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pinning control and controllability of Complex Dynamical Networks

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International Journal of Automation and computing 2017年第1期14卷 1-9页

作者： Guanrong Chen Department of Electronic Engineering City University of Hong Kong Hong Kong China

In this article, the notion of pinning control for directed networks of dynamical systems is introduced, where the nodes could be either single-input single-output （SISO） or multi-input multi-output （MIMO） dynamical systems, and could be non-identical and nonlinear in general but will be specified to be identical linear time-invariant （LTI） systems here in the study of network controllability. Both state and structural controllability problems will be discussed, illustrating how the network topology, node-system dynamics, external control inputs and inner dynamical interactions altogether affect the controllability of a general complex network of LTI systems, with necessary and sufficient conditions presented for both SISO and MIMO settings. To that end, the controllability of a special temporally switching directed network of linear time-varying （LTV） node systems will be addressed, leaving some more general networks and challenging issues to the end for research outlook.

关键词： Complex network pinning control controllability linear time-invarJant (LTI) system temporally switching network,graph theory.

pinning control of a generalized complex dynamical network model

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控制理论与应用（英文版） 2009年第1期7卷 1-8页

作者： Huizhong YANG Li SHENG School of Communication and control Engineering Jiangnan University Wuxi Jiangsu 214122 China

This paper investigates the local and global synchronization of a generalized complex dynamical network model with constant and delayed coupling. Without assuming symmetry of the couplings, we proved that a single controller can pin the generalized complex network to a homogenous solution. Some previous synchronization results are generalized. In this paper, we first discuss how to pin an array of delayed neural networks to the synchronous solution by adding only one controller. Next, by using the Lyapunov functional method, some sufficient conditions are derived for the local and global synchronization of the coupled systems. The obtained results are expressed in terms of LMIs, which can be efficiently checked by the Matlab LMI toolbox. Finally, an example is given to illustrate the theoretical results.

关键词： Complex network Neural network pinning control Synchronization Delayed coupling

pinning control of general complex dynamical networks with optimization

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Science China(Information Sciences) 2010年第4期53卷 813-822页

作者： ZHAO JunChan, LU JunAn* & WU XiaoQun School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China School of Mathematics and Statistics Wuhan University Wuhan China

This paper addresses optimal pinning control of general complex dynamical networks. A pinning scheme with linear feedback is proposed to globally exponentially stabilize a network onto a homogeneous state. In particular, we answer an important and fundamental question about pinning control: how to select an optimal combination between the number of pinned nodes and the feedback control gain? Three illustrative examples are provided to show the effectiveness of the proposed technique.

关键词： complex dynamical networks optimization pinning control linear feedback

Disturbance rejection and H_∞ pinning control of linear complex dynamical networks

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Chinese Physics B 2009年第12期18卷 5228-5234页

作者：李忠奎段志生陈关荣 State Key Laboratory for Turbulence and Complex Systems Department of Mechanics and Aerospace EngineeringCollege of EngineeringPeking University

This paper concerns the disturbance rejection problem of a linear complex dynamical network subject to external disturbances. A dynamical network is said to be robust to disturbance, if the H∞ norm of its transfer function matrix from the disturbance to the performance variable is satisfactorily small. It is shown that the disturbance rejection problem of a dynamical network can be solved by analysing the H∞ control problem of a set of independent systems whose dimensions are equal to that of a single node. A counter-intuitive result is that the disturbance rejection level of the whole network with a diffusive coupling will never be better than that of an isolated node. To improve this, local feedback injections are applied to a small fraction of the nodes in the network. Some criteria for possible performance improvement are derived in terms of linear matrix inequalities. It is further demonstrated via a simulation example that one can indeed improve the disturbance rejection level of the network by pinning the nodes with higher degrees than pinning those with lower degrees.

关键词： complex dynamical network pinning control H∞ control robustness

Novel pinning control strategies for synchronisation of complex networks with nonlinear coupling dynamics

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Chinese Physics B 2010年第9期19卷 250-260页

作者：刘兆冰张化光孙秋野 College of Information Science and Engineering Northeastern University

This paper considers the global stability of controlling an uncertain complex network to a homogeneous trajectory of the uncoupled system by a local pinning control strategy. Several sufficient conditions are derived to guarantee the network synchronisation by investigating the relationship among pinning synchronisation, network topology, and coupling strength. Also, some fundamental and yet challenging problems in the pinning control of complex networks are discussed：（1） what nodes should be selected as pinned candidates？（2） How many nodes are needed to be pinned for a fixed coupling strength？ Furthermore, an adaptive pinning control scheme is developed. In order to achieve synchronisation of an uncertain complex network, the adaptive tuning strategy of either the coupling strength or the control gain is utilised. As an illustrative example, a network with the Lorenz system as node self-dynamics is simulated to verify the efficacy of theoretical results.

关键词： uncertain complex network pinning control synchronisation adaptive tuning

Cluster consensus of second-order multi-agent systems via pinning control

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Chinese Physics B 2010年第12期19卷 90-96页

作者：路晓庆 Francis Austin 陈士华 School of Mathematics and Statistics Wuhan University Wuhan 430072 China Department of Applied Mathematics The Hong Kong Polytechnic University Hong Kong China

This paper investigates the cluster consensus problem for second-order multi-agent systems by applying the pinning control method to a small collection of the agents. Consensus is attained independently for different agent clusters according to the community structure generated by the group partition of the underlying graph and sufficient conditions for both cluster and general consensus are obtained by using results from algebraic graph theory and the LaSalle Invariance Principle. Finally, some simple simulations are presented to illustrate the technique.

关键词： second-order multi-agent systems cluster consensus pinning control LaSalle invariance principle

Exponential synchronization of coupled memristive neural networks via pinning control

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Chinese Physics B 2013年第5期22卷 203-212页

作者：王冠沈轶尹泉 Department of control Science and Engineering Huazhong University of Science and Technology Key Laboratory of Ministry of Education for Image Processing and Intelligent control

This paper is concerned with the exponential synchronization problem of coupled memristive neural networks. In contrast to general neural networks, memristive neural networks exhibit state-dependent switching behaviors due to the physical properties of memristors. Under a mild topology condition, it is proved that a small fraction of controlled sub- systems can efficiently synchronize the coupled systems. The pinned subsystems are identified via a search algorithm. Moreover, the information exchange network needs not to be undirected or strongly connected. Finally, two numerical simulations are performed to verify the usefulness and effectiveness of our results.

关键词： synchronization memristor coupled neural networks pinning control

Cost and effect of pinning control for network synchronization

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Chinese Physics B 2009年第1期18卷 106-118页

作者：李嵘段志生陈关荣 State Key Laboratory for Turbulence and Complex Systems Department of Mechanics and Aerospace EngineeringCollege of EngineeringPeking University

The problem of pinning control for the synchronization of complex dynamical networks is discussed in this paper. A cost function of the controlled network is defined by the feedback gain and the coupling strength of the network. An interesting result is that a lower cost is achieved by using the control scheme of pinning nodes with smaller degrees. Some strict mathematical analyses are presented for achieving a lower cost in the synchronization of different star-shaped networks. Numerical simulations on some non-regular complex networks generated by the Barabasi-Albert model and various star-shaped networks are performed for verification and illustration.

关键词： complex dynamical network pinning control exponential stability

Distributed Secondary control Strategy Based on Q-learning and pinning control for Droop-controlled Microgrids

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Journal of Modern Power Systems and Clean Energy 2022年第5期10卷 1314-1325页

作者： Wei Liu Jun Shen Sicong Zhang Na Li Ze Zhu Liang Liang Zhen Wen IEEE Department of Electrical Engineering School of Automation Nanjing University of Science and TechnologyNanjing 210094China State Grid Zhejiang Electric Power Co. Ltd. Jiaxing Power Supply CompanyJiaxing230022China

A distributed secondary control(DSC) strategy that combines Q-learning and pinning control is originally proposed to achieve a fully optimal DSC for droop-controlled microgrids(MGs). It takes advantages of cross-fusion of the two algorithms to realize the high efficiency and self-adaptive control in MGs. It has the following advantages. Firstly, it adopts the advantages of reinforcement learning in autonomous learning control and intelligent decision-making, driving the action value of pinning control for feedback adaptive correction. Secondly, only a small part of points selected as pinned points needs to be controlled and pre-learned, hence the actual control problem is transformed into a synchronous tracking problem and the installation number of controllers is further ***, the pinning matrix can be modified to adapt to plugand-play operation under the distributed control ***, the effectiveness and versatility of the proposed strategy are demonstrated with a typical droop-controlled MG model.

关键词： Microgrid distributed secondary control pinning control Q-learning