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

adjoint active surfaces for localization and imaging this paper addresses the problem of localizing and segmenting regions embedded within a surrounding medium by characterizing their boundaries as opposed to imaging the entirety of the volume active surfaces are used to directly reconstruct the shape of the region of interest we describe the procedure for finding the optimal surface which is computed iteratively via gradient descent that exploits the sensitivity of an error minimization functional to changes of the active surface in doing so we introduce the adjoint model to compute the sensitivity and in this respect the method shares common ground with several other disciplines such as optimal control finally we illustrate the proposed active surface technique in the framework of wave propagation governed by the scalar helmholtz equation potential applications include electromagnetics acoustics geophysics nondestructive testing and medical imaging

exponential synchronization of chaotic neural networks with time varying delay via intermittent output feedback approach abstract this paper is dealt with the problem of exponential synchronization for chaotic neural networks with time varying delay by using intermittent output feedback control based on the lyapunov krasovskii functional method and the lower bound lemma for reciprocally convex technique a novel criterion for existence of the controller is first established to ensure synchronization between the master and slave systems moreover from the delay point of view the derived criterion is extended to the relaxed case because of introducing an adjustable parameter in the lyapunov krasovskii functional finally a numerical simulation is carried out to demonstrate the effectiveness of the proposed synchronization law

observer based adaptive fuzzy tracking control of nonlinear systems with time delay and input saturation this paper studies the problem of adaptive output tracking control for a class of nonlinear systems subject to unknown time delay and input saturation to address the delay and the input saturation some reasonable assumptions and an auxiliary system are introduced the fuzzy logic approach is employed to approximate the unknown functions in the system an observer is designed to estimate the unavailable system states the dynamic surface control dsc technique is utilized to avoid the problem of explosion of complexity by combining the backstepping and dsc methods a bounded control input is designed to ensure that all signals of the closed loop system are bounded and the tracking error can fluctuate around the origin within a small neighborhood finally two examples are presented to demonstrate the effectiveness and potential of the proposed new design techniques

stability analysis and design of impulsive control systems with time delay a class of impulsive control systems with time varying delays is considered by establishing an impulsive delay differential inequality we analyze the global exponential stability of the impulsive delay systems and estimate the exponential convergence rate on the basis of the analysis a design procedure of impulsive controller is presented the designed impulsive controller not only can globally exponentially stabilize the time delay systems but also can control the exponential convergence rate of the systems two numerical examples are given to illustrate the effectiveness of the method

coupled complex adjoint sensitivities for frequency domain fluorescence tomography theory and vectorized implementation we present a computationally efficient and accurate adjoint method for calculating coupled sensitivities of complex frequency domain excitation and emission fluence to any underlying optical parameters in highly scattering media the method is shown to be general and accurate novel vectorized implementations for finite element global matrix assembly and adjoint sensitivity calculations are shown to speed up calculations by orders of magnitude over traditional loop implementations thereby making least squares approaches to fluorescence tomography computationally practical

perturbed optimization in banach spaces i a general theory based on a weak directional constraint qualification using a directional form of constraint qualification weaker than robinson s we derive an implicit function theorem for inclusions and use it for first and second order sensitivity analyses of the value function in perturbed constrained optimization we obtain holder and lipschitz properties and under a no gap condition first order expansions for exact and approximate solutions as an application differentiability properties of metric projections in hilbert spaces are obtained using a condition generalizing polyhedricity we also present in the appendix a short proof of a generalization of the convex duality theorem in banach spaces

no gap second order optimality conditions for optimal control problems with a single state constraint and control the paper deals with optimal control problems with only one control variable and one state constraint of arbitrary order we consider the case of finitely many boundary arcs and touch times we obtain a no gap theory of second order conditions allowing to characterize second order quadratic growth

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

stability analysis of optimal control problems with a second order state constraint this paper gives stability results for nonlinear optimal control problems subject to a regular state constraint of second order the strengthened legendre clebsch condition is assumed to hold and no assumption on the structure of the contact set is made under a weak second order sufficient condition taking into account the active constraints we show that the solutions are lipschitz continuous w r t the perturbation parameter in the l 2 norm and holder continuous in the l infty norm we use a generalized implicit function theorem in metric spaces by dontchev and hager siam j control optim 36 1998 pp 698 718 the difficulty is that multipliers associated with second order state constraints have a low regularity they are only bounded measures we obtain lipschitz stability of a primitive of the state constraint multiplier

a comparison of exact and approximate adjoint sensitivities in fluorescence tomography many approaches to fluorescence tomography utilize some form of regularized nonlinear least squares algorithm for data inversion thus requiring repeated computation of the jacobian sensitivity matrix relating changes in observable quantities such as emission fluence to changes in underlying optical parameters such as fluorescence absorption an exact adjoint formulation of these sensitivities comprises three terms reflecting the individual contributions of 1 sensitivities of diffusion and decay coefficients at the emission wavelength 2 sensitivities of diffusion and decay coefficients at the excitation wavelength and 3 sensitivity of the emission source term simplifying linearity assumptions are computationally attractive in that they cause the first and second terms to drop out of the formulation the relative importance of the three terms is thus explored in order to determine the extent to which these approximations introduce error computational experiments show that while the third term of the sensitivity matrix has the largest magnitude the second term becomes increasingly significant as target fluorophore concentration or volume increases image reconstructions from experimental data confirm that neglecting the second term results in overestimation of sensitivities and consequently overestimation of the value and volume of the fluorescent target whereas contributions of the first term are so low that they are probably not worth the additional computational costs

effect of parameter mismatch on the mechanism of chaos synchronization loss in coupled systems using the example of two coupled logistic maps we investigate the effect of nonidentical subsystems on the bifurcations of saddle periodic orbits embedded in a symmetric chaotic attractor these bifurcations determine the process of loss of chaos synchronization we show that if bifurcations conditioned by the symmetry of the system take part in the synchronization loss process nonidentity changes the bifurcation scenario of the transition to a nonsynchronous regime in this case for example the transition to the bubbling behavior is determined not by bifurcation of an orbit embedded in the chaotic attractor but by the smooth shift of it and the saddle repeller bifurcation of the birth of new orbits in the vicinity of the quasisymmetric region s1063 651x 98 10909 1 pacs number s 05 45 1b

event triggered sampling control for stability and stabilization of memristive neural networks with communication delays this paper investigates the global asymptotic stability and stabilization of memristive neural networks mnns with communication delays via event triggered sampling control first based on the novel approach in lemma 1 the concerned mnns are converted into traditional neural networks with uncertain parameters next a discrete event triggered sampling control scheme which only needs supervision of the system state at discrete instants is designed for mnns for the first time thanks to this controller the number of control updates could greatly reduce then by getting utmost out of the usable information on the actual sampling pattern a newly augmented lyapunov krasovskii functional lkf is constructed to formulate stability and stabilization criteria it should be mentioned that the lkf is positive definite only at endpoints of each subinterval of the holding intervals but not necessarily positive definite inside the holding intervals finally the feasibility and effectiveness of the proposed results are tested by two numerical examples

finite time dissipative control for stochastic interval systems with time delay and markovian switching the finite time stochastically boundedness ftsb and the finite time strictly stochastically exponential dissipative ftssed control problems for the stochastic interval systems which are encountered the time delay and markovian switching are investigated in this paper the stochastic delayed interval systems with markovian switching sdisswms are equivalently transformed into a kind of stochastic uncertain time delay systems with markovian switching by interval matrix transformation some sufficient conditions of ftsb and ftssed for the stochastic delayed interval systems with markovian switching are obtained and the ftsb and ftssed controllers are designed by solving a series of linear matrix inequalities which are solvable by lmis toolbox finally a numerical example with simulations is given to illustrate the correctness of the obtained results and the effectiveness of the designed controller

exponential synchronization of hybrid coupled networks with delayed coupling this paper investigates exponential synchronization of coupled networks with hybrid coupling which is composed of constant coupling and discrete delay coupling there is only one transmittal delay in the delayed coupling the fact is that in the signal transmission process the time delay affects only the variable that is being transmitted from one system to another then it makes sense to assume that there is only one single delay contributing to the dynamics some sufficient conditions for synchronization are derived based on lyapunov functional and linear matrix inequality lmi in particular the coupling matrix may be asymmetric or nondiagonal moreover the transmittal delay can be different from the one in the isolated system a distinctive feature of this work is that the synchronized state will vary in comparison with the conventional synchronized solution especially the degree of the nodes and the inner delayed coupling matrix heavily influence the synchronized state finally a chaotic neural network is used as the node in two regular networks to show the effectiveness of the proposed criteria

impulsive effects on quasi synchronization of neural networks with parameter mismatches and time varying delay this paper is concerned with the exponential synchronization issue of nonidentically coupled neural networks with time varying delay due to the parameter mismatch phenomena existed in neural networks the problem of quasi synchronization is thus discussed by applying some impulsive control strategies based on the definition of average impulsive interval and the extended comparison principle for impulsive systems some criteria for achieving the quasi synchronization of neural networks are derived more extensive ranges of impulsive effects are discussed so that impulse could either play an effective role or play an adverse role in the final network synchronization in addition according to the extended formula for the variation of parameters with time varying delay precisely exponential convergence rates and quasi synchronization errors are obtained respectively in view of different types impulsive effects finally some numerical simulations with different types of impulsive effects are presented to illustrate the effectiveness of theoretical analysis

quasi synchronization of heterogeneous dynamic networks via distributed impulsive control this paper studies leader follower synchronization in heterogeneous dynamic networks via distributed impulsive control the goal is to drive the followers to approximately synchronize with the leader within a nonzero error bound referred to as quasi synchronization some fundamental and yet challenging problems are addressed 1 how to obtain a tight quasi synchronization error bound 2 how many and which nodes should be controlled 3 how to design the coupling strength to select the pinned nodes and to determine the impulse intervals to optimize the error bound or to achieve quasi synchronization within a prescribed error bound first some general quasi synchronization conditions are derived with explicit expressions of the error bound second the pinning strategy and the coupling strength in achieving quasi synchronization are explored and expressed in term of impulse intervals it is interesting to find that a large coupling strength will destroy synchrony in contrast to continuous pinning control furthermore the common requirement that the leader has a directed path to every node is needed only in the case that the impulse intervals can be arbitrarily small a new concept referred to as impulse pinning controllability is introduced to the case that impulses cannot take place too frequently third an optimization of the error bound is discussed and formulated under a prescribed error bound the design problem of the coupling strength pinned nodes and impulse intervals is solved finally three examples are given to verify the theoretical results

pinning control of scale free dynamical networks abstract recently it has been demonstrated that many large complex networks display a scale free feature that is their connectivity distributions have the power law form in the present work control of a scale free dynamical network by applying local feedback injections to a fraction of network nodes is investigated the specifically and randomly pinning schemes are considered the specifically pinning of the most highly connected nodes is shown to require a significantly smaller number of local controllers as compared to the randomly pinning scheme the method is applied to an array of chua s oscillators as an example

stability of asymmetric hopfield networks in this paper we discuss dynamical behaviors of recurrently asymmetrically connected neural networks in detail we propose an effective approach to study global and local stability of the networks many of well known existing results are unified in our framework which gives much better test conditions for global and local stability sufficient conditions for the uniqueness of the equilibrium point and its stability conditions are given too

some relaxation problems in optimal control theory usually the space u r is a space lp q endowed with its weak topology the space y g is a sobolev space w y q endowed with its weak topology or with the l q topology in the one dimensional case and condition ii is guaranteed by some boundedness or growth hypotheses on j and a when condition i is not fulfilled in general the existence of a solution of 1 1 may fail nevertheless it may be interesting to study the asymptotic 212 0022 247x 87 3 00

state estimation for stochastic discrete time systems with multiplicative noises and unknown inputs over fading channels abstract this paper deals with robust state estimation problem for a class of stochastic discrete time systems with multiplicative noises and unknown inputs over fading channels an unbiased unknown input insensitive filter is designed such that the variance of the estimation error is minimized in the sense of the so called p estimation the filter gain matrix is derived through solving a recursive riccati equation and a generalized lyapunov equation a necessary and sufficient condition that guarantees the existence of the filter is given which establishes a fundamental limit on the mean square capacity of each fading channel unknown input estimation and finite horizon stability of the proposed filter are also discussed to illustrate the effectiveness of the proposed approach the proposed algorithm is applied to a faulty remote controlled uninterruptible power system where both the state and the fault are estimated

synchronization error estimation and controller design for delayed lur e systems with parameter mismatches this paper investigates the problem of master slave synchronization of two delayed lur e systems in the presence of parameter mismatches first by analyzing the corresponding synchronization error system synchronization with an error level which is referred to as quasi synchronization is established some delay dependent quasi synchronization criteria are derived an estimation of the synchronization error bound is given and an explicit expression of error levels is obtained second sufficient conditions on the existence of feedback controllers under a predetermined error level are provided the controller gains are obtained by solving a set of linear matrix inequalities finally a delayed chua s circuit is chosen to illustrate the effectiveness of the derived results

synchronization of coupled reaction diffusion neural networks with time varying delays via pinning impulsive controller in this paper global exponential synchronization stability in an array of linearly diffusively coupled reaction diffusion neural networks with time varying delays is investigated by adding impulsive controller to a small fraction of nodes pinning impulsive controller in order to overcome the difficulty resulting from the fact that the impulsive controller affects only the dynamical behaviors of the controlled nodes a new analysis method is developed by using the developed method two known lemmas on stability of delayed functional differential equation with and without impulses and lyapunov stability theory several novel and easily verified synchronization criteria guaranteeing the whole network will be pinned to a homogenous solution are derived moreover the effects of the pinning impulsive controller and the dynamics of the uncontrolled nodes and the diffusive couplings on the synchronization process are explicitly expressed in the obtained criteria our results also show that we can always de

brief paper a unified synchronization criterion for impulsive dynamical networks this paper focuses on the problem of globally exponential synchronization of impulsive dynamical networks two types of impulses are considered synchronizing impulses and desynchronizing impulses in previous literature all of the results are devoted to investigating these two kinds of impulses separately thus a natural question arises is there any unified synchronization criterion which is simultaneously effective for synchronizing impulses and desynchronizing impulses in this paper a unified synchronization criterion is derived for directed impulsive dynamical networks by proposing a concept named average impulsive interval the derived criterion is theoretically and numerically proved to be less conservative than existing results numerical examples including scale free and small world structures are given to show that our results are applicable to large scale networks

three dimensional bayesian optical image reconstruction with domain decomposition most current efforts in near infrared optical tomography are effectively limited to two dimensional reconstructions due to the computationally intensive nature of full three dimensional 3 d data inversion previously we described a new computationally efficient and statistically powerful inversion method apprize automatic progressive parameter reducing inverse zonation and estimation the apprize method computes minimum variance estimates of parameter values here spatially variant absorption due to a fluorescent contrast agent and covariance while simultaneously estimating the number of parameters needed as well as the size shape and location of the spatial regions that correspond to those parameters estimates of measurement and model error are explicitly incorporated into the procedure and implicitly regularize the inversion in a physically based manner the optimal estimation of parameters is bounds constrained precluding infeasible values in this paper the apprize method for optical imaging is extended for application to arbitrarily large 3 d domains through the use of domain decomposition the effect of subdomain size on the performance of the method is examined by assessing the sensitivity for identifying 112 randomly located single voxel heterogeneities in 58 3 d domains also investigated are the effects of unmodeled heterogeneity in background optical properties the method is tested on simulated frequency domain photon migration measurements at 100 mhz in order to recover absorption maps owing to fluorescent contrast agent this study provides a new approach for computationally tractable 3 d optical tomography

relaxation of constrained control problems the problem of relaxation of optimal control problems with state and control constraints is formulated in this paper we determine that if the original problem consists of minimizing over control functions z g x t subject to d x ds f s x z t s leq t and h s x s z s leq 0 for a e t leq s leq t then the relaxed problem consists of minimizing over measure valued control functions m g xhat t subject to d xhat ds int z f s xhat s z m s dz and m s esssup z h s xhat s z leq 0 for a e t leq s leq t for each s this is the essential supremum of h in z with respect to the measure m s

l2 l synchronization for singularly perturbed complex networks with semi markov jump topology abstract this paper is concerned with the problem of l 2 l synchronization for singularly perturbed complex networks spcns with semi markov jump topology in which the phenomenon of the singular perturbation is fully taken into consideration the topology of complex dynamical network is time varying switching regulated by the semi markov jump mechanism the priority of this work is to obtain some conditions which ensure the underlying complex dynamical network cdn is stochastically synchronized with a stated l 2 l performance level based on lyapunov method and convex optimization technique the synchronization conditions can be obtained via solving convex optimization problems finally the correctness and validity of our proposed synchronization method are well demonstrated by a simulation example

second order necessary conditions in pontryagin form for optimal control problems in this article we state and prove first and second order necessary conditions in pontryagin form for optimal control problems with pure state and mixed control state constraints we say that a lagrange multiplier of an optimal control problem is a pontryagin multiplier if it is such that pontryagin s minimum principle holds and we call optimality conditions in pontryagin form those which only involve pontryagin multipliers our conditions rely on a technique of partial relaxation and apply to pontryagin local minima

discretization error analysis and adaptive meshing algorithms for fluorescence diffuse optical tomography part ii for imaging problems in which numerical solutions need to be computed for both the inverse and the underlying forward problems discretization can be a major factor that determines the accuracy of imaging in this work we analyze the effect of discretization on the accuracy of fluorescence diffuse optical tomography we model the forward problem by a pair of diffusion equations at the excitation and emission wavelengths and consider a finite element discretization method for the numerical solution of the forward problem for the inverse problem we use an optimization framework which allows incorporation of a priori information in the form of zeroth and first order tikhonov regularization terms next we convert the inverse problem into a variational problem and use galerkin projection to discretize the inverse problem following the discretization we analyze the error in reconstructed images due to the discretization of the forward and inverse problems and present two theorems which point out the factors that may lead to high error such as the mutual dependence of the forward and inverse problems the number of sources and detectors their configuration and their positions with respect to fluorophore concentration and the formulation of the inverse problem finally we demonstrate the results and implications of our error analysis by numerical experiments in the second part of the paper we apply our results to design novel adaptive discretization algorithms

sensitivity analysis for relaxed optimal control problems with final state constraints in this article we compute a second order expansion of the value function of a family of relaxed optimal control problems with final state constraints parameterized by a perturbation variable the sensitivity analysis is performed for controls that we call r strong solutions they are optimal solutions with respect to the set of feasible controls with a uniform norm smaller than a given r and having an associated trajectory in a small neighborhood for the uniform norm in this framework relaxation enables us to consider a wide class of perturbations and therefore to derive sharp estimates of the value function

relaxation of control systems under state constraints in this paper we provide a relaxation result for control systems under both equality and inequality constraints involving the state and the control in particular we show that the mangasarian fromowitz constraint qualification allows us to rewrite constrained systems as differential inclusions with locally lipschitz right hand side then the filippov wazewski relaxation theorem may be applied to show that ordinary solutions are dense in the set of relaxed solutions if besides agreeing with the above constraints the state has to remain in a control independent set k then the mangasarian fromowitz condition cannot hold this case is investigated as well by means of a condition on the feasible velocities on the boundary of k

computation of centre manifolds and some codimension one bifurcations for impulsive delay differential equations abstract based on the centre manifold theorem for impulsive delay differential equations we derive impulsive evolution equations and boundary conditions associated to a concrete representation of the centre manifold in euclidean space as well as finite dimensional impulsive differential equations associated to the evolution on these manifolds though the centre manifolds are not unique their taylor expansions agree up to prescribed order and we present an implicit formula for the quadratic term using a variation of the method of characteristics we use our centre manifold reduction to derive analogues of the saddle node and hopf bifurcation for impulsive delay differential equations and the latter leads to a novel bifurcation pattern to an invariant cylinder examples are provided to illustrate the correctness of the bifurcation theorems and to visualize the geometry of centre manifolds in the presence of impulse effects

sampled data synchronization of chaotic lur e systems via input delay dependent free matrix zero equality approach abstract this paper focuses on the sampled data synchronization problem of chaotic lur e systems clss by using sampled output of the systems with variable sampling rates one novel approach input delay dependent free matrix zero equality iddfmze approach is proposed for the first time the iddfmze approach can not only fully capture the available information on the actual sampling pattern but deploy more system information at the dynamic partitioning point a new lyapunov krasovskii functional lkf with some new terms is constructed which can use more information of the activation function at the dynamic partitioning point based on the presented iddfmze approach and the constructed lkf developed synchronization criterion is obtained in the form of linear matrix inequalities lmis the desired sampled data controller is designed under larger sampling period finally the superiority of proposed results is shown by two numerical examples