Complex systems and networks can describe the characteristics of a large number of existing systems, and have been widely concerned by scholars at home and abroad in the past decades. With the rapid development of communication, computer and information technology, people can deal with large-scale data that can not be processed by traditional methods. In recent years, the research on complex systems and networks has been extended to networked control systems, information physical systems, logical networks, neural networks and other related fields. More importantly, new technologies such as wireless sensor networks, decentralized control and deep learning need distributed control strategies to ensure the system robustness, flexibility, scalability, low cost or easy to configure and maintain.
Since the end of the last century, the research on complex systems and networks has made great progress and obtained many insightful results and effective methods. Complex systems and networks have been widely used in civil and military fields. Typical examples include transportation systems, State Grid, health and medical fields, aerospace and industrial systems and other professional fields. With the requirements of clean energy, low cost, high security and health, the research of complex system and network has attracted more and more attention from academia and industry.
In this context, fitee, a journal of Chinese Academy of engineering, organized this special issue of "complex systems and networks and their applications", aiming to promote the research of complex systems and networks, and to summarize the latest progress in theory and application. After strict evaluation, 12 papers were selected, including 2 reviews and 10 research papers.
Li Xiaodi and others give a comprehensive overview of pulse control based on complex networks. It focuses on pulse control and pulse perturbation, involving several aspects of complex dynamic networks with pulse effects: synchronous and asynchronous pulses, adaptive pulse synchronization, check pulse synchronization and complex dynamic networks with random and pulse effects. At the same time, some future research directions are pointed out. Li Haitao and others reviewed the latest research progress of the design of logic control network controller in detail, including reachable set method, control design, control Lyapunov function method and sampling control method.
Cao Jinde et al. Discussed the multiple mittag Leffler stability of fractional quaternion neural networks with impulsive characteristics. The author proves that when Lipschitz condition is guaranteed, the existence of the equilibrium point can be proved by the tool derived from the geometric characteristics of the activation function. In addition, with the help of Lyapunov stability theory, the global miattag Leffler stability problem of multiple equilibrium points of fractional order quaternion numerical neural network with impulses is further studied. The effectiveness of the proposed method is verified by numerical examples.
As one of the typical forms of gene regulatory network modeling, logic network has always been a hot topic, which has been widely used in system biology, power grid, internal combustion engine, game theory, encryption and robotics. The development of algebraic state space method has greatly promoted the research on the structure and dynamics of logical control networks, as well as the analysis and synthesis of logical control networks, even extended to Boolean and multivalued logical networks.
GUI Weihua and so on proposed the output feedback stabilizer design method of Boolean network based on the network structure. Different from the traditional control design method, the design strategy is independent of the state transition matrix of the Boolean network, and can effectively determine the control nodes and reduce the computational complexity. The simulation and experiment of signal transduction network and polar gene network of Drosophila show that the method has good performance and adaptability. Lu Jianquan et al. Discussed the stability of the switched aperiodic sampling Boolean control network. The problem of global stability of Boolean control network under the control of aperiodic sampling data is solved. Compared with the global stability study of switched Boolean networks of other unstable subsystems, the aperiodic sampling control problem is more difficult and complex.
In recent years, synchronization and consistency have attracted people's attention to the mechanism of cluster behavior in network systems. Kurts et al. Proposed a new method of probabilistic Boolean control network stability based on state feedback control of double simulation, which can be used to reduce computational complexity. On the basis of strong matrix operation, a necessary and sufficient condition is given, and the stabilization problem of probability 1 between two quasi probabilistic Boolean control networks is considered. Li Lulu et al. Studied the complete synchronization problem of coupled delay Boolean networks, in which the state delay and output delay may not be equal, and the state delay in each Boolean network may be different, proposed a sufficient and necessary condition for complete synchronization, and gave the corresponding algorithm.
Based on the cascaded aggregation Boolean network, pan Jinfeng and Meng min consider the optimal single bit disturbance, making the expected attractor domain the largest, but not the expected attractor domain the smallest. Based on the aggregation method, a necessary and sufficient condition is given for the attractor to be invariant after a single bit disturbance. The feasibility and effectiveness of this method are verified by experiments on T cell receptor network.
As a basic form of Boolean control network decomposition, cascade decomposition is an interesting and practical concept in theory. Li Yifeng and Zhu Jiandong use graph theory to study two kinds of cascading decomposition problems of Boolean control networks. They put forward the concept of "nested completely equal vertex division", and obtain the necessary and sufficient conditions for diagrams. In addition, by constructing coordinate transformation, the corresponding cascade decomposition form is given, and the feasibility and effectiveness of the method are verified by experimental data.
Due to the time-consuming process of DNA transcription and RNA translation, time lag is inevitable in the process of gene regulation and plays a key role in organism development. Recently, researchers in the field of delay logic control networks have obtained some interesting results. Based on the theory of set stability, Zheng Yating and Feng June studied the output tracking problem of delay logic control networks with state and control constraints. Based on the transformation of the state transition matrix, several necessary and sufficient conditions are derived, and the design scheme of the admissible state feedback controller is proposed. Experiments show that the method is feasible and effective.
The potential application value of neural network in the fields of medical image edge detection, medical event detection, pattern recognition and robot technology makes the neural network develop rapidly. Cao Yang et al. Studied the inertia bi-directional associative memory neural network with mixed delay and impulsive effect. With the help of differential inequality technique, the existence, uniqueness and global exponential stability criteria of the antiperiodic solution were given. Finally, an example is given to verify the effectiveness of the results.
The availability of traffic information has great potential for vehicle power system control. Kang Mingxin and Gao Jinwu describe a shift control scheme, in which the shift strategy of control design can be formulated in the framework of logical system. In order to realize this control scheme, the vehicle dynamics model adopts Markov process. In the framework of logic system, the fuel optimization problem is solved by rolling horizon optimal control. Dynamic programming is used to solve the optimal problem. The simulation results verify the effectiveness of the design.
This issue covers a large number of current research contents and latest progress on complex systems, logical networks and neural networks, including the stability, tracking and decoupling of logical networks, analysis and synthesis of neural networks, synchronization strategies of complex networks based on pulse control, and practical engineering problems such as vehicle fuel efficiency optimization. We hope that this special issue will be helpful to researchers in these fields and promote the research of complex systems and logical networks, neural networks and related fields.
The smooth publication of this special issue benefited from the support and selfless help of many scholars, including the author and anonymous reviewer. In addition, we thank the journal editors for their great assistance and the editors pan Yunhe and Professor Lu Xicheng for their valuable opportunities.
This paper is translated from Cao JD, Liu y, Lu JQ, et al., 2020. Complex systems and networks with their applications. Front information technical electron eng, 21 (2): 195-198. Https://doi.org/10.1631/fitee.2020000
Article directory:
Editorial
※ Complex systems and networks with their applications
Jin-de CAO, Yang LIU, Jian-quan LU, Leszek RUTKOWSKI
Review Articles
※ A survey on complex dynamical networks with impulsive effects
Xiu-ping HAN, Yong-shun ZHAO, Xiao-di LI
※ New developments in control design techniques of logical control networks
Xiang-shan KONG, Shu-ling WANG, Hai-tao LI, FuadE. ALSAADI
Research Articles
※ Mittag-Leffler stability analysis of multiple equilibrium points in impulsive fractional-order quaternion-valued neural networks
K. UDHAYAKUMAR, R. RAKKIYAPPAN, Jin-de CAO,Xue-gang TAN
※ Output feedback stabilizer design of Boolean networks based on network structure
Jie ZHONG, Bo-wen LI, Yang LIU, Wei-hua GUI
※ Switching-based stabilization of aperiodic sampled-data Boolean control networks with all subsystems unstable
Liang-jie SUN, Jian-quan LU, Wai-Ki CHING
※ Bisimulation-based stabilization of probabilistic Boolean control networks with state feedback control
Nan JIANG, Chi HUANG, Yao CHEN, Jürgen KURTHS
※ Complete synchronization of coupled Boolean networks with arbitrary finite delaysJie LIU, Lulu LI, Habib M. FARDOUN※ Optimal one-bit perturbation in Boolean networks based on cascading aggregation
Jin-feng PAN, Min MENG
※ Cascading decomposition of Boolean control networks: a graph-theoretical method
Yi-feng LI, Jian-dong ZHU※ Output tracking of delayed logical control networks with multi-constraint
Ya-ting ZHENG, Jun-e FENG
※ New results on impulsive type inertial bidirectional associative memory neural networks
Chaouki AOUITI, Mahjouba Ben REZEG, Yang CAO
※ Design of an eco-gearshift control strategy under a logic system framework
Ming-xin KANG, Jin-wu GAO
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Professor Cao Jinde (editor in chief of the special issue), obtained bachelor's degree from Anhui Normal University, master's degree from Yunnan University and doctor's degree from Sichuan University in 1986, 1989 and 1998 respectively, majoring in Mathematics / applied mathematics. At present, he is the chief professor of Southeast University, Dean of School of mathematics, director of Jiangsu Key Laboratory of network group intelligence, and director of complex systems and network science research center. He won the first national innovation competition award and the international Obada award. He is a global highly cited scientist in the fields of engineering, computer science and mathematics, an IEEE member, an academician of the European Academy of Sciences, an academician of the European Academy of Sciences and arts, an academician of the Pakistan Academy of Sciences and an academician of the International Academy of systems and Control Sciences. Research directions include complex networks and complex systems, neurodynamics and optimization, and multi-agent systems.
Professor Liu Yang received his bachelor's degree in mathematics from Zhejiang Normal University in 2003 and his doctor's degree from Tongji University in 2008. At present, he is a professor of mathematics and Computer College of Zhejiang Normal University and deputy director of Personnel Department of Zhejiang Normal University. Served as editorial board member of near process lett. He was awarded the outstanding young scholars fund of Zhejiang Province, the outstanding doctoral thesis award of Shanghai City, and was selected as the global high cited scientist of Thomson Reuters / Kerui Wei'an, and the outstanding teacher of Zhejiang Province. The research direction includes hybrid system and logic system.
Professor Lu Jianquan, 2003