some variants of king s fourth order family of methods for nonlinear equations abstract in this paper we present fourth order families of new variants of king s fourth order family of methods for solving nonlinear equations per iteration the obtained methods require two evaluations of the given function and one of its first derivative the classical traub ostrowski method is obtained as a special variant of king s method several numerical examples are given to illustrate the efficiency and performance of the presented methods

pinning dynamic systems of networks with markovian switching couplings and controller node set in this paper we study pinning control problem of coupled dynamical systems with stochastically switching couplings and stochastically selected controller node set here the coupling matrices and the controller node sets change with time induced by a continuous time markov chain by constructing lyapunov functions we establish tractable sufficient conditions for exponential stability of the coupled system two scenarios are considered here first we prove that if each subsystem in the switching system i e with the fixed coupling can be stabilized by the fixed pinning controller node set and in addition the markovian switching is sufficiently slow then the time varying dynamical system is stabilized second we conclude that if the system with the average coupling and pinning gains can be stabilized and the switching is sufficiently fast the time varying system is stabilized two numerical examples are provided to demonstrate the validity of these theoretical results including a switching dynamical system between several stable subsystems and a dynamical system with mobile nodes and spatial pinning control towards the nodes when these nodes are being in a pre designed region

synchronization via pinning control on general complex networks this paper studies synchronization via pinning control on general complex dynamical networks such as strongly connected networks networks with a directed spanning tree weakly connected networks and directed forests a criterion for ensuring network synchronization on strongly connected networks is given it is found that the vertices with very small in degrees should be pinned first in addition it is shown that the original condition with controllers can be reformulated such that it does not depend on the form of the chosen controllers which implies that the vertices with very large out degrees may be pinned then a criterion for achieving synchronization on networks with a directed spanning tree which can be composed of many strongly connected components is derived it is found that the strongly connected components with very few connections from other components should be controlled and the components with many connections from other components can achieve synchronization even without controls

an improved input delay approach to stabilization of fuzzy systems under variable sampling in this paper we investigate the problem of stabilization for sampled data fuzzy systems under variable sampling a novel lyapunov krasovskii functional lkf is defined to capture the characteristic of sampled data systems and an improved input delay approach is proposed by the use of an appropriate enlargement scheme new stability and stabilization criteria are obtained in terms of linear matrix inequalities lmis compared with the existing results the newly obtained ones contain less conservatism some illustrative examples are given to show the effectiveness of the proposed method and the significant improvement on the existing results

supervisory control of a class of discrete event processes this paper studies the control of a class of discrete event processes i e processes that are discrete asynchronous and possibly nondeter ministic the controlled process is described as the generator of a formal language while the controller or supervisor is constructed from the grammar of a specified target language that incorporates the desired closed loop system behavior the existence problem for a supervisor is reduced to finding the largest controllable language contained in a given legal language two examples are provided

opacity of nondeterministic transition systems a bi simulation relation approach in this paper we propose several opacity preserving bi simulation relations for nondeterministic transition systems ntss in terms of initial state opacity current state opacity k step opacity and infinite step opacity we also show how one can leverage quotient constructions to compute such relations as a result although the opacity verification problem for infinite ntss is generally undecidable if one can find such an opacity preserving relation from an infinite nts to a finite one the lack of opacity of the infinite nts can be easily verified over the finite one which is decidable

synchronization control for nonlinear stochastic dynamical networks pinning impulsive strategy in this paper a new control strategy is proposed for the synchronization of stochastic dynamical networks with nonlinear coupling pinning state feedback controllers have been proved to be effective for synchronization control of state coupled dynamical networks we will show that pinning impulsive controllers are also effective for synchronization control of the above mentioned dynamical networks some generic mean square stability criteria are derived in terms of algebraic conditions which guarantee that the whole state coupled dynamical network can be forced to some desired trajectory by placing impulsive controllers on a small fraction of nodes an effective method is given to select the nodes which should be controlled at each impulsive constants the proportion of the controlled nodes guaranteeing the stability is explicitly obtained and the synchronization region is also derived and clearly plotted numerical simulations are exploited to demonstrate the effectiveness of the pinning impulsive strategy proposed in this paper

sampled data synchronization of chaotic lur e systems with time delays this paper studies the problem of sampled data control for master slave synchronization schemes that consist of identical chaotic lur e systems with time delays it is assumed that the sampling periods are arbitrarily varying but bounded in order to take full advantage of the available information about the actual sampling pattern a novel lyapunov functional is proposed which is positive definite at sampling times but not necessarily positive definite inside the sampling intervals based on the lyapunov functional an exponential synchronization criterion is derived by analyzing the corresponding synchronization error systems the desired sampled data controller is designed by a linear matrix inequality approach the effectiveness and reduced conservatism of the developed results are demonstrated by the numerical simulations of chua s circuit and neural network

reduced length checking sequences here the method proposed by ural wu and zhang 1997 for constructing minimal length checking sequences based on distinguishing sequences is improved the improvement is based on optimizations of the state recognition sequences and their use in constructing test segments it is shown that the proposed improvement further reduces the length of checking sequences produced from minimal completely specified and deterministic finite state machines

on minimizing the lengths of checking sequences a general model for constructing minimal length checking sequences employing a distinguishing sequence is proposed the model is based on characteristics of checking sequences and a set of state recognition sequences some existing methods are shown to be special cases of the proposed model and are proven to construct checking sequences the minimality of the resulting checking sequences is discussed and a heuristic algorithm for the construction of minimal length checking sequences is given

test generation for multiple state table faults in finite state machines a test generation procedure to detect multiple state table faults in finite state machines is proposed the importance of multiple state table faults and their advantages as test generation objectives to avoid the need for checking experiments are considered the proposed procedure is based on a new method for implicit enumeration of large numbers of multiple faults by using incompletely specified faulty machines experimental results are presented to demonstrate the effectiveness of implicit fault enumeration in detecting large numbers of multiple faults and in guaranteeing detection of all the faults or all the faults up to a specific multiplicity

global h_ infty pinning synchronization of complex networks with sampled data communications this paper investigates the global h infty pinning synchronization problem for a class of complex networks with aperiodic samplings combined with the writinger based integral inequality a new less conservative criterion is presented to guarantee the global pinning synchronization of the complex network furthermore a novel condition is proposed under which the complex network is globally pinning synchronized with a given h infty performance index it is shown that the h infty performance index gamma has a positive correlation with the upper bound of the sampling intervals finally the validity and the advantage of the theoretic results obtained are verified by means of the applications in chua s circuit and pendulum

wirtinger based integral inequality application to time delay systems in the last decade the jensen inequality has been intensively used in the context of time delay or sampled data systems since it is an appropriate tool to derive tractable stability conditions expressed in terms of linear matrix inequalities lmis however it is also well known that this inequality introduces an undesirable conservatism in the stability conditions and looking at the literature reducing this gap is a relevant issue and always an open problem in this paper we propose an alternative inequality based on the fourier theory more precisely on the wirtinger inequalities it is shown that this resulting inequality encompasses the jensen one and also leads to tractable lmi conditions in order to illustrate the potential gain of employing this new inequality with respect to the jensen one two applications on time delay and sampled data stability analysis are provided

a new approach for the verification of infinite step and k step opacity using two way observers abstract in the context of security analysis for information flow properties where a potentially malicious observer intruder tracks the observed behavior of a given system infinite step opacity respectively k step opacity holds if the intruder can never determine for sure that the system was in a secret state for any instant within infinite steps respectively k steps prior to that particular instant we present new algorithms for the verification of the properties of infinite step opacity and k step opacity for partially observed discrete event systems modeled as finite state automata our new algorithms are based on a novel separation principle for state estimates that characterizes the information dependence in opacity verification problems and they have lower computational complexity than previously proposed ones in the literature specifically we propose a new information structure called the two way observer that is used for the verification of infinite step and k step opacity based on the two way observer a new upper bound for the delay in k step opacity is derived which also improves previously known results

a constructive method for solving the equation xa b in rn a generalization of division in rn abstract in this paper we present a new approach of defining division of vectors in r n for arbitrary dimension n our approach is based on constructing a class of solutions of the equation x a b for any two known vectors a b r n for arbitrary dimension n by using some basic properties of octonions the defined procedure differs depending on the dimension of the vectors being analyzed the cases 1 n 7 and n 7 we present an algorithm for computing divisions of vectors in multidimension space and some numerical examples are given to confirm the presented theoretical results lastly our algorithm is applied to extend several known methods of scalar case to multidimensional cases and some numerical tests are made to compare the performance of the nonlinear system solvers

computing the shortest network under a fixed topology we show that in any given uniform orientation metric plane the shortest network interconnecting a given set of points under a fixed topology can be computed by solving a linear programming problem whose size is bounded by a polynomial in the number of terminals and the number of legal orientations when the given topology is restricted to a steiner topology our result implies that the steiner minimum tree under a given steiner topology can be computed in polynomial time in any given uniform orientation metric with spl lambda legal orientations for any fixed integer spl lambda spl ges 2 this settles an open problem posed by brazil thomas and weng 2000

pinning synchronization of directed networks with switching topologies a multiple lyapunov functions approach this paper studies the global pinning synchronization problem for a class of complex networks with switching directed topologies the common assumption in the existing related literature that each possible network topology contains a directed spanning tree is removed in this paper using tools from m matrix theory and stability analysis of the switched nonlinear systems a new kind of network topology dependent multiple lyapunov functions is proposed for analyzing the synchronization behavior of the whole network it is theoretically shown that the global pinning synchronization in switched complex networks can be ensured if some nodes are appropriately pinned and the coupling is carefully selected interesting issues of how many and which nodes should be pinned for possibly realizing global synchronization are further addressed finally some numerical simulations on coupled neural networks are provided to verify the theoretical results

optimizing the length of checking sequences a checking sequence generated from a finite state machine is a test sequence that is guaranteed to lead to a failure if the system under test is faulty and has no more states than the specification the problem of generating a checking sequence for a finite state machine m is simplified if m has a distinguishing sequence an input sequence d with the property that the output sequence produced by m in response to d is different for the different states of m previous work has shown that where a distinguishing sequence is known an efficient checking sequence can be produced from the elements of a set a of sequences that verify the distinguishing sequence used and the elements of a set spl gamma of subsequences that test the individual transitions by following each transition t by the distinguishing sequence that verifies the final state of t in this previous work a is a predefined set and spl gamma is defined in terms of a the checking sequence is produced by connecting the elements of spl gamma and a to form a single sequence using a predefined acyclic set e sub c of transitions an optimization algorithm is used in order to produce the shortest such checking sequence that can be generated on the basis of the given a and e sub c however this previous work did not state how the sets a and e sub c should be chosen this paper investigates the problem of finding appropriate a and e sub c to be used in checking sequence generation we show how a set a may be chosen so that it minimizes the sum of the lengths of the sequences to be combined further we show that the optimization step in the checking sequence generation algorithm may be adapted so that it generates the optimal e sub c experiments are used to evaluate the proposed method

stabilization for sampled data systems under noisy sampling interval in engineering practice the sampling interval for a sampled data system often fluctuates around a nominal ideal value based on certain probability distributions that can be specified a priori through statistical tests in this paper a fundamental stabilization problem is investigated for a class of sampled data systems under noisy sampling interval the stochastic sampled data control system under consideration is first converted into a discrete time system whose system matrix is represented as an equivalent yet tractable form via the matrix exponential computation then by introducing a vandermonde matrix the mathematical expectation of the quadratic form of the system matrix is computed by recurring to the kronecker product operation the sampled data stabilization controller is designed such that the closed loop system is stochastically stable in the presence of noisy sampling interval subsequently a special case is considered where the sampling interval obeys the continuous uniform distribution and the corresponding stabilization controller is designed finally a numerical simulation example is provided to demonstrate the effectiveness of the proposed design approach

brief paper wirtinger s inequality and lyapunov based sampled data stabilization discontinuous lyapunov functionals appeared to be very efficient for sampled data systems fridman 2010 naghshtabrizi hespanha teel 2008 in the present paper new discontinuous lyapunov functionals are introduced for sampled data control in the presence of a constant input delay the construction of these functionals is based on the vector extension of wirtinger s inequality these functionals lead to simplified and efficient stability conditions in terms of linear matrix inequalities lmis the new stability analysis is applied to sampled data state feedback stabilization and to a novel sampled data static output feedback problem where the delayed measurements are used for stabilization

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

exponential synchronization of complex networks of linear systems and nonlinear oscillators a unified analysis a unified approach to the analysis of synchronization for complex dynamical networks i e networks of partial state coupled linear systems and networks of full state coupled nonlinear oscillators is introduced it is shown that the developed analysis can be used to describe the difference between the state of each node and the weighted sum of the states of those nodes playing the role of leaders in the networks thus making it feasible to consider the error dynamics for the whole network system different from the other various methods given in the existing literature the analysis employed in this paper is demonstrated successfully in not only providing the consistent convergence analysis with much simpler form but also explicitly specifying the convergence rate

observability of finite labeled transition systems finite labeled transition systems are nondeterministic and nontotal systems with finitely many inputs states and outputs this paper provides algorithms for verifying the observability of finite labeled transition systems in the so called multiple experiment case the simple experiment case and the arbitrary experiment case respectively where these algorithms run in exponential time exponential time and quartic polynomial time respectively and are more effective than the existing algorithms in the literature

applicability of fair simulation in this paper we compare four notions of fair simulation direct 9 delay 12 game 19 and exists 16 our comparison refers to three main aspects the time complexity of constructing the fair simulation the ability to use it for minimization and the relationship between the fair simulations and universal branching time logics we developed a practical application that is based on this comparison the application is a new implementation for the assume guarantee modular framework presented by grumberg at al in acm transactions on programming languages and systems toplas 16 1994 843 the new implementation significantly improves the complexity of the framework

on nfas where all states are final initial or both we examine questions involving nondeterministic finite automata where all states are final initial or both initial and final first we prove hardness results for the nonuniversality and inequivalence problems for these nfas next we characterize the languages accepted finally we discuss some state complexity problems involving such automata

criteria for global pinning controllability of complex networks in this paper we study pinning controllability of networks of coupled dynamical systems in particular we study the problem of asymptotically driving a network of coupled identical oscillators onto some desired common reference trajectory by actively controlling only a limited subset of the whole network the reference trajectory is generated by an exogenous independent oscillator and pinned nodes are coupled to it through a linear state feedback we describe the time evolution of the complex dynamical system in terms of the error dynamics thereby we reformulate the pinning controllability problem as a global asymptotic stability problem by using lyapunov stability theory and algebraic graph theory we establish tractable sufficient conditions for global pinning controllability in terms of the network topology the oscillator dynamics and the linear state feedback

testing finite state machines state identification and verification we study the complexity of two fundamental problems in the testing of finite state machines 1 distinguishing sequences state identification we show that it is pspace complete to determine whether a finite state machine has a preset distinguishing sequence there are machines that have distinguishing sequences but only of exponential length we give a polynomial time algorithm that determines whether a finite state machine has an adaptive distinguishing sequence the previous classical algorithms take exponential time furthermore if there is an adaptive distinguishing sequence then we give an efficient algorithm that constructs such a sequence of length at most n n spl minus 1 2 which is the best possible where n is the number of states 2 unique input output sequences state verification it is pspace complete to determine whether a state of a machine has a unique input output sequence there are machines whose states have unique input output sequences but only of exponential length

verification of initial state opacity in security applications of discrete event systems in this paper we formulate and analyze methodologies for verifying the notion of initial state opacity in discrete event systems that are modeled as non deterministic finite automata with partial observation on their transitions a system is initial state opaque if the membership of its true initial state to a set of secret states remains opaque i e uncertain to an intruder who observes system activity through some projection map initial state opacity can be used to characterize security requirements in a variety of applications including tracking problems in sensor networks in order to model and analyze the intruder capabilities regarding initial state opacity we first address the initial state estimation problem in a non deterministic finite automaton via the construction of an initial state estimator we analyze the properties and complexity of the initial state estimator and show how the complexity of the verification method can be greatly reduced in the special case when the set of secret states is invariant we also establish that the verification of initial state opacity is a pspace complete problem

multidimensional generalization of iterative methods for solving nonlinear problems by means of weight function procedure in this paper from traub s method and by applying weight function technique a bi parametric family of predictor corrector iterative schemes with optimal fourth order of convergence for solving nonlinear equations is presented by using some algebraic manipulations and a divided difference operator we extend this family to the multidimensional case preserving its order of convergence some numerical test are made in order to confirm the theoretical results and to compare the new methods with other known ones

some fourth order modifications of newton s method abstract in this paper we construct some fourth order modifications of newton s method for solving nonlinear equations any two existing fourth order methods can be effectively used to give rise to new fourth order methods per iteration the new methods require two evaluations of the function and one of its first derivative numerical examples are given to show the performance of the presented methods

graph theory based pinning synchronization of stochastic complex dynamical networks this paper is concerned with the adaptive pinning synchronization problem of stochastic complex dynamical networks cdns based on algebraic graph theory and lyapunov theory pinning controller design conditions are derived and the rigorous convergence analysis of synchronization errors in the probability sense is also conducted compared with the existing results the topology structures of stochastic cdn are allowed to be unknown due to the use of graph theory in particular it is shown that the selection of nodes for pinning depends on the unknown lower bounds of coupling strengths finally an example on a chua s circuit network is given to validate the effectiveness of the theoretical results