synchronization of arbitrarily switched boolean networks this paper investigates the complete synchronization problem for the drive response switched boolean networks sbns under arbitrary switching signals where the switching signals of the response sbn follow those generated by the drive sbn at each time instant first the definition of complete synchronization is introduced for the drive response sbns under arbitrary switching signals second the concept of switching reachable set starting from a given initial state set is put forward based on it a necessary and sufficient condition is derived for the complete synchronization of the drive response sbns last we give a simple algebraic expression for the switching reachable set in a given number of time steps and two computable algebraic criteria are obtained for the complete synchronization of the sbns a biological example is given to demonstrate the effectiveness of the obtained main results

a note on observability of boolean control networks abstract the observability of boolean control networks is investigated the pairs of states are classified into three classes i diagonal ii h distinguishable and iii h indistinguishable for h indistinguishable pairs we construct a matrix w called the transferable matrix which indicates the control transferability among h indistinguishable pairs modifying w yields a boolean matrix u 0 which is used as the initial matrix for an iterative algorithm after finite iterations a stable u is reached which is called the observability matrix it is proved that a boolean control network is observable if and only if the last column of u col r 1 u 1 r some numerical examples are presented

output feedback stabilization control design for boolean control networks this paper investigates the output feedback stabilization of boolean control networks bcns by using the semi tensor product method and presents a number of new results first based on the algebraic expression of bcns a necessary and sufficient condition is presented for the existence of output feedback stabilizers second a constructive procedure is proposed to design output feedback stabilization controllers for bcns the study of an illustrative example shows that the new results obtained in this paper are very effective in designing output feedback stabilizers for bcns

stability analysis for switched boolean networks under arbitrary switching signals this note investigates the stability of switched boolean networks sbns under arbitrary switching signal by using the tool of semi tensor product of matrices first an algebraic expression is given for the sbn via the semi tensor product based on it a necessary and sufficient condition is presented for the switching point reachability of the system second using the switching point reachability the pointwise stabilizability is studied and a necessary and sufficient condition is obtained finally the global stability of sbns under arbitrary switching signal is investigated and an easily verifiable necessary and sufficient condition is presented two illustrative examples are presented to show that the main results are effective in analyzing the stability of sbns

synchronization in an array of output coupled boolean networks with time delay this brief presents an analytical study of synchronization in an array of coupled deterministic boolean networks bns with time delay two kinds of models are considered in one model the outputs contain time delay while in another one the outputs do not one restriction in this brief is that the state delay and output delay are restricted to be equal by referring to the algebraic representations of logical dynamics and using the techniques of semitensor product of matrices some necessary and sufficient conditions are derived for the synchronization of delay coupled bns examples including a practical epigenetic example are given for illustration

number and length of attractors in a critical kauffman model with connectivity one the kauffman model describes a system of randomly connected nodes with dynamics based on boolean update functions though it is a simple model it exhibits very complex behavior for critical parameter values at the boundary between a frozen and a disordered phase and is therefore used for studies of real network problems we prove here that the mean number and mean length of attractors in critical random boolean networks with connectivity one both increase faster than any power law with network size we derive these results by generating the networks through a growth process and by calculating lower bounds

fuzzy field extensions abstract we introduce the concept of fuzzy field extension linear disjointness for fuzzy field extensions and the composite of two fuzzy subfields the concepts of pure inseparability and separability for fuzzy field extensions are introduced

identification of boolean control networks in this paper the identification of boolean control networks is addressed first necessary and sufficient conditions are obtained for the identification of state equation from input state data then a necessary and sufficient condition for a controllable boolean network to be observable is presented based on these two results a necessary and sufficient condition for the identification from input output data is achieved to practically identify the model a numerical algorithm is proposed two particular cases i identification of systems with a known network graph ii identification of a higher order boolean network are also investigated finally the approximate identification for large size networks is explored

minimal positive solutions to some singular second order differential equations abstract the existence of a minimal c1 0 1 positive solution is established for some second order singular boundary value and initial value problems by new schemes which are related to x our nonlinearity may be singular at t 0 1 x 0 or x 0

pinning control design for the stabilization of boolean networks in this brief pinning control design for the stabilization of boolean network bn is addressed using the semitensor product of matrices transition matrix of the bn can be obtained we achieve global stability to the fixed point or the elementary cycle for the bn by changing the columns of the transition matrix then pinning nodes can be chosen and pinning control design algorithms are proposed finally an example is employed to show the proposed control design procedure

the homomorphic image of a fuzzy subgroup is always a fuzzy subgroup let l be a completely distributive complete lattice with universal bound 0 and 1 and x any group we will prove that the image of a fuzzy group x l under a homomorphism f x y is always a fuzzy group without any restriction on and f

optimal infinite horizon control for probabilistic boolean networks external control of a genetic regulatory network is used for the purpose of avoiding undesirable states such as those associated with disease heretofore intervention has focused on finite horizon control i e control over a small number of stages this paper considers the design of optimal infinite horizon control for context sensitive probabilistic boolean networks pbns it can also be applied to instantaneously random pbns the stationary policy obtained is independent of time and dependent on the current state this paper concentrates on discounted problems with bounded cost per stage and on average cost per stage problems these formulations are used to generate stationary policies for a pbn constructed from melanoma gene expression data the results show that the stationary policies obtained by the two different formulations are capable of shifting the probability mass of the stationary distribution from undesirable states to desirable ones

fuzzy hypervector spaces based on fuzzy singletons we introduce and study fuzzy hypervector spaces based on fuzzy singletons in this regard by considering the notion of fuzzy singletons we characterize a fuzzy hypervector space fuzzily spanned by a fuzzy subset then we use these results to introduce the concept of fuzzy freeness of a fuzzy subset m of a hypervector space v and finally we characterize it in terms of linear independence in the usual sense

observability of boolean networks via matrix equations from the new perspective of logical matrix equations observability of boolean networks bns is investigated in this paper first it is shown that one bn is locally observable on the set of reachable states if and only if the constructed matrix equations have a unique canonical solution then combining with an equivalence relation a novel condition is established to verify global observability finally an example is worked out to illustrate the obtained results

an improved criterion for controllability of boolean control networks this paper tackles the controllability problem of boolean control networks bcns by resorting to the semi tensor product technique and the warshall algorithm several improved novel reachability and controllability criteria are obtained for the bcns through constructing a sequence of rigorous boolean matrices controllability matrix of the considered bcns is derived iteratively it is worth pointing out that the proposed method has lower computational complexity and thus facilitates the reachability and controllability analysis for bcns in addition the issue concerning controllability of bcns with undesirable interior states is investigated by checking a set of designated boolean matrices finally to test the effectiveness of the obtained theoretical results a genetic network model known as the lambda switch is used as an example for numerical simulation

observability of boolean networks a graph theoretic approach boolean networks bns are discrete time dynamical systems with boolean state variables and outputs bns are recently attracting considerable interest as computational models for genetic and cellular networks we consider the observability of bns that is the possibility of uniquely determining the initial state given a time sequence of outputs our main result is that determining whether a bn is observable is np hard this holds for both synchronous and asynchronous bns thus unless p np there does not exist an algorithm with polynomial time complexity that solves the observability problem we also give two simple algorithms with exponential complexity that solve this problem our results are based on combining the algebraic representation of bns derived by d cheng with a graph theoretic approach some of the theoretical results are applied to study the observability of a bn model of the mammalian cell cycle

minimum time control of boolean networks boolean networks bns are discrete time dynamical systems with boolean state variables bns have recently been attracting considerable interest as computational models for biological systems and in particular gene regulating networks boolean control networks bcns are boolean networks with boolean inputs we consider the problem of steering a bcn from a given state to a desired state in minimal time using the algebraic state space representation assr of bcns we derive several necessary conditions stated in the form of maximum principles mps for a control to be time optimal in the assr every state and input vector is a canonical vector using this special structure yields an explicit state feedback formula for all time optimal controls to demonstrate the theoretical results we develop a bcn model for the genetic switch controlling the lambda phage development upon infection of a bacteria our results suggest that this biological switch is designed in a way that guarantees minimal time respon

brief paper controllability of boolean control networks via the perron frobenius theory boolean control networks bcns are recently attracting considerable interest as computational models for genetic and cellular networks addressing control theoretic problems in bcns may lead to a better understanding of the intrinsic control in biological systems as well as to developing suitable protocols for manipulating biological systems using exogenous inputs we introduce two definitions for controllability of a bcn and show that a necessary and sufficient condition for each form of controllability is that a certain nonnegative matrix is irreducible or primitive respectively our analysis is based on a result that may be of independent interest namely a simple algebraic formula for the number of different control sequences that steer a bcn between given initial and final states in a given number of time steps while avoiding a set of forbidden states

brief paper controllability of probabilistic boolean control networks this paper deals with the controllability of probabilistic boolean control networks first a survey on the semi tensor product approach to probabilistic boolean networks is given second the controllability of probabilistic boolean control networks via two kinds inputs is studied finally examples are given to show the efficiency of the obtained results

controllability and observability of boolean control networks the controllability and observability of boolean control networks are investigated after a brief review on converting a logic dynamics to a discrete time linear dynamics with a transition matrix some formulas are obtained for retrieving network and its logical dynamic equations from this network transition matrix based on the discrete time dynamics the controllability via two kinds of inputs is revealed by providing the corresponding reachable sets precisely then the problem of observability is also solved by giving necessary and sufficient conditions

fuzzy ideals and fuzzy subalgebras of lie algebras abstract a fuzzy idea l of a lie algebra l factors it into a lie algebra l l called a fuzzy quotient lie algebra this fuzzy algebra lie algebra is always a fuzzy partition of l and a fuzzy partition of l will be a fuzzy quotient lie algebra if and only if its associated fuzzy similarity relation is compatible with the lie algebra operations relationship between the operations of the lie algebras l i t and zadeh s extension principle are studied we also study homomorphisms of lie algebras and the relationship between them and fuzzy ideals and fuzzy subalgebras of the domains and the co domains of these homomorphisms finally solvability of fuzzy ideals and studied in defining these solvable fuzzy ideals we use zadeh s extension principle

fuzzy linear and affine spaces abstract elementary properties of fuzzy linear and affine spaces are studied the concept of a basis for a fuzzy linear space is defined and an algorithm for computing a basis when the underlying space is finite dimensional is given

simultaneous stabilization for a set of boolean control networks abstract this paper investigates simultaneous stabilization of a collection of boolean control networks bcns by using the semi tensor product method and presents a number of new results first an algebraic expression of the bcns is obtained by the semi tensor product based on which some necessary and sufficient conditions are presented to solve the simultaneous stabilization problem by a free control sequence a state feedback control and an output feedback control respectively second using the column stacking form of matrices a new procedure is established to design both state feedback and output feedback controllers for the simultaneous stabilization problem the study of two illustrative examples shows that the new results obtained in this paper are very effective in solving simultaneous stabilization of a collection of bcns

singular mixed boundary value problem abstract we study singular boundary value problems with mixed boundary conditions of the form u f t u u 0 u 0 0 u t 0 where 0 t r d 0 0 f is a nonnegative function and satisfies the caratheodory conditions on 0 t d here f can have a time singularity at t 0 and or t t and a space singularity at x 0 and or y 0 we present conditions for the existence of solutions positive on 0 t and having continuous first derivatives on 0 t

realization of boolean control networks based on the linear expression of the dynamics of boolean networks the coordinate transformation of boolean variables is defined it follows that the state space coordinate transformation for the dynamics of boolean networks is revealed using it the invariant subspace for a boolean control network is defined then the structure of a boolean control network is analyzed and the controllable and observable normal forms and the kalman decomposition form are presented finally the realization problem including minimum realization of boolean control networks is investigated

controllability of probabilistic boolean control networks based on transition probability matrices in this paper we propose a new approach to investigate the controllability and reachability of probabilistic boolean control networks pbcns with forbidden states we first give a simple algebraic formula for the transition probability between two states in a given number of time step while avoiding a set of forbidden states then we construct the controllability matrix based on a new operator and some necessary and sufficient conditions are obtained for the controllability and reachability of pbcns a numerical example is given to illustrate the efficiency of the obtained results

boolean dynamics of networks with scale free topology the dynamics of boolean networks with scale free topology are studied the existence of a phase transition from ordered to chaotic dynamics governed by the value of the scale free exponent of the network is shown analytically by analyzing the overlap between two distinct trajectories the phase diagram shows that the phase transition occurs for values of the scale free exponent in the open interval 2 2 5 since the boolean networks under study are directed graphs the scale free topology of the input connections and that of the output connections are studied separately ultimately these two topologies are shown to be equivalent a numerical study of the attractor structure of the configuration space reveals that this structure is similar in both networks with scale free topologies and networks with homogeneous random topologies however an important result of this work is that the fine tuning usually required to achieve stability in the dynamics of networks with homogeneous random topologies is no longer necessary when the network topology is scale free finally based on the results presented in this work it is hypothesized that the scale free topology favors the evolution and adaptation of network functioning from a biological perspective

input state incidence matrix of boolean control networks and its applications the input state incidence matrix of a control boolean network is proposed it is shown that this matrix contains complete information of the input state mapping using it an easily verifiable necessary and sufficient condition for the controllability of a boolean control network is obtained the corresponding control which drives a point to a given reachable point is designed moreover certain topological properties such as the fixed points and cycles of a boolean control network are investigated then as another application a sufficient condition for the observability is presented finally the results are extended to mix valued logical control systems

output tracking control of boolean control networks via state feedback this paper investigates the state feedback based output tracking control of boolean control networks bcns with a constant reference signal by using the semi tensor product method based on the algebraic expression of bcns and by constructing a series of reachable sets a general procedure is proposed for the design of the state feedback laws for bcns to track a constant reference signal the study of an illustrative example shows that the obtained new results are effective in designing state feedback based output tracking controllers for bcns to track a constant reference signal

positive solutions for singular systems of three point boundary value problems this paper investigates the following singular systems of nonlinear second order three point boundary value problems u f t v email protected 0 1 v g t u email protected 0 1 u 0 v 0 0 u 1 email protected h v 1 email protected h where email protected 0 1 0 email protected 1 f and g may be singular at t 0 and or t 1 under some weaker conditions the existence of positive solutions is obtained by applying the fixed point theorem of cone expansion and compression two examples are then presented to demonstrate the application of our main results

aggregation algorithm towards large scale boolean network analysis the analysis of large scale boolean network dynamics is of great importance in understanding complex phenomena where systems are characterized by a large number of components the computational cost to reveal the number of attractors and the period of each attractor increases exponentially as the number of nodes in the networks increases this paper presents an efficient algorithm to find attractors for medium to large scale networks this is achieved by analyzing subnetworks within the network in a way that allows to reveal the attractors of the full network with little computational cost in particular for each subnetwork modeled as a boolean control network the input state cycles are found and they are composed to reveal the attractors of the full network the proposed algorithm reduces the computational cost significantly especially in finding attractors of short period or any periods if the aggregation network is acyclic also this paper shows that finding the best acyclic aggregation is equivalent to finding the strongly connected components of the network graph finally the efficiency of the algorithm is demonstrated on two biological systems namely a t cell receptor network and an early flower development network

control design for output tracking of delayed boolean control networks abstract this paper investigates the output tracking control of delayed boolean control networks dbcns by using the algebraic state space representation method firstly the output tracking control problem of dbcns is formulated and the dynamics of dbcns is converted into an equivalent algebraic form secondly based on the algebraic form and controllability of dbcns a necessary and sufficient condition is presented for the output tracking control of dbcns without state constraints thirdly a necessary and sufficient condition is presented for the output tracking control of dbcns with state constraints by constructing a constrained reachability matrix the study of an illustrative example shows the effectiveness of the obtained new results

complete synchronization of boolean networks we examine complete synchronization of two deterministic boolean networks bns coupled unidirectionally in the drive response configuration a necessary and sufficient criterion is presented in terms of algebraic representations of bns as a consequence we show that complete synchronization can occur only between two conditionally identical bns when the transition matrix of the drive network is nonsingular two examples are worked out to illustrate the obtained results

disturbance decoupling control design for switched boolean control networks abstract this paper investigates a kind of disturbance decoupling problems ddps for switched boolean control networks bcns that is the disturbance independent output decoupling problem via the semi tensor product of matrices by converting the dynamics of switched bcns into an algebraic form and using the redundant variable separation technique all possible state feedback controllers are designed for the disturbance independent output decoupling problem then based on the obtained state feedback disturbance decoupling controllers and the system s output equation a constructive procedure is proposed to design all possible output feedback disturbance decoupling controllers the study of two illustrative examples shows that the new results obtained in this paper are effective in designing disturbance decoupling controllers for switched bcns

existence of positive solutions to some singular and nonsingular second order boundary value problems abstract the topological transversality theorem is employed to study existence of solutions to a variety of singular and nonsingular second order boundary value problems of the form y f t y y 0 0 t t 0 t 1 y 0 and or y 0 the principal tools are the arzela ascoli theorem essential maps and a priori bounds on solutions

reachability of higher order logical control networks via matrix method this paper investigates the reachability of higher order logical control networks first with semi tensor product method the matrix expression of a higher order logical control network is given then a partitioned matrix is constructed which intuitively shows the input state mapping information with this matrix some conditions are obtained for the reachability of higher order logical control networks finally an algorithm is designed to find control sequences that drive a given initial state to a given destination state

positive solutions of singular boundary value problems for nonlinear differential systems in this paper by constructing a special cone and applying the fixed index theory in the cone the existence of positive solutions for nonlinear ordinary differential systems with singularities is investigated and an example is developed to demonstrate our main results

redefined observability matrix for boolean networks and distinguishable partitions of state space this paper redefines the observability matrix and defines the observability index for boolean networks bns in the new definition a bn is observable if and only if the observability matrix is of full rank the observability matrix is calculated by a simple algorithm and is applied to the problem of distinguishability of partitions a partition of the state space is said to be distinguishable if any two distinct subsets are distinguishable and the finest distinguishable partition fdp is finer than any other distinguishable partition a necessary and sufficient condition is proposed for checking the distinguishability of any given partition and an algorithm is proposed for calculating the fdp the proposed results are illustrated by examples

further results on feedback stabilization control design of boolean control networks abstract this paper investigates designing all possible feedback stabilizers for boolean control networks bcns some new results on the feedback stabilization control design of bcns are presented the main tool used in the paper is the semi tensor product of matrices first the complete family of reachable sets is defined for bcns then it is shown that all the complete families of reachable sets determine all possible state feedback stabilizers second using all the complete families of reachable sets all possible state feedback stabilizers are obtained third a necessary and sufficient condition is obtained for the existence of output feedback stabilizers based on this condition all possible output feedback stabilizers are designed for bcns finally the obtained new results are applied to the regulation of the lactose operon in escherichia coli

stability and stabilization of boolean networks with impulsive effects abstract this paper investigates the stability and stabilization of boolean networks with impulsive effects after giving a survey on semi tensor product of matrices we convert a boolean network with impulsive effects into impulsive discrete time dynamics then some necessary and sufficient conditions are given for the stability and stabilization of boolean networks with impulsive effects finally examples are provided to illustrate the efficiency of the obtained results

mix valued logic based formation control the formation control fc problem is investigated via a mix valued logic based approach first a trajectory tracking algorithm of mix valued logic control networks is proposed then a new formulation of fc problems is established and a feedback control is designed to solve fc problems the mathematical description of partial formation control pfc problems is then designed as a structure of logical networks an interesting practical example of pfc is also presented and discussed in detail

synchronization for the realization dependent probabilistic boolean networks this paper investigates the synchronization problem for the realization dependent probabilistic boolean networks pbns coupled unidirectionally in the drive response configuration the realization of the response pbn is assumed to be uniquely determined by the realization signal generated by the drive pbn at each discrete time instant first the drive response pbns are expressed in their algebraic forms based on the semitensor product method and then a necessary and sufficient condition is presented for the synchronization of the pbns second by resorting to a newly defined matrix operator the reachable set from any initial state is expressed by a column vector consequently an easily computable algebraic criterion is derived assuring the synchronization of the drive response pbns finally three illustrative examples are employed to demonstrate the applicability and usefulness of the developed theoretical results

solvability of some nonlinear boundary value problems on etablit l existence des solutions positives de problemes a deux points limites singuliers pour des equations differentielles de la forme y f t y y o o t 1

stability and set stability in distribution of probabilistic boolean networks we propose a new concept stability in distribution sd of a probabilistic boolean network pbn which determines whether the probability distribution converges to the distribution of the target state namely a one point distributed random variable in a pbn stability with probability one stability in the stochastic sense and sd are equivalent the sd is easily generalized to subset stability i e to set stability in distribution ssd we prove that the transition probability from any state to an invariant subset or to a fixed point is nondecreasing in time this monotonicity is an important property in establishing stability criteria and in calculating or estimating the transient period we also obtain a verifiable necessary and sufficient condition for sd of pbns with independently and identically distributed switching we then show that sd problems of pbns with markovian switching and pbn synchronizations can be recast as ssd problems of markov chains after calculating the largest invariant subset of a markov chain in a given set by the newly proposed algorithm we propose a necessary and sufficient condition for ssds of markov chains the proposed method and results are supported by examples

convex fuzzy mappings abstract in this note the concept of convexity and logarithmic convexity for fuzzy mappings are introduced and some applications to optimization are discussed

unbounded solutions for singular boundary value problems on the semi infinite interval upper and lower solutions and multiplicity this paper presents a lower and upper solution technique for singular second order boundary value problems on the half line and discusses sufficient and necessary conditions for the existence of positive solutions also multiplicity is discussed using the fixed point index

positive solutions of some second order nonlinear singular differential equations abstract with new schemes the existence of the positive solutions is proved to some second order nonlinear singular boundary value problems and initial value problems which have higher order singularities

fuzzy logic based generalized decision theory with imperfect information the existing decision models have been successfully applied to solving many decision problems in management business economics and other fields but nowadays arises a need to develop more realistic decision models the main drawback of the existing utility theories starting from von neumann moregnstern expected utility to the advanced non expected models is that they are designed for laboratory examples with simple well defined gambles which do not adequately enough reflect real decision situations in real life decision making problems preferences are vague and decision relevant information is imperfect as described in natural language nl vagueness of preferences and imperfect decision relevant information require using suitable utility model which would be fundamentally different to the existing precise utility models precise utility models cannot reflect vagueness of preferences vagueness of objective conditions and outcomes imprecise beliefs etc the time has come for a new generation of decision theories in this study we propose a decision theory which is capable to deal with vague preferences and imperfect information the theory discussed here is based on a fuzzy valued non expected utility model representing linguistic preference relations and imprecise beliefs

invertibility and nonsingularity of boolean control networks invertibility is an interesting and classical control theoretic problem however there has been no result for the invertibility of boolean control networks bcns so far we first adopt the theory of symbolic dynamics to characterize it first it is shown that a bcn generates a continuous mapping from the space of input trajectories to the space of output trajectories based on it the concepts of nonsingularity and invertibility of bcns are first defined as the injectivity and bijectivity of the mapping respectively second combined symbolic dynamics with the semi tensor product stp of matrices an equivalent test criterion for invertibility is given easily computable algorithms to construct the inverse bcn for an invertible bcn are presented and it is proved that invertibility remains invariant under coordinate transformations third an equivalent test criterion for nonsingularity is given via defining a novel directed graph that is called weighted pair graph lastly as an application of invertibility to systems biology we prove that the bcn model proposed in faure et al 2006 is not invertible i e we prove that arbitrarily controlling mammalian cell cycles is unfeasible at the theoretical level

on controllability of delayed boolean control networks this paper is devoted to studying the trajectory and state controllability of boolean control networks bcns with time delay in contrast to bcns without time delay the dynamics of delayed bcns are determined by a sequence of initial states named here trajectories trajectory controllability means that there exists a control signal steering a system from an initial trajectory to a desired trajectory while state controllability means that there exists a control signal steering an initial state to a given state here both trajectory controllability and state controllability will be studied it should be noted that in this paper trajectory controllability does not mean tracking or following a given trajectory in fact it means to control bcns to a destination trajectory of length mu at the k th step using the semi tensor product of matrices the delayed bcns are first converted into an equivalent algebraic description and then some necessary and sufficient conditions are derived for the trajecto

controllability of higher order boolean control networks using the semi tensor product method this paper investigates the controllability of a th order boolean control network after a brief introduction on semi tensor product of matrices to th order boolean control networks the controllability issue is studied first a systematic procedure to reconstruct the logical dynamic of a th order boolean control network from its network transition matrix is presented for design purpose then the controllability via two types of controls is considered necessary and sufficient conditions are provided for each case the application of input state incidence matrix to the controllability of th order boolean control networks is studied finally as an application examples are given to illustrate the effectiveness of the obtained results

on reachability and controllability of switched boolean control networks this paper investigates the reachability and controllability of switched boolean control networks bcns by using the semi tensor product method first a kind of switching input state transfer graph is defined based on which and the algebraic expression of switched bcns we thus propose a new kind of switching input state incidence matrix that contains the complete information of the switching input state transfer graph second by the switching input state incidence matrix several necessary and sufficient conditions are obtained for the reachability and controllability of switched bcns finally an algorithm is established to find a switching sequence and a control scheme to realize the reachability of switched bcns in the shortest time the study of an illustrative example shows that the new results obtained in this paper are very effective in investigating the reachability and controllability of switched bcns

unbounded solutions of the singular boundary value problems for second order differential equations on the half line this paper presents some results on the existence of multiple unbounded solutions for the boundary value problems for second order differential equations on half line and on the uniqueness of unbounded solution

controllability analysis and control design for switched boolean networks with state and input constraints this paper investigates the controllability analysis and the control design for switched boolean networks sbns with state and input constraints by using the semi tensor product method and presents a number of new results on their controllability optimal control and stabilization first the constrained incidence matrix is proposed for sbns based on which several necessary and sufficient conditions are obtained for the controllability second using the results on the controllability two algorithms are established to design proper switching sequence and controls that minimize the cost functional in a fixed designed shortest termination time third the constrained sbn is converted to an equivalent unconstrained one based on which some necessary and sufficient conditions are presented for the stabilization of the constrained sbn with open loop and closed loop controls respectively finally a practical example of the apoptosis network is studied by using the new results obtained in this paper the s

controllability decomposition of dynamic algebraic boolean control networks two types of controllability of dynamic algebraic boolean control networks are first presented the necessary and sufficient conditions of such controllability are derived a similar concept of coo

free fuzzy modules and their bases abstract the notions of a basis for fuzzy modules and of a free fuzzy module are defined and the elementary properties of both are studied it is shown that a fuzzy module possesses a basis if and only if it is free results on the existence of a basis are obtained

bases of fuzzy vector spaces abstract let v be a vector space over a field f let a be a fuzzy subspace of v over f we give sufficient conditions for a to have a basis over a fuzzy subfield k of f we also show that if a has the sup property then a has a fully free basis over f but not necessarily a fully free basis over k

controllability and observability of boolean control networks with time variant delays in states this brief investigates the controllability and observability of boolean control networks with not necessarily bounded time variant delays in states after a brief introduction to converting a boolean control network to an equivalent discrete time bilinear dynamical system via the semi tensor product of matrices the system is split into a finite number of subsystems constructed forest with no time delays by using the idea of splitting time that is proposed in this brief then the controllability and observability of the system are investigated by verifying any so called controllability constructed path and any so called observability constructed paths in the above forest respectively which generalize some recent relevant results matrix test criteria for the controllability and observability are given the corresponding control design algorithms based on the controllability theorems are given we also show that the computing complexity of our algorithm is much less than that of the existing algorithms

on a singular boundary value problem arising in the theory of shallow membrane caps abstract we investigate the following singular boundary value problem which originates from the theory of shallow membrane caps t 3 u t t 3 1 8 u 2 t a 0 u t b 0 t 2 4 0 lim t 0 t 3 u t 0 u 1 0 where a 0 b 0 and are given constants we show the existence of a positive solution to the above problem by means of a generalized lower and upper functions method involving limiting processes we illustrate the theory by numerical experiments in which we used the new version of the matlab code sbvp based on polynomial collocation to approximate the solution of the membrane problem

galois theory for fuzzy fields abstract the aim of this paper is to present a generalized form of the galois connection between the intermediate fields of a field extension and the subgroups of the corresponding galois group we prove that the fundamental theorem of galois theory accepts a generalization in the fuzzy framework

state feedback stabilization for probabilistic boolean networks abstract a probabilistic boolean network pbn is a discrete time system composed of a family of boolean networks bns between which the pbn switches in a stochastic fashion studying control related problems in pbns may provide new insights into the intrinsic control in biological systems and enable us to develop strategies for manipulating complex biological systems using exogenous inputs this paper investigates the problem of state feedback stabilization for pbns based on the algebraic representation of logic functions a necessary and sufficient condition is derived for the existence of a globally stabilizing state feedback controller and a control design method is proposed when the presented condition holds it is shown that the controller designed via the proposed procedure can simultaneously stabilize a collection of pbns that are composed of the same constituent bns

set stability and set stabilization of boolean control networks based on invariant subsets this study addresses the set stability of boolean networks bns and set stabilization of boolean control networks bcns set stability determines whether a bn converges to a given subset whereas set stabilizability addresses the issue of whether a bcn can be stabilized to a given subset many problems can be viewed as special cases of set stability and set stabilization including synchronization partial stability and partial stabilization problems the concepts of invariant subset and control invariant subset are introduced then algorithms for the largest invariant subset and the largest control invariant subset contained in a given subset are proposed based on the invariant subsets obtained the necessary and sufficient conditions for set stability and set stabilizability are established and formulae are provided to calculate the shortest transient periods for respective initial states a design procedure is proposed for finding all the time optimal set stabilizers finally an example is used to show the application of the proposed results to the synchronization problem of bns

control of large scale boolean networks via network aggregation a major challenge to solve problems in control of boolean networks is that the computational cost increases exponentially when the number of nodes in the network increases we consider the problem of controllability and stabilizability of boolean control networks address the increasing cost problem by partitioning the network graph into several subnetworks and analyze the subnetworks separately easily verifiable necessary conditions for controllability and stabilizability are proposed for a general aggregation structure for acyclic aggregation we develop a sufficient condition for stabilizability it dramatically reduces the computational complexity if the number of nodes in each block of the acyclic aggregation is small enough compared with the number of nodes in the entire boolean network

fuzzy linear spaces over valued fields abstract the concept of fuzzy linear spaces was introduced by nanda 3 the purpose of the present paper is to introduce some further concepts such as convex fuzzy sets etc in fuzzy linear spaces over any valued field

observability of boolean control networks a unified approach based on finite automata the problem on how to determine the observability of boolean control networks bcns has been open for five years already in this technical note we propose a unified approach to determine all the four types of observability of bcns in the literature we define the concept of weighted pair graphs for bcns in the sense of each observability we use the so called weighted pair graph to transform a bcn to a finite automaton and then we use the automaton to determine observability in particular the two types of observability that rely on initial states and inputs in the literature are determined finally we show that no pairs of the four types of observability are equivalent which reveals the essence of nonlinearity of bcns