three step iterations for variational inequalities and nonexpansive mappings in this paper we introduce a new three step iterative scheme for finding the common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality using the technique of updating the solution we show that the sequence converges strongly to a common element of two sets under some control conditions results proved in this paper may be viewed as an improvement and refinement of the recent results of noor and huang m aslam noor z huang three step methods for nonexpansive mappings and variational inequalities appl math comput in press and yao and yao y yao j c yao on modified iterative method for nonexpansive mappings and monotone mappings appl math comput in press

on equivalence of two stability criteria for continuous time switched systems with dwell time constraint in this note a study on the equivalence of two stability criteria for continuous time switched linear systems with dwell time constraint is presented it is demonstrated that for any dwell time satisfying the conditions in stability criterion proposed in geromel and colaneri 2006 the conditions in stability criterion of allerhand and shaked 2011 also hold as long as the number of decision variables and related lmis is sufficiently large which implies the two stability criteria are intrinsically equivalent the equivalence is obtained by showing that two criteria can be derived from each other with a sufficiently large number of decision variables and lmis a numerical example is proposed to illustrate the theoretical results and an extension to uncertain case is briefly presented

viscosity approximation methods for nonexpansive mapping sequences in banach spaces abstract let e be a real strictly convex banach space with a uniformly g teaux differentiable norm and k be a nonempty closed convex subset of e suppose that t n n 1 2 is a uniformly asymptotically regular sequence of nonexpansive mappings from k to itself such that f n 1 f t n 0 for arbitrary initial value x 0 k and fixed contractive mapping f k k define iteratively a sequence x n as follows x n 1 n 1 f x n 1 n 1 t n 1 x n n 0 where n 0 1 satisfies lim n n 0 and n 1 n suppose for any nonexpansive mapping t k k z t strongly converges to a fixed point z of t as t 0 where z t is the unique element of k which satisfies z t t f z t 1 t t z t then as n x n z our results extend and improve the corresponding ones of o hara et al j g o hara p pillay h k xu iterative approaches to finding nearest common fixed point of nonexpansive mappings in hilbert spaces nonlinear anal 54 2003 1417 1426 and j s jung iterative approaches to common fixed points of nonexpansive mappings in banach spaces j math anal appl 302 2005 509 520 and h k xu viscosity approximation methods for nonexpansive mappings j math anal appl 298 2004 279 291

an iterative algorithm for solving fixed point problems variational inequality problems and mixed equilibrium problems abstract in this paper we introduce an iterative algorithm for finding a common element of the set of solutions of a mixed equilibrium problem the set of fixed points of an infinite family of nonexpansive mappings and the set of solutions of some variational inequality furthermore we prove that the proposed iterative algorithm converges strongly to a common element of the above three sets our results extend and improve the corresponding results of zeng and yao l c zeng and j c yao a hybrid iterative scheme for mixed equilibrium problems and fixed point problems j comput appl math 214 2008 186 201 takahashi and takahashi s takahashi and w takahashi viscosity approximation methods for equilibrium problems and fixed point problems in hilbert spaces j math anal appl 331 2007 506 515 and many others

three dimensional circular formations via set stabilization the paper addresses distributed stabilization of a class of circular formations for steered kinematic particles in three dimensional euclidean space information exchange between the particles is modeled by a bidirectional graph which is assumed to have a spanning tree distributed control design is based on a hierarchical approach that relies on set stabilization and a reduction principle for asymptotic stability of closed sets the approach allows to solve for different formation specifications in a decoupled manner

consensus of high order multi agent systems with large input and communication delays we study in this paper the consensus problem for multi agent systems with agents characterized by high order linear systems with time delays in both the communication network and inputs provided that the open loop dynamics of the agents is not exponentially unstable but may be polynomially unstable and the communication topology contains a directed spanning tree a truncated predictor feedback approach is established to solve the consensus problem it is shown that if the delays are constant and exactly known the consensus problems can be solved by both full state feedback and observer based output feedback protocols for arbitrarily large yet bounded delays if it is further assumed that the open loop dynamics of the agents only contains zero eigenvalues the delays are allowed to be time varying and unknown numerical examples are worked out to illustrate the effectiveness of the proposed approaches

robust stability and stabilization of linear switched systems with dwell time sufficient conditions are given for the stability of linear switched systems with dwell time and with polytopic type parameter uncertainty a lyapunov function in quadratic form which is non increasing at the switching instants is assigned to each subsystem during the dwell time this function varies piecewise linearly in time after switching occurs it becomes time invariant afterwards this function leads to asymptotic stability conditions for the nominal set of subsystems that can be readily extended to the case where these subsystems suffer from polytopic type parameter uncertainties the method proposed is then applied to stabilization via state feedback both for the nominal and the uncertain cases

solutions of system of equilibrium and variational inequality problems on fixed points of infinite family of nonexpansive mappings in this paper we introduce a hybrid viscosity approximation scheme for finding a common element of the solution set for a system of equilibrium problems the solution set for a system of variational inequality problems and the common fixed point set for an infinite family of nonexpansive mappings in hilbert spaces then we prove the strong convergence of the proposed iterative scheme our results improve and extend the results announced by ceng and yao 2008 4

stability of a class of linear switching systems with applications to two consensus problems in this paper we first establish a stability result for a class of linear switched systems involving kronecker product the problem is interesting in that the system matrix does not have to be hurwitz at any time instant this class of linear switched systems arises in the control of multi agent systems under switching network topology as applications of this stability result we give the solvability conditions for both the leaderless consensus problem and the leader following consensus problem for general marginally stable linear multi agent systems under switching network topology in contrast with some existing results our results only assume that the dynamic graph is uniformly connected

a general iterative method for nonexpansive mappings in hilbert spaces let h be a real hilbert space consider on h a nonexpansive mapping t with a fixed point a contraction f with coefficient 0 0 let 0

a graph laplacian approach to coordinate free formation stabilization for directed networks this paper concentrates on coordinate free formation control for directed networks for which the dynamic motion of each agent is assumed to be governed only by a local control we develop a graph laplacian approach to solve the global and exponential formation stablization problem using merely relative position measurements between neighbors first to capture the sensing and control architectures that are needed to maintain the shape of a formation a necessary and sufficient topological condition is proposed second a laplacian based control law is developed for the stablization problem of a group of mobile agents to a desired formation shape under both fixed and switching topologies due to temporal node failures simulation results are provided to demonstrate that our laplacian based formation control strategy is inherently fault tolerant and robust to node failures

time varying formation control for general linear multi agent systems with switching directed topologies time varying formation analysis and design problems for multi agent systems with general linear dynamics and switching directed interaction topologies are investigated different from the previous results the formation in this paper can be defined by specified piecewise continuously differentiable vectors and the switching topologies are directed firstly necessary and sufficient conditions for general linear multi agent systems with switching directed topologies to achieve time varying formations are proposed where a description of the feasible time varying formation set and approaches to expand the feasible formation set are given then an explicit expression of the time varying formation reference function is derived to describe the macroscopic movement of the whole formation an approach to assign the motion modes of the formation reference is provided moreover an algorithm consisting of four steps to design the formation protocol is presented in the case where the given time varying formation belongs to the feasible formation set it is proven that by designing the formation protocol using the proposed algorithm time varying formation can be achieved by multi agent systems with general linear dynamics and switching directed topologies if the dwell time is larger than a positive threshold finally numerical simulations are presented to demonstrate the effectiveness of the theoretical results

iterative convergence to cesaro means for continuous pseudocontractive mappings abstract let f be a fixed strongly pseudocontractive mapping and t be a continuous pseudocontractive mapping with f t 0 the sequence z m is iteratively defined as follows z m t m f z m 1 t m 1 m 1 j 0 m t j z m m 0 where t m 0 1 satisfies the condition lim m t m 0 we prove that z m converges strongly to the unique solution p to some variational inequality in f t our results develop and complement the corresponding ones by matsushita daishi kuroiwa j math anal appl 294 2004 206 214 and shioji takahashi arch math 72 1999 354 359 and moore nnoli j math anal appl 260 2001 269 278 and su li appl math comput 181 2006 332 341 and song chen appl math comput 186 2007 1120 1128 and wangkeeree appl math comput 201 2008 239 249

viscosity approximation methods for nonexpansive mappings abstract viscosity approximation methods for nonexpansive mappings are studied consider a nonexpansive self mapping t of a closed convex subset c of a banach space x suppose that the set fix t of fixed points of t is nonempty for a contraction f on c and t 0 1 let x t c be the unique fixed point of the contraction x tf x 1 t tx consider also the iteration process x n where x 0 c is arbitrary and x n 1 n f x n 1 n tx n for n 1 where n 0 1 if x is either hilbert or uniformly smooth then it is shown that x t and under certain appropriate conditions on n x n converge strongly to a fixed point of t which solves some variational inequality

decentralized control of vehicle formations this paper investigates a method for decentralized stabilization of vehicle formations using techniques from algebraic graph theory the vehicles exchange information according to a pre specified communication digraph g a feedback control is designed using relative information between a vehicle and its in neighbors in g we prove that a necessary and sufficient condition for an appropriate decentralized linear stabilizing feedback to exist is that g has a rooted directed spanning tree we show the direct relationship between the rate of convergence to formation and the eigenvalues of the directed laplacian of g various special situations are discussed including symmetric communication graphs and formations with leaders several numerical simulations are used to illustrate the results

strong convergence theorems for a new iterative method of k strictly pseudo contractive mappings in hilbert spaces in this paper we introduce a new iterative method of a k strictly pseudo contractive mapping for some email protected k 1 and prove that the sequence x n converges strongly to a fixed point of t which solves a variational inequality related to the linear operator a our results have extended and improved the corresponding results of y j cho s m kang and x qin some results on k strictly pseudo contractive mappings in hilbert spaces nonlinear anal 70 2008 1956 1964 and many others

iterative algorithms for finding common solutions of variational inequalities and systems of equilibrium problems and fixed points of families and semigroups of nonexpansive mappings abstract we introduce iterative algorithms for finding a common element of the set of solutions of a system of equilibrium problems and of the set of fixed points of a finite family and a left amenable semigroup of nonexpansive mappings in a hilbert space we prove the strong convergence of the proposed iterative algorithm to the unique solution of a variational inequality which is the optimality condition for a minimization problem our results extend for example the recent result of v colao g marino h k xu an iterative method for finding common solutions of equilibrium and fixed point problems j math anal appl 344 2008 340 352 to systems of equilibrium problems

approximating fixed points of holomorphic mappings in the hilbert ball abstract we approximate fixed points of holomorphic and nonexpansive self mappings of the hilbert ball using both continuous and discrete schemes

hybrid control for connectivity preserving flocking in this technical note we address the combined problem of motion and network topology control in a group of mobile agents with common objective the flocking behavior of the group instead of assuming network connectivity we enforce it by means of distributed topology control that decides on both deletion and creation of communication links between agents adapting the network to the group s spatial distribution with this protocol ensuring network connectivity a decentralized motion controller aligns agent velocity vectors and regulates inter agent distances to maintain existing network links the stability of the flocking controller is established in continuous time by means of an observability argument on a quadratic form of the graph laplacian that exploits the time delay between link deletion and creation caused by the topology control protocol which induces a dwell time between network switches

viscosity approximation methods for pseudo contractive semigroups in banach spaces abstract we study the strong convergence of two viscosity iteration processes for pseudo contractive semigroup and for strongly pseudo contractive mapping in uniformly convex banach spaces with uniformly g teaux differentiable norm as special cases we get strong convergence of two viscosity iteration processes for approximating common fixed points of nonexpansive semigroups in certain banach spaces the results presented in this paper extend and generalize previous results

strong convergence theorems of modified ishikawa iterative process with errors for an infinite family of strict pseudo contractions abstract in this paper we study modified ishikawa iterative process with errors to have strong convergence for an infinite family of strict pseudo contractions in the framework of q uniformly smooth banach spaces our results improve and extend the recent ones announced by many others

fixed point solutions of variational inequalities for a finite family of asymptotically nonexpansive mappings without common fixed point assumption let e be a real banach space with a uniformly gateaux differentiable norm and which possesses uniform normal structure k a nonempty bounded closed convex subset of e t i i 1 n a finite family of asymptotically nonexpansive self mappings on k with common sequence k n n 1 1 t n s n be two sequences in 0 1 such that s n t n 1 n 1 and f be a contraction on k under suitable conditions on the sequences s n t n we show the existence of a sequence x n satisfying the relation x n 1 1k n x n s nk nf x n t nk nt r n nx n where n l nn r n for some unique integers l n 0 and 1 r n n further we prove that x n converges strongly to a common fixed point of t i i 1 n which solves some variational inequality provided x n t ix n 0 as n for i 1 2 n as an application we prove that the iterative process defined by z 0 k z n 1 1 1k n z n s nk nf z n t nk nt r n nz n converges strongly to the same common fixed point of t i i 1 n

optical orthogonal codes design analysis and applications an optical orthogonal code ooc is a family of 0 1 sequences with good auto and cross correlation properties i e the autocorrelation of each sequence exhibits the thumbtack shape and the cross correlation between any two sequences remains low throughout the use of optical orthogonal codes enables a large number of asynchronous users to transmit information efficiently and reliably the thumbtack shaped autocorrelation facilitates the detection of the desired signal and low profile cross correlation reduces interference from unwanted signals theoretical upper and lower bounds on the maximum possible size of oocs are derived methods for the design and analysis of oocs using tools from projective geometry the greedy algorithm iterative constructions algebraic coding theory block design and various other combinational disciplines are discussed

relaxed viscosity approximation methods for fixed point problems and variational inequality problems abstract let x be a real strictly convex and reflexive banach space with a uniformly g teaux differentiable norm and c be a nonempty closed convex subset of x let t n n 1 be a sequence of nonexpansive self mappings on c such that the common fixed point set f n 1 f t n 0 and f c c be a given contractive mapping and n be a sequence of nonnegative numbers in 0 1 consider the following relaxed viscosity approximation method x n 1 1 n n x n n f y n n w n y n y n 1 n x n n w n x n n 1 where w n is the w mapping generated by t n t n 1 t 1 and n n 1 1 for each n 1 it is proven that under very mild conditions on the parameters the sequence x n of approximate solutions generated by the proposed method converges strongly to some p f where p is the unique solution in f to the following variational inequality i f p j p x 0 x f

event based cluster synchronization of coupled genetic regulatory networks abstract in this paper the cluster synchronization of coupled genetic regulatory networks with a directed topology is studied by using the event based strategy and pinning control an event triggered condition with a threshold consisting of the neighbors discrete states at their own event time instants and a state independent exponential decay function is proposed the intra cluster states information and extra cluster states information are involved in the threshold in different ways by using the lyapunov function approach and the theories of matrices and inequalities we establish the cluster synchronization criterion it is shown that both the avoidance of continuous transmission of information and the exclusion of the zeno behavior are ensured under the presented triggering condition explicit conditions on the parameters in the threshold are obtained for synchronization the stability criterion of a single grn is also given under the reduced triggering condition numerical examples are provided to validate the theoretical results

strong convergence for a minimization problem on solutions of systems of equilibrium problems and common fixed points of an infinite family and semigroup of nonexpansive mappings in this paper we introduce a suitable mann type algorithm for finding a common element of the set of solutions of systems of equilibrium problems and the set of common fixed points of an infinite family and left amenable semigroup of nonexpansive mappings in hilbert spaces then we prove the strong convergence of the proposed iterative scheme to the unique solution of the minimization problem on the solution of systems of equilibrium problems and the common fixed points of an infinite family and left amenable semigroup of nonexpansive mappings our results extend and improve the recent result of colao and marino v colao and g marino strong convergence for a minimization problem on points of equilibrium and common fixed points of an infinite family of nonexpansive mappings nonlinear anal 73 2010 3513 3524 and many others

optical orthogonal codes their bounds and new optimal constructions a v k spl lambda sub a spl lambda sub c optical orthogonal code ooc c is a family of 0 1 sequences of length v and weight k satisfying the following two correlation properties 1 spl sigma sub 0 spl les t spl les v 1 x sub t x sub t i spl les spl lambda sub a for any x x sub 0 x sub 1 spl middot spl middot spl middot x sub v 1 spl isin c and any integer i not equivalent 0 mod v and 2 spl sigma sub 0 spl les t spl les v 1 x sub t y sub t i spl les spl lambda sub b for any x x sub 0 x sub 1 spl middot spl middot spl middot x sub v 1 spl isin c y y sub 0 y sub 1 spl middot spl middot spl middot y sub v 1 spl isin c with x spl ne y and any integer i where the subscripts are taken modulo v the study of optical orthogonal codes is motivated by an application in optical code division multiple access communication systems in this paper upper bounds on the size of an optical orthogonal code are discussed several new constructions for optimal optical orthogonal codes with weight k spl ges 4 and correlation constraints spl lambda sub a spl lambda sub c 1 are described by means of optimal cyclic packings many new infinite series of such optimal optical orthogonal codes are thus produced

hard limiting performance analysis of 2 d optical codes under the chip asynchronous assumption the traditional chip synchronous assumption used in the analyses of optical codes in optical code division multiple access gives a pessimistic performance upper bound while a more realistic chip asynchronous assumption gives a more accurate performance it is also known that a hard limiter can be placed at the front end of an optical decoder to reduce the effects of multiple access interference and the near far problem in this paper the hard limiting performance of two dimensional 2 d optical codes is analyzed under the chip asynchronous assumption we apply a markov chain method for a more accurate analysis which can be generalized to 2 d optical codes with arbitrary maximum cross correlation values the performance of 2 d optical codes with the hard limiting and chip asynchronous assumptions is also compared with the soft limiting and chip synchronous assumptions

viscosity approximative methods to cesaro mean iterations for nonexpansive nonself mappings in banach spaces let e be a real uniformly convex banach space which admits a weakly sequentially continuous duality mapping from e to e e c a closed convex subset of e which is also a sunny nonexpansive retract of e let t c et c e be a nonexpansive nonself mapping with f t f t and f c cf c c be a fixed contractive mapping the implicit viscosity iterative sequence zm zm is defined by tm 0 1 tm 0 1 zm 1m 1 j 0mp tmf zm 1 tm tp jzm for m 0m 0 and two explicit viscosity iterative sequences xn xn and yn yn are given by x0 c xn 1 nf xn 1 n 1n 1 j 0n pt jxn and y0 c yn 1 1n 1 j 0np nf yn 1 n tp jyn for n 0n 0 where n n is a sequence in 0 1 0 1 and p is a sunny nonexpansive retraction of e onto c we prove that under appropriate conditions imposed on tm tm and n n the sequences zm zm xn xn and yn yn converge strongly to some fixed point of t which solves some variational inequalities the results presented extend and improve the corresponding results of matsushita and kuroiwa s matsushita d kuroiwa strong convergence of averaging iterations of nonexpansive nonself mappings j math anal appl 294 2004 206 214 song and chen y song r chen viscosity approximation methods to cesaro means for nonexpansive mappings appl math comput 186 2007 1120 1128 and many authors

atmospheric optical cdma communication systems via optical orthogonal codes we propose and consider using a class of multiple access sequences namely optical orthogonal codes oocs in atmospheric optical code division multiple access systems we obtain analytical solutions to the error probability for various channel models using positive intrinsic negative diode and avalanche photodiode photodetectors in our analysis the effects of atmospheric turbulence ambient light thermal noise and multiuser interference are considered in the context of a semiclassical photon counting approach the performance of the systems taking advantage of space diversity and error correcting codes are also evaluated two common and widely used optical modulations on off keying and pulse position modulation are considered receiver structures based on correlator and chip level are used for ooc detection unlike the traditional chip level receiver here a generalized form of chip level structure with two threshold levels is considered upper and lower bounds on the error probability for the above chip level receiver structure is obtained from our analytical results we can deduce that the chip level receiver outperforms a simple correlator in the absence or weak atmospheric fading however in a strong fading environment the simple correlator outperforms the chip level receiver

global stabilization of rigid formations in the plane this paper considers the problem of distributed control of rigid formation shapes in the plane for multi agent systems a constructive perturbation method is proposed and combined with the conventional gradient control law the proposed control law stabilizes the desired rigid formation in a global sense for all initial conditions except the case when a pair of communicating agents happen to have the same initial location it also avoids collisions between any two communicating agents during the motion simulation results are provided to illustrate the effectiveness of the control algorithm

iterative schemes for computing fixed points of nonexpansive mappings in banach spaces abstract let x be a real banach space with a normalized duality mapping uniformly norm to weak continuous on bounded sets or a reflexive banach space which admits a weakly continuous duality mapping j with gauge let f be an contraction and t n a sequence of nonexpansive mappings we study the strong convergence of explicit iterative schemes 1 x n 1 n f x n 1 n t n x n with a general theorem and then recover and improve some specific cases studied in the literature k aoyoma y kimura w takahashi m toyoda approximation of common fixed point of a countable family of nonexpansive mappings nonlinear anal 67 8 2007 2350 2360 g lopez v martin h k xu perturbation techniques for nonexpansive mappings with applications nonlinear anal real world appl in press available online 4 may 2008 h k xu viscosity approximation methods for nonexpansive mappings j math anal appl 298 1 2004 279 291 t h kim h k xu strong convergence of modified mann iterations nonlinear anal 61 1 2 2005 51 60 y song r chen strong convergence theorems on an iterative method for a family of finite nonexpansive mappings appl math comput 180 2006 275 287 y song r chen viscosity approximation methods for nonexpansive nonself mappings j math anal appl 321 1 2006 316 326 j chen l zhang t fan viscosity approximation methods for nonexpansive mappings and monotone mappings j math anal appl 334 2 2007 1450 1461 y kimura w takahashi m toyoda convergence to common fixed points of a finite family of nonexpansive mappings arch math 84 2005 350 363

distributed control for uniform circumnavigation of ring coupled unicycles the paper studies the general circumnavigation problem for a team of unicycle type agents with the goal of achieving specific circular formations and circling on different orbits centered at a target of interest a novel distributed solution is proposed in which the control laws are heterogeneous for the agents such that some agents are repellant from the target while attractive to its unique neighbor and some agents are attractive to the target while repellant from its neighbor a systematic procedure is developed to design the control parameters according to the specific radii of the orbits and the formations that the agents are desired to converge to moreover this control scheme uses a minimum number of information flow links between the agents and local measurements of relative position only based on the block diagonalization of circulant matrices by a fourier transform asymptotic convergence properties are analyzed rigorously the validity of the proposed control algorithm is also demonstrated through numerical simulations

ocdma coded free space optical links for wireless optical mesh networks we propose a wireless optical mesh network based on optical code division multiple access ocdma coded free space optical links the performance of the proposed network under intermediate and strong turbulence channel conditions is investigated for synchronous and asynchronous ocdma we show that synchronous ocdma using complementary walsh hadamard codes operating at a raw bit rate of 622 mb s per user can achieve a bit error rate of 10 sup 9 this is achievable in channels with strong turbulence and high temporal correlation or in channels with intermediate turbulence conditions reasonable conditions based on channel characteristics inferred from the refractive index spectrum for asynchronous ocdma using optical orthogonal codes oocs using a lower bound we show that asynchronous ocdma using oocs cannot achieve acceptable performance for the same channel conditions due to interference limitations

viscosity approximation methods for fixed points problems the aim of this work is to propose viscosity approximation methods which amounts to selecting a particular fixed point of a given nonexpansive self mapping

h_ infty consensus achievement of multi agent systems with directed and switching topology networks the consensus problems with h infty and weighted h infty bounds for a homogeneous team of linear time invariant lti multi agent systems with a switching topology and directed communication network graph are studied in this technical note sufficient conditions to design distributed controllers are proposed based on state feedback corresponding to bounded l 2 gain and rms bounded disturbances based on the solution of an algebraic riccati equation that circumvents the need to solve linear matrix inequalities lmis a design methodology is proposed to properly select the controller gains the stability properties of the proposed controllers are then investigated based on lyapunov analysis the effectiveness of our proposed consensus algorithms are then illustrated by performing simulations for diving consensus of a team of unmanned underwater vehicles uuvs

consensus seeking in multiagent systems under dynamically changing interaction topologies this note considers the problem of information consensus among multiple agents in the presence of limited and unreliable information exchange with dynamically changing interaction topologies both discrete and continuous update schemes are proposed for information consensus this note shows that information consensus under dynamically changing interaction topologies can be achieved asymptotically if the union of the directed interaction graphs have a spanning tree frequently enough as the system evolves

h sub spl infin control for networked systems with random communication delays this note is concerned with a new controller design problem for networked systems with random communication delays two kinds of random delays are simultaneously considered i from the controller to the plant and ii from the sensor to the controller via a limited bandwidth communication channel the random delays are modeled as a linear function of the stochastic variable satisfying bernoulli random binary distribution the observer based controller is designed to exponentially stabilize the networked system in the sense of mean square and also achieve the prescribed h sub spl infin disturbance attenuation level the addressed controller design problem is transformed to an auxiliary convex optimization problem which can be solved by a linear matrix inequality lmi approach an illustrative example is provided to show the applicability of the proposed method

h consensus control with spectrum constraints for stochastic multi agent systems subject to x u v dependent noises abstract this paper is concerned with the problem of h consensus control with spectrum constraints for continuous time multi agent systems mass with x u v dependent noises by means of the spectrum technique the definition of stability is introduced and the relationship between the convergence rate of state responses and the stability is discussed for the closed loop system the aim of the addressed problem is to design a static output feedback controller such that the closed loop system is stable and the prescribed h performance requirement is satisfied in virtue of the stochastic analysis method and kronecker product sufficient conditions are obtained for the existence of h consensus controller two examples are provided to illustrate the availability of the proposed techniques

containment control in mobile networks in this paper the problem of driving a collection of mobile robots to a given target destination is studied in particular we are interested in achieving this transfer in an orderly manner so as to ensure that the agents remain in the convex polytope spanned by the leader agents while the remaining agents only employ local interaction rules to this aim we exploit the theory of partial difference equations and propose hybrid control schemes based on stop go rules for the leader agents non zenoness liveness and convergence of the resulting system are also analyzed

an extragradient like approximation method for variational inequality problems and fixed point problems the purpose of this paper is to investigate the problem of finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of a variational inequality problem for a monotone lipschitz continuous mapping we introduce an extragradient like approximation method which is based on so called extragradient method and viscosity approximation method we establish a strong convergence theorem for two iterative sequences generated by this method

time varying formation tracking for linear multiagent systems with multiple leaders time varying formation tracking problems for linear multiagent systems with multiple leaders are studied where the states of followers form a predefined time varying formation while tracking the convex combination of the states of multiple leaders followers are classified into well informed ones and uninformed ones where the neighbor set of the former contains all the leaders whereas the latter contains no leaders a formation tracking protocol is constructed using only neighboring relative information necessary and sufficient conditions for multiagent systems with multiple leaders to achieve time varying formation tracking are proposed by utilizing the properties of the laplacian matrix where the formation tracking feasibility constraints are also given an approach to design the formation tracking protocol is presented by solving an algebraic riccati equation the obtained results can be applied to deal with time varying formation tracking problems target enclosing problems and consensus tracking problems for linear multiagent systems with one or multiple targets leaders numerical simulations are provided to demonstrate the effectiveness of the theoretical results

strong convergence of viscosity approximation methods for finding zeros of accretive operators in banach spaces abstract in this paper we introduce a composite iterative scheme by viscosity approximation method for finding a zero of an accretive operator in banach spaces then we establish strong convergence theorems for the composite iterative scheme the main theorems improve and generalize the recent corresponding results of kim and xu t h kim h k xu strong convergence of modified mann iterations nonlinear anal 61 2005 51 60 qin and su x qin y su approximation of a zero point of accretive operator in banach spaces j math anal appl 329 2007 415 424 and xu h k xu strong convergence of an iterative method for nonexpansive and accretive operators j math anal appl 314 2006 631 643 as well as aoyama et al k aoyama y kimura w takahashi m toyoda approximation of common fixed points of a countable family of nonexpansive mappings in banach spaces nonlinear anal 67 2007 2350 2360 benavides et al t d benavides g l acedo h k xu iterative solutions for zeros of accretive operators math nachr 248 249 2003 62 71 chen and zhu r chen z zhu viscosity approximation fixed points for nonexpansive and m accretive operators fixed point theory and appl 2006 2006 1 10 and kamimura and takahashi s kamimura w takahashi approximation solutions of maximal monotone operators in hilberts spaces j approx theory 106 2000 226 240

on relaxed viscosity iterative methods for variational inequalities in banach spaces in this paper we suggest and analyze a relaxed viscosity iterative method for a commutative family of nonexpansive self mappings defined on a nonempty closed convex subset of a reflexive banach space we prove that the sequence of approximate solutions generated by the proposed iterative algorithm converges strongly to a solution of a variational inequality our relaxed viscosity iterative method is an extension and variant form of the original viscosity iterative method the results of this paper can be viewed as an improvement and generalization of the previously known results that have appeared in the literature

a general iterative scheme for k strictly pseudo contractive mappings and optimization problems in this paper we introduce a new general iterative scheme for finding fixed points of a strictly pseudo contractive mapping and then prove that the sequence generated by the proposed iterative scheme converges strongly to a fixed point of the mapping which is a solution of a certain optimization problem related to a strongly positive bounded linear operator additional results of the main result are also obtained

some iterative methods for finding fixed points and for solving constrained convex minimization problems the present paper is divided into two parts in the first part we introduce implicit and explicit iterative schemes for finding the fixed point of a nonexpansive mapping defined on the closed convex subset of a real hilbert space we establish results on the strong convergence of the sequences generated by the proposed schemes to a fixed point of a nonexpansive mapping such a fixed point is also a solution of a variational inequality defined on the set of fixed points in the second part we propose implicit and explicit iterative schemes for finding the approximate minimizer of a constrained convex minimization problem and prove that the sequences generated by our schemes converge strongly to a solution of the constrained convex minimization problem such a solution is also a solution of a variational inequality defined over the set of fixed points of a nonexpansive mapping the results of this paper extend and improve several results presented in the literature in the recent past