duality and statistical tests of optimality for two stage stochastic programs we present alternative methods for verifying the quality of a proposed solution to a two stage stochastic program with recourse our methods revolve around implications of a dual problem in which dual multipliers on the nonanticipativity constraints play a critical role using randomly sampled observations of the stochastic elements we introduce notions of statistical dual feasibility and sampled error bounds additionally we use the nonanticipativity multipliers to develop connections to reduced gradient methods finally we propose a statistical test based on directional derivatives we illustrate the applicability of these tests via some examples

almost invariant subspaces an approach to high gain feedback design part ii almost conditionally invariant subspaces in part i of this paper almost controlled invariant subspaces were studied in this part we will consider their duals the almost conditionally invariant subspaces these concepts give immediately by dualization of the almost disturbance decoupling control by state feedback the solution of the almost disturbance decoupled estimation problem finally we consider the problem of approximate disturbance decoupling by measurement feedback and it is shown that this problem is solvable to any arbitrary degree of accuracy if and only if 1 almost disturbance decoupling by state feedback and 2 almost disturbance decoupled estimation of the to be controlled output are both possible

a stochastic soft constraints fuzzy model for a portfolio selection problem the financial market behavior is affected by several non probabilistic factors such as vagueness and ambiguity in this paper we develop a multistage stochastic soft constraints fuzzy program with recourse in order to capture both uncertainty and imprecision as well as to solve a portfolio management problem the results we obtained confirm the studies carried out in literature addressed to integrate stochastic and possibilistic programming

possibilistic mean variance models and efficient frontiers for portfolio selection problem in this paper it is assumed that the rates of return on assets can be expressed by possibility distributions rather than probability distributions we propose two kinds of portfolio selection models based on lower and upper possibilistic means and possibilistic variances respectively and introduce the notions of lower and upper possibilistic efficient portfolios we also present an algorithm which can derive the explicit expression of the possibilistic efficient frontier for the possibilistic mean variance portfolio selection problem dealing with lower bounds on asset holdings

stabilization of uncertain systems via linear control this note considers the problem of stabilizing a linear dynamical system whose state equation includes a time varying uncertain parameter vector q cdot given the dynamics dot x t a q t x t b q t u t and a bounding set q for the values q t the objective is to choose a control law u t p x t guaranteeing uniform asymptotic stability for all admissible variations of q cdot our results differ from previous work in one fundamental way that is we show that when working with linear controllers it is possible to dispense with all assumptions on b cdot which have been made by previous authors e g see 1 9 this elimination of hypotheses on b cdot is accomplished roughly as follows the system sigma underline underline delta a q b q is shown to be equivalent to another system sigma underline underline delta a q b as far as stabilization is concerned since b is a constant matrix independent of q the desired result is readily obtained

range limited centrality measures in complex networks here we present a range limited approach to centrality measures in both nonweighted and weighted directed complex networks we introduce an efficient method that generates for every node and every edge its betweenness centrality based on shortest paths of lengths not longer than ensuremath ell 1 l in the case of nonweighted networks and for weighted networks the corresponding quantities based on minimum weight paths with path weights not larger than w ensuremath ell ensuremath ell ensuremath delta ensuremath ell 1 2 l r ensuremath delta these measures provide a systematic description on the positioning importance of a node edge with respect to its network neighborhoods one step out two steps out etc up to and including the whole network they are more informative than traditional centrality measures as network transport typically happens on all length scales from transport to nearest neighbors to the farthest reaches of the network we show that range limited centralities obey universal scaling laws for large nonweighted networks as the computation of traditional centrality measures is costly this scaling behavior can be exploited to efficiently estimate centralities of nodes and edges for all ranges including the traditional ones the scaling behavior can also be exploited to show that the ranking top list of nodes edges based on their range limited centralities quickly freezes as a function of the range and hence the diameter range top list can be efficiently predicted we also show how to estimate the typical largest node to node distance for a network of n nodes exploiting the afore mentioned scaling behavior these observations were made on model networks and on a large social network inferred from cell phone trace logs ensuremath sim 5 5 ifmmode times else texttimes fi 10 6 nodes and ensuremath sim 2 7 ifmmode times else texttimes fi 10 7 edges finally we apply these concepts to efficiently detect the vulnerability backbone of a network defined as the smallest percolating cluster of the highest betweenness nodes and edges and illustrate the importance of weight based centrality measures in weighted networks in detecting such backbones

a cutting plane algorithm for mv portfolio selection model this paper deals with a portfolio selection problem with fuzzy return rates a possibilistic mean variance fmvc portfolio selection model was proposed the possibilistic programming problem can be transformed into a linear optimal problem with an additional quadratic constraint by possibilistic theory for such problems there are no special standard algorithms we propose a cutting plane algorithm to solve fmvc the nonlinear programming problem can be solved by sequence linear programming problem a numerical example is given to illustrate the behavior of the proposed model and algorithm

extremum statistics in scale free network models we investigate the statistics of the most connected node in scale free networks for a scale free network model with homogeneous nodes we show by means of extensive simulations that the exponential truncation due to the finite size of the network of the degree distribution governs the scaling of the extreme values and that the distribution of maxima follows the gumbel statistics for a scale free network model with heterogeneous nodes we show that scaling no longer holds and that the truncation of the degree distribution no longer controls the maxima distribution

decision problems under risk and chance constrained programming dilemmas in the transition some important conceptual problems concerning the application of chance constrained programming ccp to risky practical decision problems are discussed by comparing ccp to stochastic programming with recourse spr we expand on garstka s distinction between mathematical equivalence and economic equivalence showing that much of practical usefulness is lost in the transition between spr and ccp by examining the literature on ccp applications we conclude that there is little evidence that ccp is used with the care that is necessary finally we conclude that ccp is seriously deficient as a modeling technique and of limited value as a computational device

structure of shells in complex networks we define shell l in a network as the set of nodes at distance l with respect to a given node and define rl as the fraction of nodes outside shell l in a transport process information or disease usually diffuses from a random node and reach nodes shell after shell thus understanding the shell structure is crucial for the study of the transport property of networks we study the statistical properties of the shells of a randomly chosen node for a randomly connected network with given degree distribution we derive analytically the degree distribution and average degree of the nodes residing outside shell l as a function of rl further we find that rl follows an iterative functional form rl phi rl 1 where phi is expressed in terms of the generating function of the original degree distribution of the network our results can explain the power law distribution of the number of nodes bl found in shells with l larger than the network diameter d which is the average distance between all pairs of nodes for real world networks the theoretical prediction of rl deviates from the empirical rl we introduce a network correlation function c rl identical with rl phi rl 1 to characterize the correlations in the network where rl is the empirical value and phi rl 1 is the theoretical prediction c rl 1 indicates perfect agreement between empirical results and theory we apply c rl to several model and real world networks we find that the networks fall into two distinct classes i a class of poorly connected networks with c rl 1 where a larger smaller fraction of nodes resides outside inside distance l from a given node than in randomly connected networks with the same degree distributions examples include the watts strogatz model and networks characterizing human collaborations such as citation networks and the actor collaboration network ii a class of well connected networks with c rl 1 examples include the barabasi albert model and the autonomous system internet network

globally stable robust tracking of nonlinear systems using variable structure control and with an application to a robotic manipulator the globally stable robust output tracking for a class of nonlinear systems is considered based only on the knowledge of the bounds on the uncertainties a variable structure control vsc law is developed under the structure matching assumption it is shown that the outputs of the closed loop system asymptotically track given output trajectories despite the uncertainties while maintaining the boundedness of all signals inside the loop all signals inside the loop are shown to be bounded for all time to illustrate the efficiency of the controller the approach is applied to the case of a two degree of freedom dof robotic manipulator with variable payload numerical simulation results are also provided

continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems we consider a dynamic system containing uncertain elements only the set of possible values of these uncertainties is known based on this information a class of state feedback controls is proposed in order to guarantee uniform ultimate boundedness of every system response within an arbitrarily small neighborhood of the zero state these feedback controls are continuous functions of the state

the effect of interdependence on the percolation of interdependent networks abstract two stochastic models are proposed to generate a system composed of two interdependent scale free sf or erd s renyi er networks where interdependent nodes are connected with an exponential or power law relation as well as different dependence strength respectively each subnetwork grows through the addition of new nodes with constant accelerating random attachment in the first model but with preferential attachment in the second model the two subnetworks interact with multi support and undirectional dependence links the effects of dependence relations and strength between subnetworks are analyzed in the percolation behavior of fully interdependent networks against random failure both theoretically and numerically and as a result for both relations interdependent sf networks show a second order percolation phase transition and the increased dependence strength decreases the robustness of the system whereas interdependent er networks show the opposite results in addition the power law relation between networks yields greater robustness than the exponential one at the given dependence strength

robustness of uncertain systems in the absence of matching assumptions abstract we consider a class of uncertain dynamical systems containing uncertain elements these may be due to model parameter uncertainty input disturbance and measurement noise we require no a priori information on the uncertain elements except that their restraint sets are assumed to be known and compact this paper describes a general approach for designing controls to assure practical stability in the absence of matching assumptions which most previous results have needed the result is applicable to non linear systems a specialization to linear systems is then given and a comparison is made with previous work

asymptotic stability for tracking control of nonlinear uncertain dynamical systems described by differential inclusions in this paper we will study the tracking control problem for nonlinear uncertain dynamical systems two generalized feedback control inputs have been proposed such that the feedback controlled systems satisfy the complete tracking control property with exponential asymptotic stability and the trajectories of the systems are steered to the pre specified observation map with an exponential convergence rate moreover an estimate of the tracking time of the trajectories attaining the observation map has also been given an example inspired from a guided missile problem illustrates the use of our main results

comparison of methodologies for fuzzy and stochastic multi objective programming abstract methods for solving a multicriteria linear program with coefficients of the objective functions and the constraints being flat fuzzy numbers and those dealing with a stochastic multicriteria linear program where imprecision of some data is modelled by probability distributions are surveyed the methodologies are compared and evaluated some ideas for future research are emphasized

feedback controlled differential inclusions and stabilization of uncertain dynamical systems deterministic design of stabilizing feedback controls for a class of uncertain dynamical systems is considered adopting a problem formulation based on differential inclusions to encompass all possible realizations of uncertainty the authors describe a class of generalized feedback controls with practical analogues in the form of discontinuous feedbacks that guarantees global uniform ultimate boundedness moreover under a matched uncertainty hypothesis this class of controls guarantees global uniform asymptotic stability of the zero state and ultimate attainment of prescribed model behaviour

enhancing the convergence efficiency of a self propelled agent system via a weighted model we investigate a weighted self propelled agent system wherein each agent s direction is determined by its spatial neighbors directions with exponential weights according to the neighbor numbers in order to describe the fact that some agents with more neighbors might have larger influence on its neighbors we introduce a scaling exponent of the neighbor number between 0 and ensuremath infty when the exponent is equal to 1 the convergence efficiency is enhanced in our simulation furthermore as the exponent increases i e the effect of weight becomes stronger the network of agents becomes easier to achieve direction consensus

the constrained lyapunov problem and its application to robust output feedback stabilization given a dynamical system whose description includes time varying uncertain parameters it is often desirable to design an output feedback controller leading to asymptotic stability of a given equilibrium point when designing such a controller one may consider static i e memoryless or dynamic compensation in this paper we show that solvability of various output feedback design problems is implied by existence of a solution to a certain constrained lyapunov problem clp the clp can be stated in purely algebraic terms once the clp is described we provide necessary and sufficient conditions for its solution to exist subsequently we consider application of the clp to a number of robust stabilization problems involving static output feedback and observer based feedback

stability radius optimization a geometric approach abstract the subject of this paper is a geometric approach to the robustness optimization problem for uncertain finite dimensional linear systems for the structurally perturbed stabilizable pair a b we show that optimally robust feedback stabilization is possible via the class of feedbacks parameterizing a b feedback invariant subspaces of codimension rk b a direct consequence of this geometric approach is a reduction in dimension of the optimization problem

weak pullback attractors of setvalued processes weak pullback attractors are defined for nonautonomous setvalued processes and their existence and upper semicontinuous convergence under perturbation is established unlike strong pullback attractors invariance and pullback attraction here are required only for at least one trajectory rather than all trajectories at each starting point the concept is useful in for example continuous time control systems and is related to that of viability

correlations in scale free networks tomography and percolation we discuss three related models of scale free networks with the same degree distribution but different correlation properties starting from the barabasi albert construction based on growth and preferential attachment we discuss two other networks emerging when randomizing it with respect to links or nodes we point out that the barabasi albert model displays dissortative behavior with respect to the nodes degrees while the node randomized network shows assortative mixing these kinds of correlations are visualized by discussing the shell structure of the networks around an arbitrary node in spite of different correlation behaviors all three constructions exhibit similar percolation properties this result for percolation is also detected for a network with finite second moment and its corresponding randomized models

a sufficient condition of output feedback stabilization of uncertain systems a sufficient condition is derived for the existence of an output constant gain feedback controller which stabilizes a single input single output dynamical system with a linear nominal part and matched uncertainties the sufficient condition is significantly less restrictive than a recently derived one 1 if such a controller exists it may readily be computed

stratification in the preferential attachment network we study structural properties of trees grown by preferential attachment in this mechanism nodes are added sequentially and attached to existing nodes at a rate that is strictly proportional to the degree we classify nodes by their depth n defined as the distance from the root of the tree and find that the network is strongly stratified most notably the distribution f n k of nodes with degree k at depth n has a power law tail f n k k n the exponent grows linearly with depth where the brackets denote an average over all nodes therefore nodes that are closer to the root are better connected and moreover the degree distribution strongly varies with depth similarly the in component size distribution has a power law tail and the characteristic exponent grows linearly with depth qualitatively these behaviors extend to a class of networks that grow by redirection

output feedback stabilization of uncertain dynamical systems given an uncertain dynamical system with a linear nominal part matched uncertainties and a measured output a sufficient condition is given for the existence of an output feedback stabilizing controller for the general multiinput multioutput case checking the sufficient condition involves the selection of a matrix f for the special class of single input single output systems f is a positive or negative scalar and it is shown that if the nominal system transfer function is strictly positive real then an output feedback stabilizing controller does indeed exist

robustness of a network formed by n interdependent networks with a one to one correspondence of dependent nodes many real world networks interact with and depend upon other networks we develop an analytical framework for studying a network formed by n fully interdependent randomly connected networks each composed of the same number of nodes n the dependency links connecting nodes from different networks establish a unique one to one correspondence between the nodes of one network and the nodes of the other network we study the dynamics of the cascades of failures in such a network of networks non caused by a random initial attack on one of the networks after which a fraction p of its nodes survives we find for the fully interdependent loopless non that the final state of the non does not depend on the dynamics of the cascades but is determined by a uniquely defined mutual giant component of the non which generalizes both the giant component of regular percolation of a single network n 1 and the recently studied case of the mutual giant component of two interdependent networks n 2 we also find that the mutual giant component does not depend on the topology of the non and express it in terms of generating functions of the degree distributions of the network our results show that for any n 2 there exists a critical p p c 0 below which the mutual giant component abruptly collapses from a finite nonzero value for p p c to zero for p 2 a rr non is stable for any n with p c 1 this results arises from the critical role played by singly connected nodes which exist in an er non and enhance the cascading failures but do not exist in a rr non

possibilistic linear programming a brief review of fuzzy mathematical programming and a comparison with stochastic programming in portfolio selection problem in this paper we review some fuzzy linear programming methods and techniques from a practical point of view in the rst part the general history and the approach of fuzzy mathematical programming are introduced using a numerical example some models of fuzzy linear programming are described in the second part of the paper fuzzy mathematical programming approaches are compared to stochastic programming ones the advantages and disadvantages of fuzzy mathematical programming approaches are exemplied in the setting of an optimal portfolio selection problem finally some newly developed ideas and techniques in fuzzy mathematical programming are briey reviewed c 2000 elsevier science b v all rights reserved

percolation in networks composed of connectivity and dependency links networks composed from both connectivity and dependency links were found to be more vulnerable compared to classical networks with only connectivity links their percolation transition is usually of a first order compared to the second order transition found in classical networks we analytically analyze the effect of different distributions of dependencies links on the robustness of networks for a random erdos renyi er network with average degree k that is divided into dependency clusters of size s the fraction of nodes that belong to the giant component p is given by p p s 1 1 exp kpp s where 1 p is the initial fraction of removed nodes our general result coincides with the known erdos renyi equation for random networks for s 1 for networks with poissonian distribution of dependency links we find that p is given by p f k p p e s 1 pf k p p 1 where f k p p 1 exp kpp and s is the mean value of the size of dependency clusters for networks with gaussian distribution of dependency links we show how the average and width of the distribution affect the robustness of the networks

output feedback control of uncertain coupled systems the stabilization of uncertain dynamical systems on n that admit a decomposition into two coupled subsystems of dimension nc and nr respectively is studied we refer to the nc dimensional sybsystem as the reduced order system and to the nr dimensional subsystem as the residual system the overall n dimensional system is termed the full system the prototype for which is a mechanical model arising in the study of the active control of structures each subsystem is modelled by a differential equation with a linear nominal part and a nonlinear perturbation of a specified class the output available for feedback purposes is an nc valued linear combination of the state components of the full system and is subject to bounded measurement noise with known bound an output feedback strategy is described and sufficient conditions are obtained for the existence of a calculable global uniform compact attractor containing the state origin for controlled systems of this class

percolation of partially interdependent networks under targeted attack we study a system composed of two partially interdependent networks when nodes in one network fail they cause dependent nodes in the other network to also fail in this paper the percolation of partially interdependent networks under targeted attack is analyzed we apply a general technique that maps a targeted attack problem in interdependent networks to a random attack problem in a transformed pair of interdependent networks we illustrate our analytical solutions for two examples i the probability for each node to fail is proportional to its degree and ii each node has the same probability to fail in the initial time we find the following i for any targeted attack problem for the case of weak coupling the system shows a second order phase transition and for the strong coupling the system shows a first order phase transition ii for any coupling strength when the high degree nodes have higher probability to fail the system becomes more vulnerable iii there exists a critical coupling strength and when the coupling strength is greater than the critical coupling strength the system shows a first order transition otherwise the system shows a second order transition

ring structures and mean first passage time in networks in this paper we address the problem of the calculation of the mean first passage time on generic graphs we focus in particular on the mean first passage time on a node s for a random walker starting from a generic unknown node x we introduce an approximate scheme of calculation which maps the original process in a markov process in the space of the so called rings described by a transition matrix of size o ln n ln k ln n ln k where n is the size of the graph and k the average degree in the graph in this way one has a drastic reduction of degrees of freedom with respect to the size n of the transition matrix of the original process corresponding to an extremely low computational cost we first apply the method to the erdos renyi random graphs for which the method allows for almost perfect agreement with numerical simulations then we extend the approach to the barabasi albert graph as an example of scale free graph for which one obtains excellent results finally we test the method with two real world graphs internet and a network of the brain for which we obtain accurate results

robustness of network of networks under targeted attack the robustness of a network of networks non under random attack has been studied recently gao et al phys rev lett 107 195701 2011 understanding how robust a non is to targeted attacks is a major challenge when designing resilient infrastructures we address here the question how the robustness of a non is affected by targeted attack on high or low degree nodes we introduce a targeted attack probability function that is dependent upon node degree and study the robustness of two types of non under targeted attack i a tree of n fully interdependent erd s renyi or scale free networks and ii a starlike network of n partially interdependent erd s renyi networks for any tree of n fully interdependent erd s renyi networks and scale free networks under targeted attack we find that the network becomes significantly more vulnerable when nodes of higher degree have higher probability to fail when the probability that a node will fail is proportional to its degree for a non composed of erd s renyi networks we find analytical solutions for the mutual giant component p as a function of p where 1 p is the initial fraction of failed nodes in each network we also find analytical solutions for the critical fraction p c which causes the fragmentation of the n interdependent networks and for the minimum average degree k over min below which the non will collapse even if only a single node fails for a starlike non of n partially interdependent erd s renyi networks under targeted attack we find the critical coupling strength q c for different n when q q c the attacked system undergoes an abrupt first order type transition when q q c the system displays a smooth second order percolation transition we also evaluate how the central network becomes more vulnerable as the number of networks with the same coupling strength q increases the limit of q 0 represents no dependency and the results are consistent with the classical percolation theory of a single network under targeted attack

cascade of failures in coupled network systems with multiple support dependence relations we study both analytically and numerically the cascade of failures in two coupled network systems a and b where multiple support dependence relations are randomly built between nodes of networks a and b in our model we assume that each node in one network can function only if it has at least a single support link connecting it to a functional node in the other network we assume that networks a and b have i sizes n a and n b ii degree distributions of connectivity links p a k and p b k iii degree distributions of support links p a k and p b k and iv random attack removes 1 r a n a and 1 r b n b nodes form the networks a and b respectively we find the fractions of nodes a and b which remain functional giant component at the end of the cascade process in networks a and b in terms of the generating functions of the degree distributions of their connectivity and support links in a special case of erd s renyi networks with average degrees a and b in networks a and b respectively and poisson distributions of support links with average degrees a and b in networks a and b respectively a r a 1 exp a b 1 exp a a and b r b 1 exp b a 1 exp b b in the limit of a and b both networks become independent and our model becomes equivalent to a random attack on a single erd s renyi network we also test our theory on two coupled scale free networks and find good agreement with the simulations

tomography of scale free networks and shortest path trees in this paper we model the tomography of scale free networks by studying the structure of layers around an arbitrary network node we find both analytically and empirically that the distance distribution of all nodes from a specific network node consists of two regimes the first is characterized by rapid growth and the second decays exponentially we also show analytically that the nodes degree distribution at each layer exhibits a power law tail with an exponential cutoff we obtain similar empirical results for the layers surrounding the root of shortest path trees cut from such networks as well as the internet

optimisation under hybrid uncertainty abstract fuzzy stochastic optimisation is emerging as a subfield of mathematical programming the disciplinary matrix of which consists of analysis of mathematical programs under fuzziness and randomness along with methods for solving them the primum movens of this paper is to describe a unifying methodological approach that is suitable for finding a satisfying solution of a mathematical program in the presence of fuzzy data and random variables properties of fuzzy random variables frvs serve as the backdrop to this approach which also lends itself better to handling mathematical programs with fuzzy random coefficients for the paper to be somewhat self contained the notion of frv is briefly discussed and a synopsis of fuzzy stochastic optimisation provided a systematically solved example aimed at illustrating the proposed approach is also included

robust output tracking for non linear systems the problem of output tracking for a single input single output non linear system in the presence of uncertainties is studied the notions relative degree and minimum phase for non linear systems are reviewed given a bounded desired tracking signal with bounded derivatives a control law is designed for minimum phase non linear systems which results in tracking of this signal by the output this control law is modified in the presence of uncertainties associated with the model vector fields to reduce the effects of these uncertainties on the tracking errors two types of uncertainties are considered those satisfying a generalized matching condition but otherwise unstructured and linear parametric uncertainties it is shown that for systems with the first type of uncertainty high gain control laws can result in small tracking errors of o where e is a small design parameter an alternative scheme based on variable structure control strategy is shown to yield zero tracking errors adaptive control te

distribution of shortest path lengths in subcritical erdős renyi networks networks that are fragmented into small disconnected components are prevalent in a large variety of systems these include the secure communication networks of commercial enterprises government agencies and illicit organizations as well as networks that suffered multiple failures attacks or epidemics the structural and statistical properties of such networks resemble those of subcritical random networks which consist of finite components whose sizes are nonextensive surprisingly such networks do not exhibit the small world property that is typical in supercritical random networks where the mean distance between pairs of nodes scales logarithmically with the network size unlike supercritical networks whose structure has been studied extensively subcritical networks have attracted relatively little attention a special feature of these networks is that the statistical and geometric properties vary between different components and depend on their sizes and topologies the overall statistics of the network can be obtained by a summation over all the components with suitable weights we use a topological expansion to perform a systematic analysis of the degree distribution and the distribution of shortest path lengths dspl on components of given sizes and topologies in subcritical erd ifmmode mbox h o else h o fi s r enyi er networks from this expansion we obtain an exact analytical expression for the dspl of the entire subcritical network in the asymptotic limit the dspl which accounts for all the pairs of nodes that reside on the same finite component fc is found to follow a geometric distribution of the form p mathrm fc l ensuremath ell ll ensuremath infty 1 ensuremath c c ensuremath ell ensuremath 1 where cl1 is the mean degree using computer simulations we calculate the dspl in subcritical er networks of increasing sizes and confirm the convergence to this asymptotic result we also obtain exact asymptotic results for the mean distance ensuremath langle l ensuremath rangle mathrm fc and for the standard deviation of the dspl ensuremath sigma l mathrm fc and show that the simulation results converge to these asymptotic results using the duality relations between subcritical and supercritical er networks we obtain the dspl on the nongiant components of er networks above the percolation transition

viable control for uncertain nonlinear dynamical systems described by differential inclusions in this paper we will study the viable control problem for a class of uncertain nonlinear dynamical systems described by a differential inclusion the goal is to construct a feedback control such that all trajectories of the system are viable in a map moreover for any initial states no viable in the map under the feedback control all solutions of the system are steered to the map with an exponential convergence rate and viable in the map after a finite time t in this case an estimate of the time t of all trajectories attaining the map is given in the nanomedicine system an example inspired from cerebral embolism and cerebral thrombosis problems illustrates the use of our main results

mapping from structure to dynamics a unified view of dynamical processes on networks although it is unambiguously agreed that structure plays a fundamental role in shaping the collective dynamics of complex systems how structure determines dynamics exactly still remains unclear we investigate a general computational transformation by which we can map the network topology directly to the dynamical patterns emergent on it independent of the nature of the dynamical processes remarkably we find that many seemingly different dynamical processes on networks such as coupled oscillators ensemble neuron firing epidemic spreading and diffusion can all be understood and unified through this same procedure utilizing the inherent multiscale nature of this structure dynamics transformation we further define a multiscale complexity measure which can quantify the functional diversity a general network can support at different organization levels using only its structure we find that a wide variety of topological features observed in real networks such as modularity hierarchy degree heterogeneity and mixing all result in higher complexity this result suggests that the demand for functional diversity is driving the structural evolution of physical networks

a universal adaptive stabilizer for a class of nonlinear systems abstract an adaptive stabilizer is described which is universal for a class of single input nonlinear systems modelled as a controlled differential inclusion on r n the stabilizer has a discontinous feedback structure and incorporates a gain of nussbaum type the analysis draws on an extension to differential inclusions of lasalle s principle for ordinary differential equations

lyapunov stability theory of nonsmooth systems this paper develops nonsmooth lyapunov stability theory and lasalle s invariance principle for a class of nonsmooth lipschitz continuous lyapunov functions and absolutely continuous state trajectories computable tests based on filipov s differential inclusion and clarke s generalized gradient are derived the primary use of these results is in analyzing the stability of equilibria of differential equations with discontinuous right hand side such as in nonsmooth dynamic systems or variable structure control

bus transport network model with ideal n depth clique network topology abstract we propose an ideal n depth clique network model in this model the original network is composed of cliques maximal complete subgraphs that overlap with each other the network expands continuously by the addition of new cliques the final diameter of the network can be set in advance namely it is controllable assuming that the diameter of the network is n the network exhibits a logistic structure with n 1 layers in this structure the 0th layer represents the original network and each node of the m th layer 1 m n corresponds to a clique in the m 1 th layer in the growth process of the network we ensure that any m th layer network is composed of overlapping cliques any node in an m th layer network corresponds to an m depth community in the original network and the diameter of an m depth community is m therefore the n 1 th layer network will contain only one clique the n th layer network will contain only one node and the diameter of the corresponding original network is n then an ideal n depth clique network will be obtained based on the ideal n depth clique network model we construct a bus transport network model with an ideal n depth clique network topology icnbtn moreover our study compares this model with the real bus transport network realbtn of three major cities in china and a recently introduced bus transport network model btn whose network properties correspond well with those of real btns the network properties of the icnbtn are much closer to those of the realbtn than those of the btn are at the same time the icnbtn has higher clustering extent of bus routes smaller network diameter which corresponds to shorter maximum transfer times in a bus network and lower average shortest path time coefficient than the btn and the realbtn therefore the icnbtn can achieve higher transfer efficiency for a bus transport system

random graphs with arbitrary degree distributions and their applications recent work on the structure of social networks and the internet has focused attention on graphs with distributions of vertex degree that are significantly different from the poisson degree distributions that have been widely studied in the past in this paper we develop in detail the theory of random graphs with arbitrary degree distributions in addition to simple undirected unipartite graphs we examine the properties of directed and bipartite graphs among other results we derive exact expressions for the position of the phase transition at which a giant component first forms the mean component size the size of the giant component if there is one the mean number of vertices a certain distance away from a randomly chosen vertex and the average vertex vertex distance within a graph we apply our theory to some real world graphs including the worldwide web and collaboration graphs of scientists and fortune 1000 company directors we demonstrate that in some cases random graphs with appropriate distributions of vertex degree predict with surprising accuracy the behavior of the real world while in others there is a measurable discrepancy between theory and reality perhaps indicating the presence of additional social structure in the network that is not captured by the random graph

percolation of a general network of networks percolation theory is an approach to study the vulnerability of a system we develop an analytical framework and analyze the percolation properties of a network composed of interdependent networks netonet typically percolation of a single network shows that the damage in the network due to a failure is a continuous function of the size of the failure i e the fraction of failed nodes in sharp contrast in netonet due to the cascading failures the percolation transition may be discontinuous and even a single node failure may lead to an abrupt collapse of the system we demonstrate our general framework for a netonet composed of n classic erd ifmmode mbox h o else h o fi s r enyi er networks where each network depends on the same number m of other networks i e for a random regular network rr formed of interdependent er networks the dependency between nodes of different networks is taken as one to one correspondence i e a node in one network can depend only on one node in the other network no feedback condition in contrast to a treelike netonet in which the size of the largest connected cluster mutual component depends on n the loops in the rr netonet cause the largest connected cluster to depend only on m and the topology of each network but not on n we also analyzed the extremely vulnerable feedback condition of coupling where the coupling between nodes of different networks is not one to one correspondence in the case of netonet formed of er networks percolation only exhibits two phases a second order phase transition and collapse and no first order percolation transition regime is found in the case of the no feedback condition in the case of netonet composed of rr networks there exists a first order phase transition when the coupling strength q fraction of interdependency links is large and a second order phase transition when q is small our insight on the resilience of coupled networks might help in designing robust interdependent systems

stability radius for structured perturbations and the algebraic riccati equation abstract in this paper we generalize the notion of stability radius introduced in 1 to allow for structured perturbations we then relate the stability radius to the existence of hermitian solutions of an algebraic riccati equation and give some applications of this result

on fuzzy stochastic optimization abstract this paper extends the applicability of optimization models to situations where both fuzzy and random data are in the state of affairs the major mathematical tool used to this end is the concept of fuzzy random variables which provides a synergistic way for dealing with the two kinds of imprecision the extension principle is canonically extended to fuzzy random variables and exploited to derive a way for handling robust fuzzy stochastic mathematical programming problems finally we provide some possible avenues for further fruitful developments in this field

evolution equation for a model of surface relaxation in complex networks during the last few years the study of complex networks has moved its focus from the study of their topology to the dynamic processes occurring on the underlying network this is because many physical and dynamic processes use complex networks as substrates recently many studies of dynamic processes on networks such as epidemic spreading 2 traffic flow 3 4 cascading failure 5 and synchronization 6 7 have demonstrated the importance of the topology of the substrate network in the dynamic process there exists much evidence that many real networks possess a scale free sf degree distribution characterized by a power law tail

percolation of partially interdependent scale free networks we study the percolation behavior of two interdependent scale free sf networks under random failure of 1 p fraction of nodes our results are based on numerical solutions of analytical expressions and simulations we find that as the coupling strength between the two networks q reduces from 1 fully coupled to 0 no coupling there exist two critical coupling strengths q 1 and q 2 which separate three different regions with different behavior of the giant component as a function of p i for q q 1 an abrupt collapse transition occurs at p p c ii for q 2 3 q 1 decreases with increasing here is the scaling exponent of the degree distribution p k proportionality k b in the hybrid transition at the q 2 0 for 3 thus the known theoretical p c 0 for a single network with 3 is expected to be valid also for strictly partial interdependent networks

targeted attack on networks coupled by connectivity and dependency links abstract coupled systems used to increase capacity were shown beneficial as long as it does not open pathways to cascades previous studies on the robustness of coupled networks except for interdependent networks are almost the cases of random attack many challenges remain exist in targeted attack problem of coupled networks since nodes within coupled networks show different functions for each network this paper both analytically and numerically analyzed the robustness of coupled networks under three types of targeted attacking strategies including attacking on nodes by considering internal and external degree internal degree only and external degree only for coupled network with both interdependent and interconnected links all degree distributions of intra and inter connectivity links are poissonian we find the system undergoes from second to first order phase transition as coupling strength q increases the fraction of nodes in the giant component p at stable state the critical phase transition threshold p c first order threshold p c i and second order threshold p c i i and the critical point p c q c separating the first and second order phase transitions are analytically obtained for three types of attacking strategies with attacking probability parameter 0 1 we also find the system becomes more vulnerable as the average degree of intra links k or inter links k decreases therefore the minimum average degrees k m i n and k m i n to maintain the system stable are obtained for the case of 0 1 moreover we discussed three typical cases of coupled networks interdependent networks k 0 interacting networks q 0 and bipartite network k 0 q 0 the analytical expressions of p p c and p c q c only for interdependent are given respectively besides we study the equivalence relations between interdependent networks and coupled networks with connectivity and dependency links for the same p c the results imply that we can adjust the parameters q k and k to make the two systems have the same robustness moreover the results imply that one should not only protect nodes with high degree of intra links or inter links but also defend nodes the sum of whose degree of intra links and inter links is big can avoid the system becoming vulnerable

on ultimate boundedness control of uncertain systems in the absence of matching assumptions this paper describes an approach to ultimate boundedness control under hypotheses less stringent than heretofore required instead of imposing the so called matching conditions of previous authors a certain decomposition of the dynamics is performed the resulting decomposed system has two parts a matched portion and a mismatched portion a certain measure of mismatch m is defined and it is shown that effective control is possible as long as m does not exceed some critical mismatch threshold m it is seen that this threshold depends on the choice of feedback hence it becomes possible to investigate the tradeoffs between the size of the mismatch threshold and the sizes of the feedback gains which achieve the desired ultimate boundedness of solutions

on the supremally regulated complex stability radius as a real robustness measure abstract the main result of this paper is the identification of a class of real systems for which the supremal hinrichsen pritchard complex stability radius is equal to the supremal hinrichsen pritchard real stability radius for this class which includes all planar linear systems with non zero input operator the remarkable differences which are known to exist between these two measures of robustness in the absence of control can be eliminated by state feedback the respective differences and equivalences are illustrated by examples of single input uncertain planar control systems