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set stability for switched Boolean networks with open-loop and closed-loop switching signals

Science China(Information Sciences) 2018年第9期61卷 232-240页

作者： Xiaohua LI Jianquan LU Jianlong QIU Xiangyong CHEN Xiaodi LI Fuad E.ALSAADI School of Automation and Engineering and Key Laboratory of Complex Systems and Intelligent Computing in Universities of Shandong Linyi University School of Mathematics and Statistics Shandong Normal University School of Mathematics Southeast University Department of Electrical and Computer Engineering King Abdulaziz University

This paper mainly analyzes the set stability of switched Boolean networks(SBNs) by considering two different methods of switching signals in the form of open-loop and closed-loop switching. First, the definitions of set stability are proposed for SBNs with such switching signals. Then, we propose two different algorithms to find the largest open-loop switching invariant set and largest closed-loop switching invariant set. Furthermore, the corresponding set stability conditions for SBNs are given in each case. In addition,the constructive procedures are presented to design the switching signal sequence to achieve set stability under the two different methods of switching signals. Finally, the effectiveness of the proposed algorithms and research results are demonstrated using two numerical examples.

关键词： switched Boolean network set stability semi-tensor product switching signal design

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set stability of Probabilistic Time-Delay Boolean Networks with Impulsive Effect

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Journal of Systems Science & Complexity 2021年第6期34卷 2182-2194页

作者： SHI Shengnan XU Yong School of Economics and Management Hebei University of TechnologyTianjin 300401China School of Science Hebei University of TechnologyTianjin 300401China

This paper investigates the set stability of probabilistic time-delay Boolean networks(PTDBN)with impulsive ***,using the algebraic state space representation,an equivalent stochastic system is established for PTDBN with impulsive ***,based on the probabilistic state transition matrix,a necessary and sufficient condition is presented for the set stability of PTDBN with impulsive ***,the obtained new result is applied to the networked evolutionary game with memories.

关键词： Boolean networks impulsive effect networked evolutionary game set stability

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set stability of Switched Boolean Networks with Function Perturbation

Set Stability of Switched Boolean Networks with Function Per...

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第43届中国控制会议

作者： Jinsuo Wang Xinling Li Xiujun Cao Shihua Fu Research Center of Semi-tensor Product of Matrices: Theory and Applications

This article investigates the set stability of switched Boolean networks(SBNs) with function perturbation under arbitrary switching signal. Firstly, the system is converted into algebraic form utilizing semi-tensor product(STP) of ***, based on algebraic expression, four cases are considered. And then, two theorems are obtained, which can be used to determine whether an SBN is set stability after function perturbation. In addition, according to the theorems, two corresponding corollaries are derived. Finally, an example is given to verify the correctness of the conclusion.

关键词： Switched Boolean networks semi-tensor product of matrices set stability function perturbation arbitrary switching signal

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set stability and Controllability for Switched Nonhomogeneous Linear Systems

Set Stability and Controllability for Switched Nonhomogeneou...

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第25届中国控制会议

作者： Cheng Daizhan,Hu Xiaoming Institute of Systems Science, AMSS,Chinese Academy of Sciences,Beijing 100080,P. R. China Optimization and Systems Theory, Royal Institute of Technology,Stockholm, Sweden

＜正＞In this paper we consider some control problems of switched non-homogeneous linear systems. First,the set stability of switched non-homogeneous linear systems is considered. It is proved that as the linear parts have a common quadratic Lyapunov function the set stability is assured. The problem of searching smallest attracting set is then considered. Then we assume the switching law is controllable and investigate the controllability condition within the attracting region. Finally, we consider the aggregation and the control of aggregation of fiocking behavior. Particularly,the results obtained are implemented to analyzing and manipulating of a group of mobile robots.

关键词： Switched system set stability Common Quadratic Lyapunov Function Controllability

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set stability of Boolean Networks via Quotient Mappings

Set Stability of Boolean Networks via Quotient Mappings

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第26届中国控制与决策会议

作者： Wang Pan Guo Yuqian School of Information Science and Engineering Central South University

ISBN: (纸本)9781479937097

The Boolean network is a powerful tool in describing, analyzing, and simulating the cellular networks. In this paper, we investigate stability of given subsets（or set stability） for Boolean networks which includes synchronization problem as a special case. First of all, based on the semi-tensor product of matrices and the algebraic expression of Boolean networks, we derive some necessary and sufficient conditions for set stability. Then we propose a quotient mapping method the main idea of which is to regard the largest invariant set contained in a pre-specified subset as a single point and then transfer the set stability problem of the original Boolean network to the stability of the multi-logical systems in the quotient space. Examples are also provided to explain the results obtained.

关键词： Boolean network set stability quotient mappings semi-tensor product

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set stability of Boolean Networks From Initial set to Destination set

Set Stability of Boolean Networks From Initial Set to Destin...

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第40届中国控制会议

作者： Wen Liu Changxi Li Shihua Fu Jianli Zhao Lijuan Guo Shujun Tian School of Mathematical Sciences Liaocheng University School of Mathematics Shandong University State Grid Technology Institute

This paper considers set stability of Boolean networks（BNs） from initial set to destination set. The existing set stability is the stability that for any initial state, i.e., there exists a finite time, such that the trajectory from any initial state belongs to the given subset after finite time. But in some cases, the interests may be not the whole state space, only a subset of the whole state space, such as the partial synchronization of a collection of locally interconnected systems. In this paper, we study the the set stability of BNs from initial set to destination set. The technique used in this paper is semi-tensor product of matrices. First, a necessary and sufficient condition is presented for set stability from initial set to destination set. Then as the application, stabilization of Boolean control network（BCN） via state-based networked controller is considered and a necessary and sufficient condition is provided. Finally, an example is provided to interpret the results.

关键词： Semi-tensor product of matrices set stability State-based networked controller Boolean networks

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Asymptotical stability of continuous-time probabilistic logic networks based on transition rate

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Science China(Information Sciences) 2023年第3期66卷 204-213页

作者： Zhitao LI Yuqian GUO Weihua GUI School of Automation Central South University

The evolution of the probability distribution for a continuous-time probabilistic logic network(CT-PLN) is determined by its transition rate matrix(TRM), which is a constant matrix that can be identified from the observed data. In the literature, the asymptotical stability criterion of a CT-PLN is expressed by using the transition probability matrix of discretization under a specific sampling period. In this paper, we derive several improved criteria that are directly expressed in terms of the TRM. We prove that a CT-PLN is asymptotically stable with respect to a given set if and only if the largest invariant subset(LIS) in the set is non-empty and the complementary set of the LIS contains no invariant subset. Thus,the asymptotical stability of a CT-PLN can be verified by applying the existing LIS algorithm twice. In addition, the condition that the complementary set of the LIS contains no invariant subset can be replaced by one of the more easily verifiable conditions, namely, the reachability condition and the rank *** reachability condition states that the LIS is reachable from every state outside, and the rank condition states that the complementary sub-matrix of the TRM with respect to the LIS is of full rank. For a CT-PLN being not asymptotically stable, a method of determining the domain of attraction is proposed. Finally,examples are provided to demonstrate the advantages of the proposed method.

关键词： asymptotical stability continuous-time probabilistic logic network semi-tensor product of matrices set stability

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Attractor Analysis of Conjunctive Boolean Networks via Dependency Graph

Attractor Analysis of Conjunctive Boolean Networks via Depen...

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第43届中国控制会议

作者： Mengyuan Qin Haitao Li Xinrong Yang School of Mathematics and Statistics Shandong Normal University

Graph theory is an effective method to analyze the network structure of Boolean *** on the dependency graph,this paper focuses on the cyclic structure of conjunctive Boolean networks(CBNs).Firstly,it is proved that the length of any limit cycle divides the loop number,and it reveals that the attractor of CBNs only contains fixed points if and only if the loop number of the dependency graph is ***,with the help of adjacency matrix,the transition period is determined when the CBN reaches the set ***,based on the relationship between the power of adjacency matrix,the loop number of dependency graph and network iteration,a method is proposed to find the fixed point and limit cycle of ***,an example is given to show the effectiveness of the main results.

关键词： Conjunctive Boolean network Attractor set stability Adjacency matrix Loop number

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stability of Switched Boolean Networks with Restricted Successors

Stability of Switched Boolean Networks with Restricted Succe...

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第40届中国控制会议

作者： Yuxia Chen Yuqian Guo Weihua Gui School of Automation Central South University

This study proposes a novel method for the set stability analysis of switched Boolean networks（SBNs） under restricted successors based on the semi-tensor product（STP） of matrices. We demonstrate that all allowable switching signals can be generated by a logic dynamical system（LDS） with free inputs, termed as the generator of switching signals（GSS）. Thus, we regard the GSS as a part of the system through series interconnection and transfer the original restricted SBN into a logic system with free inputs. Then, we merge the GSS and the SBN using the STP and prove that the set stability of the original restricted SBN is equivalent to that of the merged LDS under arbitrary switching. Based on this, a necessary and sufficient condition of set stability is obtained. Further, a numerical example is provided to illustrate the use of the proposed result.

关键词： switched Boolean networks restricted switching semi-tensor product of matrices set stability the maximum invariant subset

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