Outer synchronization between two hybrid‐coupled delayed dynamical networks via aperiodically adaptive intermittent pinning control

This article is concerned with the problem of pinning outer synchronization between two complex delayed dynamical networks via adaptive intermittent control. At first, a general model of hybrid‐coupled dynamical network with time‐varying internal delay and time‐varying coupling delay is given. Then, an aperiodically adaptive intermittent pinning‐control strategy is introduced to drive two such delayed dynamical networks to achieve outer synchronization. Some sufficient conditions to guarantee global outer‐synchronization are derived by constructing a novel piecewise Lyapunov function and utilizing stability analytical method. Moreover, a simple pinned‐node selection scheme determining what kinds of nodes should be pinned first is provided. It is noted that the adaptive pinning control type is aperiodically intermittent, where both control period and control width are non‐fixed. Finally, a numerical example is given to illustrate the validity of the theoretical results. © 2016 Wiley Periodicals, Inc. Complexity 21: 593–605, 2016     

具有多重权值的时滞复杂网络固定时间同步问题研究

文章研究了基于非周期间歇性控制的具有多重权值和耦合时滞的复杂网络固定时间同步问题.通过构建具有多重权值的复杂网络模型,并基于固定时间稳定性引理和矩阵理论,给出了实现复杂网络固定时间同步的充分条件.此外,文章设计了固定时间非周期切换控制器,获得了实现复杂网络同步的时间上界的估计值.结论证明了实现网络同步的时间与网络的初始状态无关,最后数值模拟说明了理论结果的正确性和有效性.     

Synchronization for stochastic hybrid coupled controlled systems with Lévy noise

In this paper, synchronization for stochastic hybrid-delayed coupled systems with Lévy noise on a network (SHDCLN) is investigated via aperiodically intermittent control. Here time delays, Markovian switching and Lévy noise are considered on a network simultaneously for the first time. After that, by means of Lyapunov method, graph theory, and some techniques of inequality, some sufficient conditions are derived to guarantee the synchronization for SHDCLN. In addition, the designed range of aperiodically intermittent controller parameters is shown. Meanwhile, the coupling strength and the perturbed intensity of noise have a great impact on the intensity of control. Then, we investigate synchronization for stochastic hybrid delayed Chua's circuits with Lévy noise on a network as a practical application of our theoretical results. Finally, a numerical example is given to illustrate the effectiveness of the theoretical results.     

Intermittent impulsive projective synchronization in time‐varying delayed dynamical network with variable structures

This paper studies the projective synchronization behavior in a drive‐response dynamical network with coupling time‐varying delay via intermittent impulsive control. Different from the most publications on drive‐response dynamical networks under the general impulsive control, here the impulsive effects can only exist at control windows, not during the whole time. Moreover, intermittent impulsive control does not need the limitation of the upper bound of the impulsive intervals. By utilizing the Lyapunov‐Razumikhin technique, some sufficient conditions for the projective synchronization are derived. Numerical simulations are provided to verify the correctness and effectiveness of the proposed method and results. © 2016 Wiley Periodicals, Inc. Complexity 21: 547–556, 2016     

Stabilization of novel multi-layer networks with noise-based nonlinear superior couplings via aperiodically adaptive intermittent pinning control

In this paper, novel multi-layer networks with superior couplings are proposed firstly which are established on a non-strongly connected digraph. Within the multi-layer networks, a nonlinear coupling based on white noises is introduced, which is the feature of superior couplings. We adopt aperiodically adaptive intermittent pinning control to stabilize the multi-layer networks. An concrete analysis framework about selecting the target vertex of the control is revealed. Aperiodically adaptive intermittent control is employed on the vertex systems of the first layer networks, to achieve the stabilization of the first layer networks, where the couplings of drift terms are treated as negative effects on stabilization. With the help of noise stabilization, the stabilization of the other layers networks is realized based on the stability of the first layer networks and the characteristics of the superior coupling that is based on white noises. By employing graph theory and the Lyapunov method, an almost sure exponential stabilization criterion of the multi-layer networks is acquired. As a subsequent result, the proposed theory is applied to a class of stochastic coupled oscillators with sufficient conditions being given to ensure their stability. Finally, a numerical example is provided to illustrate the feasibility of the stated theoretical results.     

Impulsive stabilization of complex-valued stochastic complex networks via periodic self-triggered intermittent control

The aim of this article is to research the stabilization issue of complex-valued stochastic Markovian switching complex networks with time delays and time-varying multi-links (CSMCTM) via periodic self-triggered intermittent impulsive control (PSIIC). Thereinto, PSIIC is designed for the first time by combining intermittent impulsive control with periodic self-triggered control for intermittent control. It is worth emphasizing that the triggered protocol is designed to be more flexible, and easier to implement than previously reported triggered protocol. Then, by means of impulsive control, intermittent control, event-driven control theory and stability analysis, a stabilization criterion of CSMCTM in the sense of exponential stability in mean square is obtained. Whereafter, the stability of a class of complex-valued inertial neural networks is researched as a practical application of our theoretical results. Ultimately, a numerical example gives a corresponding verification.     

Robust decentralized adaptive synchronization of general complex networks with coupling delayed and uncertainties

The problem of robust decentralized adaptive synchronization of general complex networks with coupling delayed and uncertainties is investigated in this article. It is only assumed that the upper normal bound of uncertain inner and outer coupling matrices is positive but its concrete structure is not also required to be known. The time‐varying coupling delay is a any nonnegative continuous and bounded function and not require its derivative to be less than one, that is, general time‐varying coupling delays and uncertainties. For such a class of uncertain complex networks, a new synchronization scheme is presented by a class of continuous memoryless robust decentralized adaptive synchronization controllers. It is also shown that the synchronization error dynamics of uncertain complex networks can be guaranteed as uniformly exponentially convergent toward a ball that can be as small as desired. Finally, numerical simulations are provided to demonstrate the effectiveness and robustness of proposed complex networks synchronization schemes. © 2013 Wiley Periodicals, Inc. Complexity 19: 10–26, 2014     

Stabilization for hybrid stochastic systems by aperiodically intermittent control

In this paper, the mean-square exponential stabilization for stochastic differential equations with Markovian switching is studied. Specifically, a new set of sufficient conditions is derived to obtain the aperiodically intermittent control design which exponentially stabilizes the addressed hybrid stochastic differential equations. Further, stabilization problem by periodically intermittent control can be deduced as a special case from the developed results. As an application, we consider the Hopfield neutral network model with simulations to illustrate the effectiveness of developed aperiodically intermittent control design.     

Intermittent control for synchronization of hybrid multi-weighted complex networks with reaction-diffusion effects

In this paper, exponential synchronization for hybrid multi-weighted complex networks is studied via aperiodically intermittent control. Different from previous work, both Markov jump and reaction-diffusion effects are simultaneously considered into multi-weighted complex networks. By employing network split technique, graph theory, and Lyapunov method, several synchronization criteria are derived. These criteria show the effects of multiple weights, Markov jump, and reaction-diffusion on exponential synchronization. Furthermore, an application to Cohen–Grossberg neural networks is conducted, and the corresponding synchronization criterion is given. Finally, some numerical simulations are presented to show the effectiveness of the obtained theoretical results.     

A graph‐theoretic method to stabilize the delayed coupled systems on networks based on periodically intermittent control

This paper mainly focus on the exponential stabilization problem of coupled systems on networks with mixed time‐varying delays. Periodically intermittent control is used to control the coupled systems on networks with mixed time‐varying delays. Moreover, based on the graph theory and Lyapunov method, two different kinds of stabilization criteria are derived, which are in the form of Lyapunov‐type theorem and coefficients‐type criterion, respectively. These laws reveal that the stability has a close relationship with the topology structure of the networks. In addition, as a subsequent result, a decision theorem is also presented. It is straightforward to show the stability of original system can be determined by that of modified system with added absolute value into the coupling weighted‐value matrix. Finally, the feasibility and validity of the obtained results are demonstrated by several numerical simulation figures.     

Adaptive cooperative control of networked uncalibrated robotic systems with time‐varying communicating delays

This paper investigates the trajectory tracking control of the networked multimanipulator with the existence of time‐varying delays and uncertainties in both kinematics and dynamics. To address time‐varying delays in the communication links, a novel control scheme is established by the design of delay–rate‐dependent networking mutual coupling strengths. Besides, to handle the kinematic and dynamic uncertainties, an adaptive controller is designed. The proposed control scheme guarantees that the networked robotic system can track a commonly desired trajectory cooperatively with the strongly connected communication graph, uncertainties, and time‐varying communicating delays. A Lyapunov–Krasovskii functional is employed to rigorously prove the asymptotic convergence of both tracking errors and synchronization errors. The simulation results are provided to verify the effectiveness of the control method proposed by this paper.     

坦克炮控伺服系统的自适应鲁棒控制研究

针对一类坦克炮控伺服系统,充分考虑系统中的未知齿隙非线性及摩擦非线性,将这些未知非线性的影响表示成有界扰动项与未知非线性动态项之和,借助ARC(自适应鲁棒控制)的思想设计控制器,当未知非线性动态项为零时,控制器即为自适应控制器,保持系统稳定的同时实现对参考信号的精确跟踪,而当系统存在未知非线性动态项时,控制器具有很好的鲁棒性,保持系统所有信号有界的同时实现对参考信号的误差跟踪,且跟踪误差可以由设计参数的取值设定来任意调节,与现有结果相比,控制器的设计建立在充分考虑系统未知非线性的影响之上,从而避免了简单的把未知非线性影响简单的考虑成系统"总扰动"所造成的被控系统性能的损失。     

Effects of time delays on the stability of collocated and noncollocated point control of discrete dynamic structural systems

The effects of time delays on collocated as well as noncollocated point control of discrete dynamic systems have been examined. Controllers of proportional-integral-derivative (PID) type have been considered. Analytical estimates of time delays to maintain/obtain stability for small gains have been given. Several new results dealing with the effect of time delays on collocated and noncollocated control designs are obtained. It is shown that undamped structural systems cannot be stabilized with pure velocity (or integral) feedback without time delays while using a controller which is not collocated with the sensor when the mass matrix is diagonal. However, with the appropriate choice of time delays for certain classes of commonly occurring structural systems, stable noncollocated control can be achieved. Analytical results providing the upper bound on the controller's gain necessary for stability have been presented. The theoretical results obtained are illustrated and verified with numerical examples.     

RBF‐based discrete sliding mode control for robust tracking of uncertain time‐delay systems with input nonlinearity

In this article, a control scheme combining radial basis function neural network and discrete sliding mode control method is proposed for robust tracking and model following of uncertain time‐delay systems with input nonlinearity. The proposed robust tracking controller guarantees the stability of overall closed‐loop system and achieves zero‐tracking error in the presence of input nonlinearity, time‐delays, time‐varying parameter uncertainties, and external disturbances. The salient features of the proposed controller include no requirement of a priori knowledge of the upper bound of uncertainties and the elimination of chattering phenomenon and reaching phase. Simulation results are presented to demonstrate the effectiveness of the proposed scheme. © 2015 Wiley Periodicals, Inc. Complexity 21: 194–201, 2016     

基于自适应控制的四元数时滞神经网络的有限时间同步

文章主要研究了自适应控制下四元数时滞神经网络的有限时间完全同步,通过设计一组有效新颖的自适应控制器,使得主从系统实现有限时间同步,并计算出停息时间的理论估计.利用Lyapunov函数方法和不等式技巧,给出了四元数时滞神经网络主从系统有限时间同步的充分条件.最后,通过数值仿真验证了所得理论结果的有效性.     

Chaos control of uncertain time‐delay chaotic systems with input dead‐zone nonlinearity

This article presents an adaptive sliding mode control (SMC) scheme for the stabilization problem of uncertain time‐delay chaotic systems with input dead‐zone nonlinearity. The algorithm is based on SMC, adaptive control, and linear matrix inequality technique. Using Lyapunov stability theorem, the proposed control scheme guarantees the stability of overall closed‐loop uncertain time‐delay chaotic system with input dead‐zone nonlinearity. It is shown that the state trajectories converge to zero asymptotically in the presence of input dead‐zone nonlinearity, time‐delays, nonlinear real‐valued functions, parameter uncertainties, and external disturbances simultaneously. The selection of sliding surface and the design of control law are two important issues, which have been addressed. Moreover, the knowledge of upper bound of uncertainties is not required. The reaching phase and chattering phenomenon are eliminated. Simulation results demonstrate the effectiveness and robustness of the proposed scheme. © 2014 Wiley Periodicals, Inc. Complexity 21: 13–20, 2016     

Robust tracking and model following for uncertain time‐delay systems with input nonlinearity

This article proposes a novel adaptive sliding mode control (SMC) scheme to realize the problem of robust tracking and model following for a class of uncertain time‐delay systems with input nonlinearity. It is shown that the proposed robust tracking controller guarantees the stability of overall closed‐loop system and achieves zero‐tracking error in the presence of input nonlinearity, time‐delays, time‐varying parameter uncertainties and external disturbances. The selection of sliding surface and the existence of sliding mode are two important issues, which have been addressed. This scheme assures robustness against input nonlinearity, time‐delays, parameter uncertainties, and external disturbances. Moreover, the knowledge of the upper bound of uncertainties is not required and chattering phenomenon is eliminated. Both theoretical analysis and illustrative examples demonstrate the validity of the proposed scheme. © 2014 Wiley Periodicals, Inc. Complexity 21: 66–73, 2015     

Cluster synchronization for T–S fuzzy complex networks using pinning control with probabilistic time‐varying delays

In this article, cluster synchronization problem for Lur'e type Takagi–Sugeno (T–S) fuzzy complex networks with probabilistic time‐varying delays is considered. Pinning control strategy is proposed. The probability distribution of the time‐varying delay is considered. In terms of the probability distribution of the delays, a new type of system model with probability‐distribution‐dependent parameter matrices is proposed. Moreover, probabilistic delay is assumed to satisfy certain probability distribution and the probability of the delay takes values in some intervals. By constructing a suitable Lyapunov–Krasovskii functional involving triple integral terms and using Kronecker product with convex combination technique, some sufficient conditions are derived to ensure the cluster synchronization of designed networks such that the linear feedback controller can be used to every cluster. The problem of controller design is converted into solving a series of linear matrix inequalities. The effectiveness of our results is verified through numerical examples and simulations. © 2014 Wiley Periodicals, Inc. Complexity 21: 59–77, 2015     

基于模糊与神经网络技术的复杂非线性跟踪控制

针对一类具有不确定性、多重时延和状态未知的复杂非线性系统,把模糊T-S模型和RBF神经网络结合起来,提出了一种基于观测器的跟踪控制方案.首先,应用模糊T-S模型对非线性系统建模,设计观测器用来观测系统状态,并由线性矩阵不等式得到模糊模型的控制律;其次,构建了自适应RBF神经网络,应用自适应RBF神经网络作为补偿器来补偿建模误差和不确定非线性部分.证明了闭环系统满足期望的跟踪性能.示例仿真结果表明了该方案的有效性.