional‐integral switching surface is introduced to simplify the task of assigning the stability of the closed‐loop error system in the sliding mode. Furthermore, the proposed synchronization scheme is then applied to a secure communication system. Computer simulations are provided to verify the effectiveness of the proposed adaptive synchronization scheme. Copyright © 2007 John Wiley & Sons, Ltd.     

Fault tolerant synchronization for a class of complex interconnected neural networks with delay

This paper is concerned with the fault tolerant synchronization problem for a class of complex interconnected neural networks against sensor faults. As sensor faults may lead to performance degradation or even instability of the whole network, fault tolerant control laws are designed to guarantee the controlled synchronization of the complex interconnected neural networks. On the basis of Lyapunov stability theory and adaptive schemes, three kinds of fault tolerant control laws are designed on the basis of linear matrix inequality technique. One is the passive fault tolerant control law, the other two are adaptive fault tolerant control laws. The latter two methods use the adaptive adjusting mechanism of the coupling coefficients to ensure the synchronization of the networks in the presence of sensor faults. Simulation results are given to verify the effectiveness of the proposed methods. Copyright © 2013 John Wiley & Sons, Ltd.     

Distributed cooperative neural control of a class of nonlinear multi-agent systems with unknown time-varying control coefficient

This article studies the leader–follower cooperative tracking problem of a class of multi-agent systems with unknown nonlinear dynamics. As the load of the following agent may be changing throughout the whole work process, we consider the control coefficient of the following agent to be time-varying and nonlinear instead of constant, which is more practical. All agents are connected by the directed communication graph with weighted topology. The followers can have unknown nonidentical nonlinear dynamics and external disturbances. The nonautonomous leader generates the reference trajectory for only part of the followers and others can only receive the information from their neighbors. To achieve the ultimate synchronization of all following agents to the leader, the novel cooperative adaptive control protocols are designed based on the neural approximation and adaptive updating mechanism. A novel singularity-avoided adaptive updating law is proposed to estimate the control coefficient and compensate for the unknown dynamics online. Lyapunov theory is used to prove the ultimate boundedness of the synchronization tracking error. The correctness and effectiveness of the presented control scheme are demonstrated by two simulations in SISO and MIMO cases, respectively.