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

multi scale second order computational homogenization of multi phase materials a nested finite element solution strategy this paper presents the detailed implementation and computational aspects of a novel second order computational homogenization procedure which is suitable for a multi scale modelling of macroscopic localization and size effects the second order scheme is an extension of the classical first order computational homogenization framework and is based on a proper incorporation of the gradient of the macroscopic deformation gradient tensor into the kinematical macro micro scale transition from the microstructural analysis the macroscopic stress and higher order stress tensors are obtained thus delivering a microstructurally based constitutive response of the macroscopic second gradient continuum the higher order macroscopic constitutive tangents are derived through static condensation of the microscopic global tangent matrix for the solution of the second gradient equilibrium problem on the macrolevel a mixed finite element formulation is developed as an example the second order computational homogenization approach is applied for the multi scale analysis of simple shear of a constrained heterogeneous strip where a pronounced boundary size effect appears

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

brief paper controllability of boolean control networks with time delays in states this paper investigates the controllability of boolean networks with time invariant delays in states after a brief introduction on converting the logic dynamics to discrete time delay systems the controllability via two kinds of controls is studied one kind of control is generated by boolean control networks another kind of control is free boolean sequences in both cases necessary and sufficient conditions of the controllability of boolean control networks are proved finally examples are given to illustrate the efficiency of the obtained results

on the periodic trajectories of boolean control networks abstract in this note we first characterize the periodic trajectories or equivalently the limit cycles of a boolean network and their global attractiveness we then investigate under which conditions all the trajectories of a boolean control network may be forced to converge to the same periodic trajectory if every trajectory can be driven to such a periodic trajectory this is possible by means of a feedback control law

on stabilization and set stabilization of multivalued logical systems the stabilization and set stabilization of a multivalued logical system are investigated in this paper by using pinning control first new algorithms are presented to redesign the transition matrix of the multivalued logical system such that the system is stable or set stable then by using reconstruction theory of a k valued logical system the pinning nodes are selected in addition the transition matrix of the pinning control is given by solving some logical matrix equations then a pinning control design algorithm is provided finally an example is employed to illustrate the proposed control design procedure

system decomposition with respect to inputs for boolean control networks abstract in this paper the problem of system decomposition with respect to inputs is investigated for boolean control networks bcns first based on the linear representation of bcns some algebraic equivalent conditions for the decomposability are obtained second the concept of perfect equal vertex partition pevp is proposed for bcns a necessary and sufficient graphical condition for the decomposability i e the existence of a pevp is proposed third for calculating a pevp an algorithm called vertex set uniting algorithm vsua is designed finally a biological example is analyzed to show the effectiveness of the proposed method

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

output regulation of boolean control networks this note investigates the output regulation of boolean control networks bcns by using the semi tensor product of matrices and presents a number of new results firstly based on an algebraic state space representation of bcns a necessary and sufficient condition is presented for the solvability of the output regulation problem secondly an effective method is proposed for the control design of the output regulation problem by using an augmented system approach the study of an illustrative example shows that the obtained new results are effective in dealing with the output regulation of bcns

a maximum principle for single input boolean control networks boolean networks have recently been attracting considerable interest as computational models for genetic and cellular networks we consider a mayer type optimal control problem for a single input boolean network and derive a necessary condition for a control to be optimal this provides an analog of pontryagin s maximum principle for single input boolean networks

state feedback stabilization for boolean control networks state feedback stabilization for boolean control networks is investigated in this technical note based on the algebraic representation of logical dynamics in terms of the semi tensor product of matrices a necessary and sufficient condition is derived for the existence of a globally stabilizing state feedback controller and a general control design approach is proposed when global stabilization is feasible via state feedback instead of designing the logical form of a stabilizing feedback law directly we first construct its algebraic representation and then convert the algebraic representation back to the logical form an example is worked out to illustrate the proposed design procedure

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

policy iteration algorithm for optimal control of stochastic logical dynamical systems this brief investigates the infinite horizon optimal control problem for stochastic multivalued logical dynamical systems with discounted cost applying the equivalent descriptions of stochastic logical dynamics in term of markov decision process the discounted infinite horizon optimal control problem is presented in an algebraic form then employing the method of semitensor product of matrices and the increasing dimension technique a succinct algebraic form of the policy iteration algorithm is derived to solve the optimal control problem to show the effectiveness of the proposed policy iteration algorithm an optimization problem of p53 mdm2 gene network is investigated

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

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

observability reconstructibility and state observers of boolean control networks the aim of this paper is to introduce and characterize observability and reconstructibility properties for boolean networks and boolean control networks described according to the algebraic approach proposed by d cheng and co authors in the series of papers 3 6 7 and in the recent monography a complete characterization of these properties based both on the boolean matrices involved in the network description and on the corresponding digraphs is provided finally the problem of state observer design for reconstructible bns and bcns is addressed and two different solutions are proposed

optimal control of boolean control networks in this paper we address the optimal control problem for boolean control networks bcns we first consider the problem of finding the input sequences that minimize a given cost function over a finite time horizon the problem solution is obtained by means of a recursive algorithm that represents the analogue for bcns of the difference riccati equation for linear systems we prove that a significant number of optimal control problems for bcns can be easily reframed into the present setup in particular the cost function can be adjusted so as to include penalties on the switchings provided that we augment the size of the bcn state variable in the second part of the paper we address the infinite horizon optimal control problem and we provide necessary and sufficient conditions for the problem solvability the solution is obtained as the limit of the solution over the finite horizon 0 t and it is always achieved in a finite number of steps finally the average cost problem over the infinite horizon investigated in optimal control of logical control networks y zhao ieee trans autom control vol 56 no 8 pp 1766 1776 aug 2011 is addressed by making use of the results obtained in the previous sections

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

optimal control of logical control networks this paper considers the infinite horizon optimal control of logical control networks including boolean control networks as a special case using the framework of game theory the optimal control problem is formulated in the sight of the algebraic form of a logical control network its cycles can be calculated algebraically then the optimal control is revealed over a certain cycle when the games using memory 1 which means the players only consider previous steps action at each step are considered the higher order logical control network is introduced and its algebraic form is also presented which corresponds to a conventional logical control network i e 1 then it is proved that the optimization technique developed for conventional logical control networks is also applicable to this memory case

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

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

a matrix approach to graph maximum stable set and coloring problems with application to multi agent systems using the semi tensor product of matrices this paper investigates the maximum weight stable set and vertex coloring problems of graphs with application to the group consensus of multi agent systems and presents a number of new results and algorithms firstly by defining a characteristic logical vector and using the matrix expression of logical functions an algebraic description is obtained for the internally stable set problem based on which a new algorithm to find all the internally stable sets is established for any graph secondly the maximum weight stable set problem is considered and a necessary and sufficient condition is presented by which an algorithm to find all the maximum weight stable sets is obtained thirdly the vertex coloring problem is studied by using the semi tensor product method and two necessary and sufficient conditions are proposed for the colorability based on which a new algorithm to find all the k coloring schemes and minimum coloring partitions is put forward finally the obtained results are applied to multi agent systems and a new protocol design procedure is presented for the group consensus problem the study of illustrative examples shows that the results algorithms presented in this paper are very effective

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

bi decomposition of multi valued logical functions and its applications abstract the bi decomposition of multi valued logical mvl functions including disjoint and non disjoint cases is considered using a semi tensor product an mvl function can be expressed in its algebraic form based on this form straightforward verifiable necessary and sufficient conditions are provided for each case respectively the constructive proofs also lead to constructing corresponding decompositions using these results the implicit function theorem ift of k valued functions as a special bi decomposition is obtained finally as an application the normalization of dynamic algebraic d a boolean networks is investigated using ift of k valued functions

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

controller design for disturbance decoupling of boolean control networks we investigate a type of disturbance decoupling problem ddp of boolean control networks using the semi tensor product of matrices the dynamics of a boolean control network is expressed in its algebraic form under the framework of output friendly subspace we give a necessary and sufficient condition for the solvability of ddp by analyzing the redundant variables and we present a computationally feasible method to construct all the valid feedback control matrices the logical functions of each controller can be recovered from the obtained feedback control matrix finally an example is provided to show the effectiveness of the proposed method

a micromechanics based approach for the derivation of constitutive elastic coefficients of strain gradient media a micromechanics based approach for the derivation of the effective properties of periodic linear elastic composites which exhibit strain gradient effects at the macroscopic level is presented at the local scale all phases of the composite obey the classic equations of three dimensional elasticity but since the assumption of strict separation of scales is not verified the macroscopic behavior is described by the equations of strain gradient elasticity the methodology uses the series expansions at the local scale for which higher order terms which are generally neglected in standard homogenization framework are kept in order to take into account the microstructural effects an energy based micro macro transition is then proposed for upscaling and constitutes in fact a generalization of the hill mandel lemma to the case of higher order homogenization problems the constitutive relations and the definitions for higher order elasticity tensors are retrieved by means of the state law associated to the derived macroscopic potential as an illustration purpose we derive the closed form expressions for the components of the gradient elasticity tensors in the particular case of a stratified periodic composite for handling the problems with an arbitrary microstructure a fft based computational iterative scheme is proposed in the last part of the paper its efficiency is shown in the particular case of composites reinforced by long fibers

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

algebraic formulation and topological structure of boolean networks with state dependent delay abstract this paper investigates the algebraic formulation topological structure and set stability of boolean networks with state dependent delay sdd firstly using the algebraic state space representation assr method the dynamics of boolean networks with sdd is converted into an equivalent augmented system secondly based on the equivalent augmented system some necessary and sufficient conditions are presented to calculate fixed points and cycles of boolean networks with sdd thirdly it is proved that the set stability of boolean networks with sdd is equivalent to the set stability of augmented system and a necessary and sufficient condition is presented by constructing a kind of set stability matrix finally the obtained results are applied to the strategy consensus of networked evolutionary games with memories

matrix approach to model matching of asynchronous sequential machines in this note we propose a matrix based approach for asynchronous sequential machines using semi tensor product of matrices we convert an asynchronous machine into a discrete time bilinear system and study its dynamics by investigating its structure matrices we give simple algorithms for cycle detection and reachability analysis and moreover provide a control design method for the model matching of two input state machines

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

the equivalence issue of two kinds of controllers in boolean control networks abstract in this paper the equivalence issue between state feedback controller and free sequence controller in boolean control network bcn is investigated based on the algebraic representation of boolean networks we prove that a boolean control network can be stabilized to a cycle or a fixed point via free sequence controller if and only if there is a state feedback controller which can derive the boolean control network to the cycle or the fixed point then two algorithms are provided to find the state feedback controller after that we prove that a bcn can be globally controllable by free sequence controller while the bcn is not necessarily globally controllable by state feedback controller at last an example is given to illustrate the results

computational second order homogenization of materials with effective anisotropic strain gradient behavior abstract a computational homogenization method to determine the effective parameters of mindlin s strain gradient elasticity sge model from a local heterogeneous cauchy linear material is developed the devised method which is an extension of the classical one based on the use of quadratic boundary conditions intents to correct the well known non physical problem of persistent gradient effects when the representative volume element rve is homogeneous those spurious effects are eliminated by introducing a microstructure dependent body force field in the homogenization scheme together with alternative definitions of the localization tensors with these modifications and by a simple application of the superposition principle the higher order stiffness tensors of sge are computed from elementary numerical calculations on rve within this new framework the convergence of sge effective properties is investigated with respect to the size of the rve finally a c1 fem procedure for simulating the behavior of the effective material at the macro scale is developed we show that the proposed model is consistent with the solutions arising from asymptotic analysis and that the computed effective tensors verify the expected invariance properties for several classes of anisotropy we also point out an issue that the present model shares with asymptotic based solutions in the case of soft inclusions applications to anisotropic effective strain gradient materials are provided as well as comparisons between fully meshed structures and equivalent homogeneous models

global robust stability and stabilization of boolean network with disturbances abstract based on semi tensor product of matrices global robust stability and stabilization of boolean network bn with disturbances are investigated firstly the definition of global robust stability for bn with disturbances is presented by using the algebraic state space representation of disturbed bn some necessary and sufficient criteria are obtained to ensure the global robust stability with respect to w r t a fixed point or w r t a limit cycle in contrast if a given disturbed bn is not globally robust stable w r t a fixed point or w r t a limit cycle system can achieve stability by a matrix transformation technique however it is a difficult task to find such a suitable matrix transformation in this paper a pinning state feedback control design is proposed to find a suitable transformation the obtained results are well illustrated by numerical example

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

output controllability and optimal output control of state dependent switched boolean control networks in the present paper we investigate the output controllability and optimal output control problems of a state dependent switched boolean control network by using the semi tensor product the algebraic form of the system is obtained then output controllability problems of the system are discussed and some necessary and sufficient conditions are given next the mayer type optimal output control issue is considered and an algorithm is provided to find out the control sequence at last an example is given to show the effectiveness of the main results

a linear representation of dynamics of boolean networks a new matrix product called semi tensor product of matrices is reviewed using it a matrix expression of logic is proposed where a logical variable is expressed as a vector a logical function is expressed as a multiple linear mapping under this framework a boolean network equation is converted into an equivalent algebraic form as a conventional discrete time linear system analyzing the transition matrix of the linear system formulas are obtained to show a the number of fixed points b the numbers of cycles of different lengths c transient period for all points to enter the set of attractors and d basin of each attractor the corresponding algorithms are developed and used to some examples

strain gradient elastic homogenization of bidimensional cellular media the present paper aims at introducing an homogenization scheme for the determination of strain gradient elastic coefficients this scheme is based on a quadratic extension of homogeneous boundary condition hbc it allows computing strain elastic effective tensors this easy to handle computational procedure will then be used to construct overall honey comb like materials behavior and to verify some theoretical predictions about strain gradient elasticity

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

a new infinity norm path following algorithm for linear programming we devise a new primal dual path following algorithm for linear programming that is based entirely on an infinity norm centering measure the algorithm makes reductions in a path parameter mu each of which is followed by a sequence of centering steps the algorithm has similarities with both long step path following and predictor corrector methods we also consider a modified version of the algorithm that uses partial updating of the projection equations the analysis of the modified algorithm has some interesting differences compared with previously devised partial updating methods in particular partial updating obtains a factor of sqrt n complexity reduction even though the permissible relative error in the approximate scaling factors is extremely small only o 1 sqrt n

strategy optimization for static games based on stp method abstract in this paper we consider the choice behavior of players in a static game and discuss solutions to static games of complete information problem via semi tensor product stp method some properties of the dominant behaviors are obtained based on which choosing the dominant strategies deleting the dominated strategies are used to optimize the strategy sets so as to obtain solutions to the considered game examples are given to show the effectiveness of the results

on the index of convergence of a class of boolean matrices with structural properties boolean matrices are of prime importance in the study of discrete event systems des which allow us to model systems across a variety of applications the index of convergence i e the number of

disturbance decoupling of boolean control networks disturbance decoupling problem ddp of boolean control networks is considered using semi tensor product of matrices and the matrix expression of logical functions a working procedure is proposed to solve the problem this procedure consists of two key design steps first how to convert a system into an output friendly coordinate frame an algorithm is provided to calculate the output friendly subspaces secondly it was shown how to find proper controllers to solve the problem if it is solvable a state variable separation form is introduced to guide the design of controllers based on the design technique necessary and sufficient conditions are obtained for the solvability of ddp

state feedback based output tracking control of probabilistic boolean networks abstract this paper studies the state feedback based output tracking control of probabilistic boolean control networks pbcns by using the semi tensor product of matrices a series of reachable sets with probability 1 is defined inductively for pbcns and some useful properties are obtained for the reachable sets based on the properties of the reachable sets a necessary and sufficient condition is presented for the state feedback based output tracking control of pbcns meanwhile a constructive procedure is proposed to design state feedback laws for pbcns to track a constant reference signal the study of two illustrative examples shows that the obtained new results are very effective