In this paper, we discuss how to transform the disordered phase into an ordered phase in random Boolean networks. To increase the effectiveness, a control scheme is proposed, which periodically freezes a fraction of t...In this paper, we discuss how to transform the disordered phase into an ordered phase in random Boolean networks. To increase the effectiveness, a control scheme is proposed, which periodically freezes a fraction of the network based on the average sensitivity of Boolean functions of the nodes. Theoretical analysis is carried out to estimate the expected critical value of the fraction, and shows that the critical value is reduced using this scheme compared to that of randomly freezing a fraction of the nodes. Finally, the simulation is given for illustrating the effectiveness of the proposed method.展开更多
Autonomous Boolean networks(ABNs)have been successfully applied to the generation of random number due to their complex nonlinear dynamics and convenient on-chip integration.Most of the ABNs used for random number gen...Autonomous Boolean networks(ABNs)have been successfully applied to the generation of random number due to their complex nonlinear dynamics and convenient on-chip integration.Most of the ABNs used for random number generators show a symmetric topology,despite their oscillations dependent on the inconsistency of time delays along links.To address this issue,we suggest an asymmetrical autonomous Boolean network(aABN)and show numerically that it provides large amplitude oscillations by using equal time delays along links and the same logical gates.Experimental results show that the chaotic features of aABN are comparable to those of symmetric ABNs despite their being made of fewer nodes.Finally,we put forward a random number generator based on aABN and show that it generates the random numbers passing the NIST test suite at 100 Mbits/s.The unpredictability of the random numbers is analyzed by restarting the random number generator repeatedly.The aABN may replace symmetrical ABNs in many applications using fewer nodes and,in turn,reducing power consumption.展开更多
One of the typical properties of biological systems is the law o f conservation o f mass,that is,the property that the mass must remain constant over time in a closed chemical reaction system.However,it is known that ...One of the typical properties of biological systems is the law o f conservation o f mass,that is,the property that the mass must remain constant over time in a closed chemical reaction system.However,it is known that Boolean networks,which are a promising model of biological networks,do not always represent the conservation law.This paper thus addresses a kind of conservation law as a generic property of Boolean networks.In particular,we consider the problem of finding network structures on which,for any Boolean operation on nodes,the number of active nodes,i.ev nodes whose state is one,is constant over time.As a solution to the problem,we focus on the strongly-connected network structures and present a necessary and sufficient condition.展开更多
Design of control strategies for gene regulatory networks is a challenging and important topic in systems biology. In this paper, the problem of finding both a minimum set of control nodes (control inputs) and a contr...Design of control strategies for gene regulatory networks is a challenging and important topic in systems biology. In this paper, the problem of finding both a minimum set of control nodes (control inputs) and a controller is studied. A control node corresponds to a gene that expression can be controlled. Here, a Boolean network is used as a model of gene regulatory networks, and control specifications on attractors, which represent cell types or states of cells, are imposed. It is important to design a gene regulatory network that has desired attractors and has no undesired attractors. Using a matrix-based representation of BNs, this problem can be rewritten as an integer linear programming problem. Finally, the proposed method is demonstrated by a numerical example on a WNT5A network, which is related to melanoma.展开更多
In this paper, verification of real-time pricing systems of electricity is considered using a probabilistic Boolean network (PBN). In real-time pricing systems, electricity conservation is achieved by manipulating the...In this paper, verification of real-time pricing systems of electricity is considered using a probabilistic Boolean network (PBN). In real-time pricing systems, electricity conservation is achieved by manipulating the electricity price at each time. A PBN is widely used as a model of complex systems, and is appropriate as a model of real-time pricing systems. Using the PBN-based model, real-time pricing systems can be quantitatively analyzed. In this paper, we propose a verification method of real-time pricing systems using the PBN-based model and the probabilistic model checker PRISM. First, the PBN-based model is derived. Next, the reachability problem, which is one of the typical verification problems, is formulated, and a solution method is derived. Finally, the effectiveness of the proposed method is presented by a numerical example.展开更多
In this paper,the issues of both reconstructibility analysis and state estimation are investigated for locally reconstructible Boolean networks(BNs),where the pinning control is employed to design a special control se...In this paper,the issues of both reconstructibility analysis and state estimation are investigated for locally reconstructible Boolean networks(BNs),where the pinning control is employed to design a special control sequence.First,this paper will focus on dealing with state unreconstructible cycle based on state set-estimation theory,and the concept of set-to-set reachability is proposed.Second,the locally reconstructible BNs are transformed to Boolean control networks(BCNs)by pinning control technique,where a logical matrix is designed by a special algorithm such that all states in the unreconstructible initial state set can evolve into the reconstructible state set,simultaneously.Third,a sufficient condition for the existence of a free Boolean control sequence is obtained,which guarantees that a locally reconstructible BN can be transformed into a reconstructible one.Besides,an optimization control algorithm is proposed to generate pinning control sequence and further optimize the reconstructibility of BNs.A kind of pinning control-based state estimation method is also developed.Finally,an example is provided to show the feasibility of the proposed methods.展开更多
Set stabilization is one of the essential problems in engineering systems, and self-triggered control(STC) can save the storage space for interactive information, and can be successfully applied in networked control s...Set stabilization is one of the essential problems in engineering systems, and self-triggered control(STC) can save the storage space for interactive information, and can be successfully applied in networked control systems with limited communication resources. In this study, the set stabilization problem and STC design of Boolean control networks are investigated via the semi-tensor product technique. On the one hand, the largest control invariant subset is calculated in terms of the strongly connected components of the state transition graph, by which a graph-theoretical condition for set stabilization is derived. On the other hand, a characteristic function is exploited to determine the triggering mechanism and feasible controls. Based on this, the minimum-time and minimum-triggering open-loop, state-feedback and output-feedback STCs for set stabilization are designed,respectively. As classic applications of self-triggered set stabilization, self-triggered synchronization, self-triggered output tracking and self-triggered output regulation are discussed as well. Additionally, several practical examples are given to illustrate the effectiveness of theoretical results.展开更多
Background:A novel data-driven Boolean model,namely,the fundamental Boolean model(FBM),has been proposed to draw genetic regulatory insights into gene activation,inhibition,and protein decay,published in 2018.This nov...Background:A novel data-driven Boolean model,namely,the fundamental Boolean model(FBM),has been proposed to draw genetic regulatory insights into gene activation,inhibition,and protein decay,published in 2018.This novel Boolean model facilitates the analysis of the activation and inhibition pathways.However,the novel model does not handle the situation well,where genetic regulation might require more time steps to complete.Methods:Here,we propose extending the fundamental Boolean modelling to address the issue that some gene regulations might require more time steps to complete than others.We denoted this extension model as the temporal fundamental Boolean model(TFBM)and related networks as the temporal fundamental Boolean networks(TFBNs).The leukaemia microarray datasets downloaded from the National Centre for Biotechnology Information have been adopted to demonstrate the utility of the proposed TFBM and TFBNs.Results:We developed the TFBNs that contain 285 components and 2775 Boolean rules based on TFBM on the leukaemia microarray datasets,which are in the form of short-time series.The data contain gene expression measurements for 13 GC-sensitive children under therapy for acute lymphoblastic leukaemia,and each sample has three time points:0 hour(before GC treatment),6/8 hours(after GC treatment)and 24 hours(after GC treatment).Conclusion:We conclude that the proposed TFBM unlocks their predecessor’s limitation,Le.,FBM,that could help pharmaceutical agents identify any side effects on clinic-related data.New hypotheses could be identified by analysing the extracted fundamental Boolean networks and analysing their up-regulatory and down-regulatory pathways.展开更多
This paper addresses the synchronization problem of Boolean networks.Based on the matrix expression of logic,solvability conditions and design procedures of the synchronization of Boolean networks with outputs are giv...This paper addresses the synchronization problem of Boolean networks.Based on the matrix expression of logic,solvability conditions and design procedures of the synchronization of Boolean networks with outputs are given for both open-loop and feedback control.Necessary and sufficient conditions on open-loop control are proposed first with a constructive design procedure.Then sufficient condition for the feedback control case is obtained,and corresponding design procedure is proposed with the help of algorithms to solve logic matrix equations.Numerical examples are also provided to illustrate the proposed control design.展开更多
This paper investigates the observabihty of free Boolean networks by using the semi-tensor product method,and presents some new results.First,the concept of observability for free Boolean networks is proposed,based on...This paper investigates the observabihty of free Boolean networks by using the semi-tensor product method,and presents some new results.First,the concept of observability for free Boolean networks is proposed,based on which and the algebraic form of Boolean networks,a kind of observabihty matrix is constructed.Second,by the observability matrix,a new necessary and sufficient condition is given for the observability of Boolean networks.Third,the concept of observabihty index for observable Boolean networks is defined,and an algorithm is established to calculate the observability index.Finally,a practical example of D.Melanogaster segmentation polarity gene networks is studied to support our new results.The study of the illustrative example shows that the new results obtained in this paper are very effective in investigating the observability of free Boolean networks.展开更多
This paper studies the state/output synchronization of switched Boolean networks （SBNs） with impulsive effects via the algebraic state space representation （ASSR） approach. First, an algebraic form is established ...This paper studies the state/output synchronization of switched Boolean networks （SBNs） with impulsive effects via the algebraic state space representation （ASSR） approach. First, an algebraic form is established for SBNs with impulsive effects via ASSR. Second, based on the algebraic form, some necessary and sufficient conditions are presented for the state/output synchronization of SBNs with impulsive effects under arbitrary switching signals. Third, two special kinds of switching signals, that is, free switching signal and feedback switching signal, are considered for the state synchroniza-tion of SBNs with impulsive effects. Finally, two illustrative examples are worked out to show the effectiveness of the obtained results.展开更多
We investigate the stability of Boolean networks(BNs)with impulses triggered by both states and random factors.A hybrid index model is used to describe impulsive BNs.First,several necessary and sufficient conditions f...We investigate the stability of Boolean networks(BNs)with impulses triggered by both states and random factors.A hybrid index model is used to describe impulsive BNs.First,several necessary and sufficient conditions for forward completeness are obtained.Second,based on the stability criterion of probabilistic BNs and the forward completeness criterion,the necessary and sufficient conditions for the finite-time stability with probability one and the asymptotical stability in distribution are presented.The relationship between these two kinds of stability is discussed.Last,examples and time-domain simulations are provided to illustrate the obtained results.展开更多
This paper investigates the set stability of probabilistic time-delay Boolean networks(PTDBN)with impulsive effect.Firstly,using the algebraic state space representation,an equivalent stochastic system is established ...This paper investigates the set stability of probabilistic time-delay Boolean networks(PTDBN)with impulsive effect.Firstly,using the algebraic state space representation,an equivalent stochastic system is established for PTDBN with impulsive effect.Then,based on the probabilistic state transition matrix,a necessary and sufficient condition is presented for the set stability of PTDBN with impulsive effect.Finally,the obtained new result is applied to the networked evolutionary game with memories.展开更多
In this study,the complete synchronization problem of coupled delayed Boolean networks(CDBNs)is investigated.The state delays and output delays may not be equal,and the state delay in each Boolean network may be diffe...In this study,the complete synchronization problem of coupled delayed Boolean networks(CDBNs)is investigated.The state delays and output delays may not be equal,and the state delay in each Boolean network may be different in the proposed CDBN model.Based on the semi-tensor product of matrices,a necessary and sufficient condition for the complete synchronization of CDBNs is obtained.Then,an efficient algorithm for solving the synchronization of CDBNs is provided.Finally,numerical examples are presented to demonstrate the effectiveness of our algorithm.展开更多
The aim of this survey paper is to provide the state of the art of the research on control and optimal control of Boolean control networks,under the assumption that all the state variables are accessible and hence ava...The aim of this survey paper is to provide the state of the art of the research on control and optimal control of Boolean control networks,under the assumption that all the state variables are accessible and hence available for feedback.Necessary and sufficient conditions for stabilisability to a limit cycle or to an equilibrium point are given.Additionally,it is shown that when such conditions are satisfied,stabilisation can always be achieved by means of state feedback.Analogous results are obtained for the safe control problem that is investigated for the first time in this survey.Finite and infinite horizon optimal control are subsequently considered,and solution algorithms are provided,based on suitable adaptations of theRiccati difference and algebraic equations.Finally,an appropriate definition of the cost function allows to restate and to solve both stabilisation and safe control as infinite horizon optimal control problems.展开更多
In genetic regulatory networks,a stable configuration can represent the evolutionary behavior of cell death or unregulated growth in genes.We present analytical investigations on output feedback stabilizer design of B...In genetic regulatory networks,a stable configuration can represent the evolutionary behavior of cell death or unregulated growth in genes.We present analytical investigations on output feedback stabilizer design of Boolean networks(BNs)to achieve global stabilization via the semi-tensor product method.Based on network structure information describing coupling connections among nodes,an output feedback stabilizer is designed to achieve global stabilization.Compared with the traditional pinning control design,the output feedback stabilizer design is not based on the state transition matrix of BNs,which can efficiently determine pinning control nodes and reduce computational complexity.Our proposed method is efficient in that the calculation of the state transition matrix with dimension 2^n×2^n is avoided;here n is the number of nodes in a BN.Finally,a signal transduction network and a D.melanogaster segmentation polarity gene network are presented to show the efficiency of the proposed method.Results are shown to be simple and concise,compared with traditional pinning control for BNs.展开更多
This paper investigates the Morgan＇s problem of Boolean control networks. Based on the matrix expression of logical functions, two key steps are proposed to solve the problem. First, the Boolean control network is co...This paper investigates the Morgan＇s problem of Boolean control networks. Based on the matrix expression of logical functions, two key steps are proposed to solve the problem. First, the Boolean control network is converted into an output- decomposed form by constructing a set of consistent outputfriendly subspaces, and a necessary and sufficient condition for the existence of the consistent output-friendly subspaces is obtained. Secondly, a type of state feedback controllers are designed to solve the Morgan＇s problem if it is solvable. By solving a set of matrix equations, a necessary and sufficient condition for converting an output-decomposed form to an input-output decomposed form is given, and by verifying the output controllability matrix, the solvability of Morgan＇s problem is obtained.展开更多
Observability is a fundamental property of a partially observed dynamical system,which means whether one can use an input sequence and the corresponding output sequence to determine the initial state.Observability pro...Observability is a fundamental property of a partially observed dynamical system,which means whether one can use an input sequence and the corresponding output sequence to determine the initial state.Observability provides bases for many related problems,such as state estimation,identification,disturbance decoupling,controller synthesis,etc.Until now,fundamental improvement has been obtained in observability of Boolean control networks(BCNs)mainly based on two methods-Edward F.Moore's partition and our observability graph or their equivalent representations found later based on the semitensor product(STP)of matrices(where the STP was proposed by Daizhan Cheng),including necessary and sufficient conditions for different types of observability,extensions to probabilistic Boolean networks(PBNs)and singular BCNs,even to nondeterministic finite-transition systems(NFTSs);and the development(with the help of the STP of matrices)in related topics,such as com-putation of smallest invariant dual subspaces of BNs containing a set of Boolean functions,multiple-experiment observability verification/decomposition in BCNs,disturbance decoupling in BCNs,etc.This paper provides a thorough survey for these topics.The contents of the paper are guided by the above two methods.First,we show that Moore's partition-based method closely relates the following problems:computation of smallest invariant dual subspaces of BNs,multiple-experiment observ-ability verification/decomposition in BCNs,and disturbance decoupling in BCNs.However,this method does not apply to other types of observability or nondeterministic systems.Second,we show that based on our observability graph,four different types of observability have been verified in BCNs,verification results have also been extended to PBNs,singular BCNs,and NFTSs.In addition,Moore's partition also shows similarities between BCNs and linear time-invariant(LTI)control systems,e.g.,smallest invariant dual subspaces of BNs containing a set of Boolean functions in BCNs vs unobservable subspaces of LTI control systems,the forms of quotient systems based on observability decomposition in both types of systems.However,there are essential differences between the two types of systems,e.g.,"all plausible definitions of observability in LTI control systems turn out to be equivalent"(by Walter M.Wonham 1985),but there exist nonequivalent definitions of observability in BCNs;the quotient system based on observability decomposition always exists in an LTI control system,while a quotient system based on multiple-experiment observability decomposition does not always exist in a BCN.展开更多
We investigate the problem of finding optimal one-bit perturbation that maximizes the size of the basin of attractions(BOAs)of desired attractors and minimizes the size of the BOAs of undesired attractors for large-sc...We investigate the problem of finding optimal one-bit perturbation that maximizes the size of the basin of attractions(BOAs)of desired attractors and minimizes the size of the BOAs of undesired attractors for large-scale Boolean networks by cascading aggregation.First,via the aggregation,a necessary and sufficient condition is given to ensure the invariance of desired attractors after one-bit perturbation.Second,an algorithm is proposed to identify whether the one-bit perturbation will cause the emergence of new attractors or not.Next,the change of the size of BOAs after one-bit perturbation is provided in an algorithm.Finally,the efficiency of the proposed method is verified by a T-cell receptor network.展开更多
Boolean control network consists of a set of Boolean variables whose state is determined by other variables in the network. Boolean network is used for modeling complex system. In this paper, we have presented a model...Boolean control network consists of a set of Boolean variables whose state is determined by other variables in the network. Boolean network is used for modeling complex system. In this paper, we have presented a model of a context-aware system used in smart home based on Boolean control networks. This modeling describes the relationship between the context elements (person, time, location, and activity) and services (Morning Call, Sleeping, Guarding, Entertainment, and normal), which is effective to logical inference. We apply semi tensor matrix product to describe the dynamic of the system. This matrix form of expression is a convenient and reasonable way to design logic control system.展开更多
基金supported in part by the National Natural Science Foundation of China (Grant Nos. 60874018,60736022,and 60821091)
文摘In this paper, we discuss how to transform the disordered phase into an ordered phase in random Boolean networks. To increase the effectiveness, a control scheme is proposed, which periodically freezes a fraction of the network based on the average sensitivity of Boolean functions of the nodes. Theoretical analysis is carried out to estimate the expected critical value of the fraction, and shows that the critical value is reduced using this scheme compared to that of randomly freezing a fraction of the nodes. Finally, the simulation is given for illustrating the effectiveness of the proposed method.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61731014,61671316,61961136002,and 61927811)the Fund from the Shanxi Scholarship Council of China(Grant No.2017-key-2).
文摘Autonomous Boolean networks(ABNs)have been successfully applied to the generation of random number due to their complex nonlinear dynamics and convenient on-chip integration.Most of the ABNs used for random number generators show a symmetric topology,despite their oscillations dependent on the inconsistency of time delays along links.To address this issue,we suggest an asymmetrical autonomous Boolean network(aABN)and show numerically that it provides large amplitude oscillations by using equal time delays along links and the same logical gates.Experimental results show that the chaotic features of aABN are comparable to those of symmetric ABNs despite their being made of fewer nodes.Finally,we put forward a random number generator based on aABN and show that it generates the random numbers passing the NIST test suite at 100 Mbits/s.The unpredictability of the random numbers is analyzed by restarting the random number generator repeatedly.The aABN may replace symmetrical ABNs in many applications using fewer nodes and,in turn,reducing power consumption.
基金supported by Grant-in-Aid for Scientific Research(B)#17H03280 from the Ministry of Education,Culture,Sports,Science and Technology of Japan.
文摘One of the typical properties of biological systems is the law o f conservation o f mass,that is,the property that the mass must remain constant over time in a closed chemical reaction system.However,it is known that Boolean networks,which are a promising model of biological networks,do not always represent the conservation law.This paper thus addresses a kind of conservation law as a generic property of Boolean networks.In particular,we consider the problem of finding network structures on which,for any Boolean operation on nodes,the number of active nodes,i.ev nodes whose state is one,is constant over time.As a solution to the problem,we focus on the strongly-connected network structures and present a necessary and sufficient condition.
文摘Design of control strategies for gene regulatory networks is a challenging and important topic in systems biology. In this paper, the problem of finding both a minimum set of control nodes (control inputs) and a controller is studied. A control node corresponds to a gene that expression can be controlled. Here, a Boolean network is used as a model of gene regulatory networks, and control specifications on attractors, which represent cell types or states of cells, are imposed. It is important to design a gene regulatory network that has desired attractors and has no undesired attractors. Using a matrix-based representation of BNs, this problem can be rewritten as an integer linear programming problem. Finally, the proposed method is demonstrated by a numerical example on a WNT5A network, which is related to melanoma.
文摘In this paper, verification of real-time pricing systems of electricity is considered using a probabilistic Boolean network (PBN). In real-time pricing systems, electricity conservation is achieved by manipulating the electricity price at each time. A PBN is widely used as a model of complex systems, and is appropriate as a model of real-time pricing systems. Using the PBN-based model, real-time pricing systems can be quantitatively analyzed. In this paper, we propose a verification method of real-time pricing systems using the PBN-based model and the probabilistic model checker PRISM. First, the PBN-based model is derived. Next, the reachability problem, which is one of the typical verification problems, is formulated, and a solution method is derived. Finally, the effectiveness of the proposed method is presented by a numerical example.
基金supported in part by the National Nature Science Foundation of China under Grant No.62373137Natural Science Foundation of Henan Province under Grant No.232300420147。
文摘In this paper,the issues of both reconstructibility analysis and state estimation are investigated for locally reconstructible Boolean networks(BNs),where the pinning control is employed to design a special control sequence.First,this paper will focus on dealing with state unreconstructible cycle based on state set-estimation theory,and the concept of set-to-set reachability is proposed.Second,the locally reconstructible BNs are transformed to Boolean control networks(BCNs)by pinning control technique,where a logical matrix is designed by a special algorithm such that all states in the unreconstructible initial state set can evolve into the reconstructible state set,simultaneously.Third,a sufficient condition for the existence of a free Boolean control sequence is obtained,which guarantees that a locally reconstructible BN can be transformed into a reconstructible one.Besides,an optimization control algorithm is proposed to generate pinning control sequence and further optimize the reconstructibility of BNs.A kind of pinning control-based state estimation method is also developed.Finally,an example is provided to show the feasibility of the proposed methods.
基金supported by the National Natural Science Foundation of China (62273201,62173209,72134004,62303170)the Research Fund for the Taishan Scholar Project of Shandong Province of China (TSTP20221103)。
文摘Set stabilization is one of the essential problems in engineering systems, and self-triggered control(STC) can save the storage space for interactive information, and can be successfully applied in networked control systems with limited communication resources. In this study, the set stabilization problem and STC design of Boolean control networks are investigated via the semi-tensor product technique. On the one hand, the largest control invariant subset is calculated in terms of the strongly connected components of the state transition graph, by which a graph-theoretical condition for set stabilization is derived. On the other hand, a characteristic function is exploited to determine the triggering mechanism and feasible controls. Based on this, the minimum-time and minimum-triggering open-loop, state-feedback and output-feedback STCs for set stabilization are designed,respectively. As classic applications of self-triggered set stabilization, self-triggered synchronization, self-triggered output tracking and self-triggered output regulation are discussed as well. Additionally, several practical examples are given to illustrate the effectiveness of theoretical results.
文摘Background:A novel data-driven Boolean model,namely,the fundamental Boolean model(FBM),has been proposed to draw genetic regulatory insights into gene activation,inhibition,and protein decay,published in 2018.This novel Boolean model facilitates the analysis of the activation and inhibition pathways.However,the novel model does not handle the situation well,where genetic regulation might require more time steps to complete.Methods:Here,we propose extending the fundamental Boolean modelling to address the issue that some gene regulations might require more time steps to complete than others.We denoted this extension model as the temporal fundamental Boolean model(TFBM)and related networks as the temporal fundamental Boolean networks(TFBNs).The leukaemia microarray datasets downloaded from the National Centre for Biotechnology Information have been adopted to demonstrate the utility of the proposed TFBM and TFBNs.Results:We developed the TFBNs that contain 285 components and 2775 Boolean rules based on TFBM on the leukaemia microarray datasets,which are in the form of short-time series.The data contain gene expression measurements for 13 GC-sensitive children under therapy for acute lymphoblastic leukaemia,and each sample has three time points:0 hour(before GC treatment),6/8 hours(after GC treatment)and 24 hours(after GC treatment).Conclusion:We conclude that the proposed TFBM unlocks their predecessor’s limitation,Le.,FBM,that could help pharmaceutical agents identify any side effects on clinic-related data.New hypotheses could be identified by analysing the extracted fundamental Boolean networks and analysing their up-regulatory and down-regulatory pathways.
基金supported by the National Natural Science Foundation of China under Grant No.61174071
文摘This paper addresses the synchronization problem of Boolean networks.Based on the matrix expression of logic,solvability conditions and design procedures of the synchronization of Boolean networks with outputs are given for both open-loop and feedback control.Necessary and sufficient conditions on open-loop control are proposed first with a constructive design procedure.Then sufficient condition for the feedback control case is obtained,and corresponding design procedure is proposed with the help of algorithms to solve logic matrix equations.Numerical examples are also provided to illustrate the proposed control design.
基金supported by the National Natural Science Foundation of China under Grant Nos.61034007,61174036,and 61374065the Research Fund for the Taishan Scholar Project of Shandong Province of China
文摘This paper investigates the observabihty of free Boolean networks by using the semi-tensor product method,and presents some new results.First,the concept of observability for free Boolean networks is proposed,based on which and the algebraic form of Boolean networks,a kind of observabihty matrix is constructed.Second,by the observability matrix,a new necessary and sufficient condition is given for the observability of Boolean networks.Third,the concept of observabihty index for observable Boolean networks is defined,and an algorithm is established to calculate the observability index.Finally,a practical example of D.Melanogaster segmentation polarity gene networks is studied to support our new results.The study of the illustrative example shows that the new results obtained in this paper are very effective in investigating the observability of free Boolean networks.
基金The research was supported by the National Natural Science Foundation of China under grant 61503225, the Natural Science Fund for Distinguished Young Scholars of Shandong Province under grant JQ201613, and the Natural Science Foundation of Shandong Province under grant ZR2015FQ003.
文摘This paper studies the state/output synchronization of switched Boolean networks （SBNs） with impulsive effects via the algebraic state space representation （ASSR） approach. First, an algebraic form is established for SBNs with impulsive effects via ASSR. Second, based on the algebraic form, some necessary and sufficient conditions are presented for the state/output synchronization of SBNs with impulsive effects under arbitrary switching signals. Third, two special kinds of switching signals, that is, free switching signal and feedback switching signal, are considered for the state synchroniza-tion of SBNs with impulsive effects. Finally, two illustrative examples are worked out to show the effectiveness of the obtained results.
基金Project supported by the National Natural Science Foundation of China(Nos.61873284,61473315,and 61321003)。
文摘We investigate the stability of Boolean networks(BNs)with impulses triggered by both states and random factors.A hybrid index model is used to describe impulsive BNs.First,several necessary and sufficient conditions for forward completeness are obtained.Second,based on the stability criterion of probabilistic BNs and the forward completeness criterion,the necessary and sufficient conditions for the finite-time stability with probability one and the asymptotical stability in distribution are presented.The relationship between these two kinds of stability is discussed.Last,examples and time-domain simulations are provided to illustrate the obtained results.
基金supported by the National Natural Science Foundation of China under Grant No.71371186。
文摘This paper investigates the set stability of probabilistic time-delay Boolean networks(PTDBN)with impulsive effect.Firstly,using the algebraic state space representation,an equivalent stochastic system is established for PTDBN with impulsive effect.Then,based on the probabilistic state transition matrix,a necessary and sufficient condition is presented for the set stability of PTDBN with impulsive effect.Finally,the obtained new result is applied to the networked evolutionary game with memories.
基金Project supported by the National Natural Science Foundation of China(No.61503115)the Fundamental Research Funds for the Central Universities,China(No.JZ2017HGTB0188)the National Innovative Program for College Students,China(No.201810359056)。
文摘In this study,the complete synchronization problem of coupled delayed Boolean networks(CDBNs)is investigated.The state delays and output delays may not be equal,and the state delay in each Boolean network may be different in the proposed CDBN model.Based on the semi-tensor product of matrices,a necessary and sufficient condition for the complete synchronization of CDBNs is obtained.Then,an efficient algorithm for solving the synchronization of CDBNs is provided.Finally,numerical examples are presented to demonstrate the effectiveness of our algorithm.
文摘The aim of this survey paper is to provide the state of the art of the research on control and optimal control of Boolean control networks,under the assumption that all the state variables are accessible and hence available for feedback.Necessary and sufficient conditions for stabilisability to a limit cycle or to an equilibrium point are given.Additionally,it is shown that when such conditions are satisfied,stabilisation can always be achieved by means of state feedback.Analogous results are obtained for the safe control problem that is investigated for the first time in this survey.Finite and infinite horizon optimal control are subsequently considered,and solution algorithms are provided,based on suitable adaptations of theRiccati difference and algebraic equations.Finally,an appropriate definition of the cost function allows to restate and to solve both stabilisation and safe control as infinite horizon optimal control problems.
基金Project supported by the National Natural Science Foundation of China(Nos.61903339,61321003,and 11671361)the Zhejiang Provincial Natural Science Foundation of China(No.LD19A010001)。
文摘In genetic regulatory networks,a stable configuration can represent the evolutionary behavior of cell death or unregulated growth in genes.We present analytical investigations on output feedback stabilizer design of Boolean networks(BNs)to achieve global stabilization via the semi-tensor product method.Based on network structure information describing coupling connections among nodes,an output feedback stabilizer is designed to achieve global stabilization.Compared with the traditional pinning control design,the output feedback stabilizer design is not based on the state transition matrix of BNs,which can efficiently determine pinning control nodes and reduce computational complexity.Our proposed method is efficient in that the calculation of the state transition matrix with dimension 2^n×2^n is avoided;here n is the number of nodes in a BN.Finally,a signal transduction network and a D.melanogaster segmentation polarity gene network are presented to show the efficiency of the proposed method.Results are shown to be simple and concise,compared with traditional pinning control for BNs.
文摘This paper investigates the Morgan＇s problem of Boolean control networks. Based on the matrix expression of logical functions, two key steps are proposed to solve the problem. First, the Boolean control network is converted into an output- decomposed form by constructing a set of consistent outputfriendly subspaces, and a necessary and sufficient condition for the existence of the consistent output-friendly subspaces is obtained. Secondly, a type of state feedback controllers are designed to solve the Morgan＇s problem if it is solvable. By solving a set of matrix equations, a necessary and sufficient condition for converting an output-decomposed form to an input-output decomposed form is given, and by verifying the output controllability matrix, the solvability of Morgan＇s problem is obtained.
文摘Observability is a fundamental property of a partially observed dynamical system,which means whether one can use an input sequence and the corresponding output sequence to determine the initial state.Observability provides bases for many related problems,such as state estimation,identification,disturbance decoupling,controller synthesis,etc.Until now,fundamental improvement has been obtained in observability of Boolean control networks(BCNs)mainly based on two methods-Edward F.Moore's partition and our observability graph or their equivalent representations found later based on the semitensor product(STP)of matrices(where the STP was proposed by Daizhan Cheng),including necessary and sufficient conditions for different types of observability,extensions to probabilistic Boolean networks(PBNs)and singular BCNs,even to nondeterministic finite-transition systems(NFTSs);and the development(with the help of the STP of matrices)in related topics,such as com-putation of smallest invariant dual subspaces of BNs containing a set of Boolean functions,multiple-experiment observability verification/decomposition in BCNs,disturbance decoupling in BCNs,etc.This paper provides a thorough survey for these topics.The contents of the paper are guided by the above two methods.First,we show that Moore's partition-based method closely relates the following problems:computation of smallest invariant dual subspaces of BNs,multiple-experiment observ-ability verification/decomposition in BCNs,and disturbance decoupling in BCNs.However,this method does not apply to other types of observability or nondeterministic systems.Second,we show that based on our observability graph,four different types of observability have been verified in BCNs,verification results have also been extended to PBNs,singular BCNs,and NFTSs.In addition,Moore's partition also shows similarities between BCNs and linear time-invariant(LTI)control systems,e.g.,smallest invariant dual subspaces of BNs containing a set of Boolean functions in BCNs vs unobservable subspaces of LTI control systems,the forms of quotient systems based on observability decomposition in both types of systems.However,there are essential differences between the two types of systems,e.g.,"all plausible definitions of observability in LTI control systems turn out to be equivalent"(by Walter M.Wonham 1985),but there exist nonequivalent definitions of observability in BCNs;the quotient system based on observability decomposition always exists in an LTI control system,while a quotient system based on multiple-experiment observability decomposition does not always exist in a BCN.
基金Project supported by the National Natural Science Foundation of China(No.61773371)。
文摘We investigate the problem of finding optimal one-bit perturbation that maximizes the size of the basin of attractions(BOAs)of desired attractors and minimizes the size of the BOAs of undesired attractors for large-scale Boolean networks by cascading aggregation.First,via the aggregation,a necessary and sufficient condition is given to ensure the invariance of desired attractors after one-bit perturbation.Second,an algorithm is proposed to identify whether the one-bit perturbation will cause the emergence of new attractors or not.Next,the change of the size of BOAs after one-bit perturbation is provided in an algorithm.Finally,the efficiency of the proposed method is verified by a T-cell receptor network.
文摘Boolean control network consists of a set of Boolean variables whose state is determined by other variables in the network. Boolean network is used for modeling complex system. In this paper, we have presented a model of a context-aware system used in smart home based on Boolean control networks. This modeling describes the relationship between the context elements (person, time, location, and activity) and services (Morning Call, Sleeping, Guarding, Entertainment, and normal), which is effective to logical inference. We apply semi tensor matrix product to describe the dynamic of the system. This matrix form of expression is a convenient and reasonable way to design logic control system.
