Chaos control of new Ikeda–Lorenz systems by GYC partial region stability theory

A new strategy to achieve chaos control by GYC partial region stability theory is proposed. By using the GYC partial region stability theory, the Lyapunov function is a simple linear homogeneous function of error states, the controllers are more simple and have less simulation error because they are in lower degree than that of traditional controllers. Simulation results for a new Ikeda–Lorenz system show the effectiveness of this strategy. Copyright © 2008 John Wiley & Sons, Ltd.     

Chaos control of new Mathieu-Van der Pol systems with new Mathieu-Duffing systems as functional system by GYC partial region stability theory

In this paper, a new strategy by using GYC partial region stability theory is proposed to achieve chaos control. Using the GYC partial region stability theory, the new Lyapunov function used is a simple linear homogeneous function of error states and the lower order controllers are much more simple and introduce less simulation error. Numerical simulations are given for new Mathieu-Van der Pol system and new Mathieu-Duffing system to show the effectiveness of this strategy.     

Chaos generalized synchronization of new Mathieu–Van der Pol systems with new Duffing–Van der Pol systems as functional system by GYC partial region stability theory

In this paper, a new strategy by using GYC partial region stability theory is proposed to achieve generalized chaos synchronization. via using the GYC partial region stability theory, the new Lyapunov function used is a simple linear homogeneous function of states and the lower order controllers are much more simple and introduce less simulation error. Numerical simulations are given for new Mathieu–Van der Pol system and new Duffing–Van der Pol system to show the effectiveness of this strategy.     

Adaptive compensation of uncertain Euler–Lagrange systems with multiple time-varying actuator faults

This work proposes the command tracking problem for uncertain Euler–Lagrange (EL) systems with multiple partial loss of effectiveness (PLOE) actuator faults. Compared to existing fault-tolerant controllers for EL systems, the proposed adaptive controller accounts for parametric uncertainties in the system and multiple time-varying actuator fault parameters. The proposed method can also handle an infinite number of fault cases. The closed-loop fault-tolerant system is treated as a switched dynamical system, and a switched system stability is established using multiple Lyapunov functions. It is shown that all signals are bounded in each sub-interval and at the switching instances, and asymptotic tracking can be obtained only for a finite number of fault occurrences, whereas tracking error is bounded for the infinite case. Finally, a simulation example on a robotic manipulator is presented to show the effectiveness of the proposed method.     

Tracking the state of the delay hyperchaotic Lü system using the coullet chaotic system via a single controller

In this article, a partial synchronization scheme is proposed based on Lyapunov stability theory to track the signal of the delay hyperchaotic Lü system using the Coullet system based on only one single controller. The proposed tracking control design has two advantages: only one controller is adopted in our approach and it can allow us to drive the hyperchaotic system to a simple chaotic system even with uncertain parameters. Numerical simulation results are given to demonstrate the effectiveness and robustness of the proposed partial synchronization scheme. © 2014 Wiley Periodicals, Inc. Complexity 21: 125–130, 2016     

Parameters estimation,mixed synchronization,and antisynchronization in chaotic systems

Mixed synchronization between two Hindmarsh–Rose neuron models is realized by optimizing the scheme of Lyapunov function with two selectable gain coefficients. Based on the Lyapunov stability theory, the distribution of synchronization region and the nonsynchronization region in the two‐parameter phase space is calculated, respectively. And then the optimized parameter observers and controllers are approached analytically. All unknown parameters with different orders of magnitude are identified accurately, and the error function for corresponding variables decreases to stable value when the two gain coefficients are given values in the synchronization region. Otherwise, only the four larger unknown parameters are estimated exactly and the error function of corresponding variables decreases stably to certain minimal value with an order about 1 × 10^?6, whereas the smallest unknown parameter is approached greatly although the error of corresponding variables are stabilized within certain transient period. © 2014 Wiley Periodicals, Inc. Complexity 20: 64–73, 2014     

Complete synchronization,phase synchronization and parameters estimation in a realistic chaotic system

The two-parameter phase space in certain nonlinear system is investigated and the chaotic region of parameters are measured to show its chaotic properties. Within the chaotic parameter region, the complete synchronization, phase synchronization and parameters estimation are discussed in detail by using adaptive synchronization scheme and Lyapunov stability theory. Two changeable gain coefficients are introduced into the controllable positive Lyapunov function and thus the parameter observers. It is found that complete synchronization or phase synchronization occurs with different controllers being used though the parameter observers are the same. Phase synchronization is observed when zero eigenvalue of Jacobi matrix, which is composed of the errors of corresponding variables in the drive and driven chaotic systems. The optimized selection of controllers can induce transition of phase synchronization and complete synchronization.     

Adaptive synchronization of new fractional‐order chaotic systems with fractional adaption laws based on risk analysis

In this paper, a new fractional‐order chaotic system and an adaptive synchronization of fractional‐order chaotic system are proposed. Parameters adaption laws are obtained to design adaptive controllers using Lyapunov stability theory of fractional‐order system. Finally, reliability of designed controllers and risk analysis of adaptive synchronization problem are formulated and, risk of using the proposed controllers in presences of external disturbances are demonstrated. Also, risk of controllers are reduced using an optimizing method. Numerical examples are used to verify the performance of the proposed controllers.     

Anti-synchronization of two hyperchaotic systems via nonlinear control

Based on the nonlinear control theory, the anti-synchronization between two different hyperchaotic systems is investigated. Through rigorous mathematical theory, the sufficient condition is drawn for the stability of the error dynamics, where the controllers are designed by using the sum of the relevant variables in hyperchaotic systems. Numerical simulations are performed for the hyperchaotic Chen system and the hyperchaotic Lü system to demonstrate the effectiveness of the proposed control strategy.     

Synchronization and anti-synchronization of a hyperchaotic Chen system

Based on the active control theory, synchronization and anti-synchronization between two identical chaotic systems is investigated. Anti-synchronization can be characterized by the vanishing of the sum of relevant variables. Through rigorous mathematical theory, the sufficient condition is drawn for the stability of the error dynamics, where the controllers are designed by using the sum of the relevant variables in chaotic systems. Numerical simulations are performed for Chen hyperchaotic dynamical system to demonstrate the effectiveness of the proposed control strategy.     

基于LMI的时滞关联模糊大系统的分散镇定

讨论了具有时滞关联的连续时间模糊大系统的分散镇定问题 ,基于李亚普诺夫稳定性理论及大系统分散控制理论 ,给出了保证该时滞模糊大系统闭环渐近稳定的 LMI形式的充分条件 .满足这些充分条件的分散化并行分布补偿 ( DPDC)控制器参数可通过 MATLAB的 LMI工具箱有效的对其进行求取 .     

Control of a novel fractional hyperchaotic system using a located control method

Fractional order dynamics and chaotics systems have been recently combined, yielding interesting behaviours. In this paper, a novel integer order hyperchaotic system is considered. Then, a fractional order hyperchaotic representation of said system is proposed using a natural fractionalization. Two different linear control methodologies to deal with the complexity which introduce such systems are proposed. Those methods are able to modify the hyperchaotic behaviour of the system and force it to move towards a fixed point; i.e. steady state. These approaches give a general framework for taming such complex systems using simple linear controllers. The main tools for analysing the controlled system are Matignon stability criterion and RouthHurwitz test. Using a reliable numerical simulation, the designed system is simulated to verify the theoretical analysis.     

具有领导者的非线性分数阶多智能体系统的一致性分析

研究了利用非线性分数阶模型描述的具有领导者的多智能体系统的一致性问题.基于智能体之间的通讯拓扑图,设计了系统的控制协议和相应的控制增益矩阵.利用广义Gronwall不等式和分数阶微分方程的稳定性理论,得到了多智能体系统达到一致的充分条件.最后,数值仿真结果显示了理论结果的有效性.     

Modified projective synchronization of chaotic system

A modified projective synchronization is proposed to acquire a general kind of proportional relationships between the drive and response systems. From rigorously control theory, a sufficient condition is attained for the stability of the error dynamics, and is applied to guiding the design of the controllers. Finally, we take Lorenz system as an example for illustration and verification.     

An approach of partial control design for system control and synchronization

In this paper, a general approach of partial control design for system control and synchronization is proposed. It turns control problems into simpler ones by reducing their control variables. This is realized by utilizing the dynamical relations between variables, which are described by the dynamical relation matrix and the dependence–influence matrix. By adopting partial control theory, the presented approach provides a simple and general way to stabilize systems to their partial or whole equilibriums, or to synchronize systems with their partial or whole states. Further, based on this approach, the controllers can be simplified. Two examples of synchronizing chaotic systems are given to illustrate its effectiveness.     

Willis环状脑动脉瘤系统的自适应模糊控制

针对不确定非线性生物系统—W illis环状脑动脉瘤系统,利用高斯型模糊逻辑系统的逼近能力及新构造的Lyapunov函数,基于模糊建模提出了一种自适应模糊控制器设计的新方案.该方案把逼近误差引入到控制器设计条件中用以改善系统的动态性能.不但设计简单还保证了控制方法的鲁棒性与稳定性.通过反向传播算法调整模糊基函数参数及递归最小二乘法调整参数向量,θ更新控制律,实现了理想跟踪.从理论上研究了脑动脉瘤内血流速度的非线性行为及控制,具有实际意义.仿真结果表明该控制方法的有效性.     

Hybrid output regulation for linear impulsive systems with aperiodic jumps: A discrete-time feedback controller design approach

This paper is concerned with the problem of hybrid output regulation for a class of linear impulsive systems with aperiodic jumps. Firstly, by leveraging time-dependent Lyapunov function technique and impulsive control theory, sufficient conditions for achieving output regulation are obtained in state feedback case. Then, the results are extended to error feedback case by constructing an impulsive observer. In this framework, two novel hybrid controllers are designed. Such controllers only need the discrete-time system state or error signal for feedback. The complete procedures for controller designs are also presented. Finally, two illustrative examples, including a numerical example and an LC circuit, are given to show the validity and applicability of the proposed control laws.     

Synchronization and antisynchronization of N‐coupled fractional‐order complex chaotic systems with ring connection

This paper is devoted to investigate synchronization and antisynchronization of N‐coupled general fractional‐order complex chaotic systems described by a unified mathematical expression with ring connection. By means of the direct design method, the appropriate controllers are designed to transform the fractional‐order error dynamical system into a nonlinear system with antisymmetric structure. Thus, by using the recently established result for the Caputo fractional derivative of a quadratic function and a fractional‐order extension of the Lyapunov direct method, several stability criteria are derived to ensure the occurrence of synchronization and antisynchronization among N‐coupled fractional‐order complex chaotic systems. Moreover, numerical simulations are performed to illustrate the effectiveness of the proposed design.     

Online optimization of LTI systems under persistent attacks: Stability,tracking, and robustness

We study the stability properties of a closed-loop system composed of a dynamical plant and a feedback controller, the latter generating control signals that can be compromised by a malicious attacker. We consider two classes of feedback controllers: a static output-feedback controller, and a dynamical gradient-flow controller that seeks to steer the output of the plant towards the solution of a convex optimization problem. In both cases, we analyze the stability properties of the closed-loop system under a class of switching attacks that persistently modify the control inputs generated by the controllers. Our stability analysis leverages the framework of hybrid dynamical systems, Lyapunov-based arguments for switching systems with unstable modes, and singular perturbation theory. Our results reveal that, under a suitable time-scale separation between plant and controllers, the stability of the interconnected system can be preserved when the attack occurs with “sufficiently low frequency” in any bounded time interval. We present simulation results in a power-grid example that corroborate the technical findings.     

The role of data transfer on the selection of a single vs. multiple mesh architecture for tightly coupled multiphysics applications

Data transfer from one mesh to another may be necessary in a number of situations including spatial adaptation, remeshing, arbitrary Lagrangian-Eulerian (ALE), and multiphysics simulation. Data transfer has the potential to introduce error into a simulation; the magnitude and impact of which depends on the application, transfer scenario, and the algorithm used to perform the data transfer. During a transient simulation, data transfer may occur many times, with the potential of error accumulation at each transfer. This paper examines data transfer error and its impact on a set of simple multiphysics problems. Data transfer error is examined using analytical functions to compare schemes based on interpolation, area-weighted averaging, and L² minimization. An example error analysis is performed to illustrate data transfer error and behavior for a simple problem. Data transfer error is also investigated for a one-dimensional time-dependent system of partial differential equations. This study concludes that data transfer error can be significant in coupled multiphysics systems. These numerical experiments suggest that error is a function of data transfer scheme, and characteristics of the field data and mesh. If there are significant differences in the meshes in a multiple mesh simulation, this study suggests that data transfer may lead to error and instability if care is not taken. Further, this work motivates that data transfer error should be included in the estimation of numerical error when data transfer is employed in a simulation.