global target aggregation and state agreement of nonlinear multi agent systems with switching topologies in this paper we discuss coordination problems of a group of autonomous agents including the target aggregation to a convex set and the state agreement the aggregation of the whole agent group consisting of leaders informed agents and followers to a given set is investigated with switching interconnection topologies described by the connectivity assumptions on the joint topology in the time interval t for any time t and then the state agreement problem is studied in a similar way an approach based on set stability and limit set analysis is given to study the multi agent convergence problems with the help of graph theory and convex analysis coordination conditions are obtained in some important cases and the results show that simple local rules can make the networked agents with first order nonlinear individual dynamics achieve desired collective behaviors

global stabilization of the generalized korteweg de vries equation posed on a finite domain this paper is concerned with the internal stabilization of the generalized korteweg de vries equation on a bounded domain the global well posedness and the exponential stability are investigated when the exponent in the nonlinear term ranges over the interval 1 4 the global exponential stability is obtained whatever the location where the damping is active confirming positively a conjecture of perla menzala vasconcellos and zuazua quart appl math 60 2002 pp 111 129

rational approximation techniques for analysis of neural networks artificial neural networks are comprised of an interconnected collection of certain nonlinear devices examples of commonly used devices include linear threshold elements sigmoidal elements and radial basis elements we employ results from harmonic analysis and the theory of rational approximation to obtain almost tight lower bounds on the size i e number of elements of neural networks the class of neural networks to which our techniques can be applied is quite general it includes any feedforward network in which each element can be piecewise approximated by a low degree rational function for example we prove that any depth d 1 network of sigmoidal units or linear threshold elements computing the parity function of n variables must have r dn sup 1 d spl epsiv size for any fixed spl epsiv 0 in addition we prove that this lower bound is almost tight by showing that the parity function can be computed with o dn sup 1 d sigmoidal units or linear threshold elements in a depth d 1 network these almost tight bounds are the first known complexity results on the size of neural networks with depth more than two our lower bound techniques yield a unified approach to the complexity analysis of various models of neural networks with feedforward structures moreover our results indicate that the in the context of computing highly oscillating symmetric boolean functions networks of continuous output units such as sigmoidal elements do not offer significant reduction in size compared with networks of linear threshold elements of binary outputs

robust consensus for continuous time multiagent dynamics this paper investigates consensus problems for continuous time multiagent systems with time varying communication graphs subject to input noise based on input to state stability and integral input to state stability robust consensus and integral robust consensus are defined with respect to l and l1 norms of the noise function respectively sufficient and or necessary connectivity conditions are obtained for the system to reach robust consensus or integral robust consensus under mild assumptions the results answer the question on how much interaction is required for a multiagent network to converge despite a certain amount of input disturbance the convergence time is obtained for the consensus computation on directed and k bidirectional graphs

admissible input elements for systems in hilbert space and a carleson measure criterion we study the control system dot x ax bu quad x in x quad u text scalar where a generates a semigroup on the hilbert space x but in general the control input element b notin x many boundary value control systems point control force situations etc can be studied in this context we define and analyze admissible input elements b and develop sufficient conditions for b to be admissible in terms of the carleson measure theorem of h p theory

general purpose computation with neural networks a survey of complexity theoretic results we survey and summarize the literature on the computational aspects of neural network models by presenting a detailed taxonomy of the various models according to their complexity theoretic characteristics the criteria of classification include the architecture of the network feedforward versus recurrent time model discrete versus continuous state type binary versus analog weight constraints symmetric versus asymmetric network size finite nets versus infinite families and computation type deterministic versus probabilistic among others the underlying results concerning the computational power and complexity issues of perceptron radial basis function winner take all and spiking neural networks are briefly surveyed with pointers to the relevant literature in our survey we focus mainly on the digital computation whose inputs and outputs are binary in nature although their values are quite often encoded as analog neuron states we omit the important learning issues

distributed cooperative adaptive identification and control for a group of continuous time systems with a cooperative pe condition via consensus in this paper we first address the uniformly exponential stability ues problem of a group of distributed cooperative adaptive systems in a general framework inspired by consensus theory distributed cooperative adaptive laws are proposed to estimate the unknown parameters of these systems it is shown that not only is the entire closed loop system stable but also both the identification tracking error and the parameter estimation error converge to zero uniformly exponentially under a cooperative persistent excitation pe condition of a regressor matrix in each system which is weaker than the traditionally defined pe condition the effects of network topology on ues of the closed loop system are also explored if the topology is time invariant it needs to be undirected and connected however when the topology is time varying it is just required that the integration of the topology over an interval with fixed length is undirected and connected the established results are then employed to identify and control several classes of linearly parameterized systems simulation examples are also provided to demonstrate the effectiveness and applications of the proposed distributed cooperative adaptive laws

an extension of lasalle s invariance principle and its application to multi agent consensus in the paper an extension of lasalle s invariance principle to a class of switched linear systems is studied one of the motivations is the consensus problem in multi agent systems unlike most existing results in which each switching mode in the system needs to be asymptotically stable this paper allows that the switching modes are only lyapunov stable under certain ergodicity assumptions an extension of lasalle s invariance principle for global asymptotic stability is obtained then it is used to solve the consensus reaching problem of certain multi agent systems in which each agent is modeled by a double integrator and the associated interaction graph is switching and is assumed to be only jointly connected

boundary smoothing properties of the kawahara equation posed on the finite domain we establish the boundary smoothing properties for the linear kawahara equation 0 1 tu x5u x3u 0 x 0 1 t 0 u x 0 0 x 0 1 u 0 t h1 t u 1 t h2 t xu 0 t h3 t xu 1 t h4 t x2u 1 t h5 t t 0 in this paper firstly by laplacian transformation we give the explicit formula of the solution of 0 1 u x t j 1512 i r i r i est j s s e j s xds then by the fine estimates on j s s j 1 2 3 4 5 we establish the boundary smoothing effect for any s 0 if the boundary data h1 t h2 t h3 t h4 t h5 t h0s 25 r h0s 25 r h0s 15 r h0s 15 r h0s5 r then the solution u c r hs 0 1 l2 r h2 s 0 1 and possesses the sharp trace regularity xku c 0 1 hs 2 k5 r fork 0 1 2

formation stability analysis of unmanned multi vehicles under interconnection topologies in this paper the overall formation stability of an unmanned multi vehicle is mathematically presented under interconnection topologies a novel definition of formation error is first given and followed by the proposed formation stability hypothesis based on this hypothesis a unique extension decomposition aggregation scheme is then employed to support the stability analysis for the overall multi vehicle formation under a mesh topology it is proved that the overall formation control system consisting of n number of nonlinear vehicles is not only asymptotically stable but also exponentially stable in the sense of lyapunov within a neighbourhood of the desired formation this technique is shown to be applicable for a mesh topology but is equally applicable for other topologies a simulation study of the formation manoeuvre of multiple aerosonde uavs unmanned aerial vehicles in 3 d space is finally carried out verifying the achieved formation stability result

on the computational power of threshold circuits with sparse activity circuits composed of threshold gates mcculloch pitts neurons or perceptrons are simplified models of neural circuits with the advantage that they are theoretically more tractable than their biological counterparts however when such threshold circuits are designed to perform a specific computational task they usually differ in one important respect from computations in the brain they require very high activity on average every second threshold gate fires sets a 1 as output during a computation by contrast the activity of neurons in the brain is much sparser with only about 1 of neurons firing this mismatch between threshold and neuronal circuits is due to the particular complexity measures circuit size and circuit depth that have been minimized in previous threshold circuit constructions in this letter we investigate a new complexity measure for threshold circuits energy complexity whose minimization yields computations with sparse activity we prove that all computations by threshold circuits of polynomial size with entropy o log n can be restructured so that their energy complexity is reduced to a level near the entropy of circuit states this entropy of circuit states is a novel circuit complexity measure which is of interest not only in the context of threshold circuits but for circuit complexity in general as an example of how this measure can be applied we show that any polynomial size threshold circuit with entropy o log n can be simulated by a polynomial size threshold circuit of depth 3 our results demonstrate that the structure of circuits that result from a minimization of their energy complexity is quite different from the structure that results from a minimization of previously considered complexity measures and potentially closer to the structure of neural circuits in the nervous system in particular different pathways are activated in these circuits for different classes of inputs this letter shows that such circuits with sparse activity have a surprisingly large computational power

a korteweg de vries type of fifth order equations on a finite domain with point dissipation abstract the paper discusses initial value problem of a korteweg de vries type of fifth order equation w t w x x x w x x x x x j 1 n a j w j w x 0 w x 0 w 0 x posed on a periodic domain x 0 2 with periodic boundary conditions w i x 0 t w i x 2 t i 0 2 3 4 and an l 2 stabilizing feedback control law w x 2 t w x 0 t 1 w x x x 0 t where n is a fixed positive integer a j j 1 2 n are real constants and 1 it is shown that for w 0 x h 1 0 2 with the boundary conditions described above the problem is locally well posed for w c 0 t h 1 0 2 with a conserved volume of w w 0 2 w x t d x moreover the solution with small initial condition exists globally and approaches to w 0 x 2 as t

consensus of high order multi agent systems with switching topologies abstract in this paper a consensus problem is investigated for high order multi agent systems with switching communication networks through which only output information instead of full state information can be transmitted to neighbors based on self state feedback and neighbor output feedback a new consensus protocol is proposed which can realize arbitrary convergence rate furthermore as an application a nonlinear heading consensus protocol is designed for a multi vehicle model finally numerical simulations are given to illustrate the theoretical results

connectivity and set tracking of multi agent systems guided by multiple moving leaders in this paper we investigate distributed multi agent tracking of a convex set specified by multiple moving leaders with unmeasurable velocities various jointly connected interaction topologies of the follower agents with uncertainties are considered in the study of set tracking based on the connectivity of the time varying multi agent system necessary and sufficient conditions are obtained for set input to state stability and set integral input to state stability for a nonlinear neighbor based coordination rule with switching directed topologies conditions for asymptotic set tracking are also proposed with respect to the polytope spanned by the leaders

average contraction and synchronization of complex switched networks this paper introduces an average contraction analysis for nonlinear switched systems and applies it to investigating the synchronization of complex networks of coupled systems with switching topology for a general nonlinear system with a time dependent switching law a basic convergence result is presented according to average contraction analysis and a special case where trajectories of a distributed switched system converge to a linear subspace is then investigated synchronization is viewed as the special case with all trajectories approaching the synchronization manifold and is thus studied for complex networks of coupled oscillators with switching topology it is shown that the synchronization of a complex switched network can be evaluated by the dynamics of an isolated node the coupling strength and the time average of the smallest eigenvalue associated with the laplacians of switching topology and the coupling fashion finally numerical simulations illustrate the effectiveness of the proposed methods

size depth tradeoffs for threshold circuits the following size depth tradeoff for threshold circuits is obtained any threshold circuit of depth d that computes the parity function on n variables must have at least n 1 c theta d edges where c 0 and theta leq 3 are constants independent of n and d previously known constructions show that up to the choice of c and theta this bound is best possible in particular the lower bound implies an affirmative answer to the conjecture of paturi and saks that a bounded depth threshold circuit that computes parity requires a superlinear number of edges this is the first superlinear lower bound for an explicit function that holds for any fixed depth and the first that applies to threshold circuits with unrestricted weights the tradeoff is obtained as a consequence of a general restriction theorem for threshold circuits with a small number of edges for any threshold circuit with n inputs depth d and at most kn edges there exists a partial assignment to the inputs that fixes the output of the circuit to a constant while leaving lfloor n c 1k c 2 theta d rfloor variables unfixed where c 1 c 2 0 and theta leq 3 are constants independent of n k and d a tradeoff between the number of gates and depth is also proved any threshold circuit of depth d that computes the parity of n variables has at least n 2 1 2 d 1 gates this tradeoff which is essentially the best possible was proved previously with a better constant in the exponent for the case of threshold circuits with polynomially bounded weights in k siu v roychowdury and t kailath ieee trans inform theory 40 1994 pp 455 466 the result in the present paper holds for unrestricted weights

technical communique a note on connectivity of multi agent systems with proximity graphs and linear feedback protocol in this note we investigate the possibility of simplifying the connectivity verification for multi agent systems with proximity graphs and the linear feedback protocol a lyapunov like approach is developed for analyzing the monotonicity of the largest edge length in the network based on this approach we provide an initial connectivity based sufficient condition for dynamic connectivity in particular when each initial node degree is not less than three fourth of the graph order initial network connectivity implies dynamic connectivity

distributed attitude synchronization control of multi agent systems with switching topologies this paper addresses the attitude synchronization problem in multi agent systems with directed and switching interconnection topologies two cases for the synchronization problem are discussed under different assumptions about the measurable information in the first case the agents can measure their rotations relative to a global reference coordinate frame whilst in the second case they can only measure the relative rotations between each other two intuitive distributed control laws based on the axis angle representations of the rotations are proposed for the two cases respectively the invariance of convex balls in so 3 is guaranteed moreover attitude synchronization is ensured under the well known mild switching assumptions the joint strong connection for the first case and joint quasi strong connection for the second case to show the effectiveness of the proposed control schemes illustrative examples are provided

constrained consensus in unbalanced networks with communication delays in this note a constrained consensus problem is studied for multi agent systems in unbalanced networks in the presence of communication delays here each agent needs to lie in a closed convex constraint set while reaching a consensus the communication graphs are directed dynamically changing and not necessarily balanced and only the union of the graphs is assumed to be strongly connected among each time interval of a certain bounded length the analysis is performed based on an undelayed equivalent system that is composed of a linear main body and an error auxiliary to tackle the loss of symmetry caused by unbalanced graphs and communication delays a novel approach is proposed the idea is to estimate the distance from each agent to the intersection set of all agents constraint sets based on the properties of the projection on convex sets so as to show consensus convergence by contradiction it is shown that the error auxiliary vanishes as time evolves and the linear main body converges to a vector with an exponential rate as a separate system it is also shown that the communication delays do not affect the consensus stability and constrained consensus is reached even if the communication delays are arbitrarily bounded finally a numerical example is included to illustrate the obtained theoretical results

on the rendezvous problem for multiple nonholonomic agents in this note a decentralized feedback control strategy that drives a system of multiple nonholonomic unicycles to a rendezvous point in terms of both position and orientation is introduced the proposed nonholonomic control law is discontinuous and time invariant and using tools from nonsmooth lyapunov theory and graph theory the stability of the overall system is examined similarly to the linear case the convergence of the multi agent system relies on the connectivity of the communication graph that represents the inter agent communication topology the control law is first defined in order to guarantee connectivity maintenance for an initially connected communication graph moreover the cases of static and dynamic communication topologies are treated as corollaries of the proposed framework

size energy tradeoffs for unate circuits computing symmetric boolean functions a unate gate is a logical gate computing a unate boolean function which is monotone in each variable examples of unate gates are and gates or gates not gates threshold gates etc a unate circuit c is a combinatorial logic circuit consisting of unate gates let f be a symmetric boolean function of n variables such as the parity function mod function and majority function let m 0 and m 1 be the maximum numbers of consecutive 0 s and consecutive 1 s in the value vector of f respectively and let l min m 0 m 1 and m max m 0 m 1 let c be a unate circuit computing f let s be the size of the circuit c that is c consists of s unate gates let e be the energy of c that is e is the maximum number of gates outputting 1 over all inputs to c in this paper we show that there is a tradeoff between the size s and the energy e of c more precisely we show that n 1 l m s e we also present lower bounds on the size s of c represented in terms of n l and m our tradeoff immediately implies that logn elogs for every unate circuit c computing the parity function of n variables

brief paper a novel approach to coordination of multiple robots with communication failures via proximity graph in this paper we investigate the coordination problem of multiple robots with limited communication ranges and communication failures a novel rendezvous algorithm via proximity graph is developed so that the robot group can achieve rendezvous when the communication links satisfy an ergodic assumption the convergence proof of the algorithm is established based on the tools from rooted graph theory the effectiveness of the algorithm is illustrated by numerical examples in a 3d space

new bounds for energy complexity of boolean functions abstract for a boolean function f 0 1 n 0 1 computed by a boolean circuit c over a finite basis b the energy complexity of c denoted by ec b c is the maximum over all inputs 0 1 n of the number gates of the circuit c excluding the inputs that output a one energy complexity of a boolean function over a finite basis b denoted by ec b f def min c ec b c where c is a boolean circuit over b computing f we study the case when b 2 2 the standard boolean basis it is known that any boolean function can be computed by a circuit with potentially large size with an energy of at most 3 n 1 n for a small n which we observe is improvable to 3 n 1 we show several new results and connections between energy complexity and other well studied parameters of boolean functions for all boolean functions f ec f o dt f 3 where dt f is the optimal decision tree depth of f we define a parameter positive sensitivity denoted by psens a quantity that is smaller than sensitivity cook et al 1986 3 and defined in a similar way and show that for any boolean circuit c computing a boolean function f ec c psens f 3 for a monotone function f we show that ec f kw f where kw f is the cost of monotone karchmer wigderson game of f restricting the above notion of energy complexity to boolean formulas we show ec f l f depth f where l f is the size and depth f is the depth of a formula f

distributed control of networked dynamical systems static feedback integral action and consensus this paper analyzes distributed control protocols for first and second order networked dynamical systems we propose a class of nonlinear consensus controllers where the input of each agent can be written as a product of a nonlinear gain and a sum of nonlinear interaction functions by using integral lyapunov functions we prove the stability of the proposed control protocols and explicitly characterize the equilibrium set we also propose a distributed proportional integral pi controller for networked dynamical systems the pi controllers successfully attenuate constant disturbances in the network we prove that agents with single integrator dynamics are stable for any integral gain and give an explicit tight upper bound on the integral gain for when the system is stable for agents with double integrator dynamics throughout the paper we highlight some possible applications of the proposed controllers by realistic simulations of autonomous satellites power systems and building temperature control

distributed nonlinear control of mobile autonomous multi agents abstract this paper studies the distributed nonlinear control of mobile autonomous agents with variable and directed topology a new distributed nonlinear design scheme is presented for multi agent systems modeled by double integrators with the new design the outputs of the controlled agents asymptotically converge to each other as long as a mild connectivity condition is satisfied moreover the velocity derivative of the output of each agent can be restricted to be within any specified neighborhood of the origin which is of practical interest for systems under such physical constraint the new design is still valid if one of the agents is a leader and the control objective is to achieve leader following as an illustration of the generality and effectiveness of the presented methodology the formation control of a group of unicycle mobile robots with nonholonomic constraints is revisited instead of assuming the point robot model the unicycle model is transformed into two double integrators by dynamic feedback linearization and the proposed distributed nonlinear design method is used to overcome the singularity problem caused by the nonholonomic constraint by properly restricting the velocities simulation results are included to illustrate the theoretical results

the leader following consensus for multiple uncertain euler lagrange systems with an adaptive distributed observer in this note we first propose an adaptive distributed observer for a linear leader system this observer only assumes those followers who are the children of the leader know the system matrix of the leader system then we further develop a distributed adaptive controller utilizing this adaptive distributed observer to solve the leader following consensus problem for multiple uncertain euler lagrange systems without assuming that all the followers need to know the system matrix of the leader system

second order tracking control for leader follower multi agent flocking in directed graphs with switching topology abstract this paper investigates the flocking problem for leader follower multi agent systems in directed graphs with switching topology a decentralized state control rule namely a second order protocol is designed for each agent to track the leader and it is proved that the proposed control scheme can effectively estimate the tracking error of each agent when the leader is active particularly to ensure the tracking error can be estimated the following two questions are solved 1 how many agents are needed to connect to the leader 2 how should these connections be distributed finally a simple example is also given to verify the effectiveness of the proposed theorems

on synchronous robotic networks part ii time complexity of rendezvous and deployment algorithms this paper analyzes a number of basic coordination algorithms running on synchronous robotic networks we provide upper and lower bounds on the time complexity of the move toward average and circumcenter laws both achieving rendezvous and of the centroid law achieving deployment over a region of interest the results are derived via novel analysis methods including a set of results on the convergence rates of linear dynamical systems defined by tridiagonal toeplitz and circulant matrices

consensus controllability observability and robust design for leader following linear multi agent systems a b s t r a c t this paper considers for leader following linear multi agent systems mas connected by switching graphs the consensus controllability and observability and extends the existing results which are valid only for fixed graph case unlike the general controllability and observability problems which require each state to be controllable and observable we only examine the consensus state to be controllable and the tracking error states between the followers and the leader to be observable as for the consensus controllability the admissible control input for each follower agent can only obtain relative and local information from its neighbors and the control objective is to render the mas to achieve consensus in the sense of convergence of each follower s state to that of a leader agent as for the consensus observability the output of the mas is the information flow in the multi agent network and the observation task is to reconstruct the tracking error states between the followers and the leader it is demonstrated in this paper that the controllability and observability of each individual system and the jointly connected switching topology including fixed topology as a special case jointly imply the consensus controllability and observability of the mas the consensus controllability property is used in the robust leader following consensus problem and the consensus observability property is used in the robust observer based leader following consensus problem both under switching topology

the korteweg de vries equation on a periodic domain with singular point dissipation this paper considers the korteweg de vries kdv equation eqalignno u t uu x u xxx 0 0 0 quad u 0 x u 0 x and the periodic boundary conditions u t 1 u t 0 u xx t 0 u xx t 1 with an l 2 stabilizing control input implemented by a feedback mechanism u x t 1 alpha u x t 0 and alpha 1 it can be shown that the solutions conserve the volume u int 1 0u t x dx and the constant state u 0 possesses the smallest energy among solutions with same volume it has been proved that the solution of the system exists and approaches u 0 as t rightarrow infty when alpha not 1 2 this paper studies the case for alpha 1 2 and gives a proof of the existence and exponential decay of the solutions by deriving estimates of the corresponding green s function and using semigroup theory the method used here also works for the other cases with alpha 1

exponential lower bounds on the size of constant depth threshold circuits with small energy complexity a complexity measure for threshold circuits called the energy complexity has been proposed to measure an amount of energy consumed during computation in the brain biological neurons need more energy to transmit a spike than not to transmit one and hence the energy complexity of a threshold circuit is defined as the number of gates in the circuit that output 1 during computation since the firing activity of neurons in the brain is quite sparse the following question arises what boolean functions can or cannot be computed by threshold circuits with small energy complexity in the paper we partially answer the question that is we show that there exists a trade off among three complexity measures of threshold circuits the energy complexity size and depth the trade off implies an exponential lower bound on the size of constant depth threshold circuits with small energy complexity for a large class of boolean functions

dynamical consensus seeking of second order multi agent systems based on delayed state compensation abstract by introducing delayed state compensation into the normal asynchronously coupled consensus algorithm a new consensus algorithm is constructed to solve the dynamical consensus problem of second order multi agent systems subjected to communication delay based on frequency domain analysis a sufficient and necessary condition which depends on the communication delay and the control parameters is obtained for two coupled second order dynamic agents converging to the dynamical consensus and it is proved that the proposed algorithm can tolerate higher communication delay than the synchronously coupled consensus algorithm according to linear fractional transformation and the small gain theorem sufficient conditions are gained for second order multi agent systems with communication delay under a general digraph simulation illustrates the correctness of the results

distributed consensus tracking for multiple uncertain nonlinear strict feedback systems under a directed graph in this brief we study the distributed consensus tracking control problem for multiple strict feedback systems with unknown nonlinearities under a directed graph topology it is assumed that the leader s output is time varying and has been accessed by only a small fraction of followers in a group the distributed dynamic surface design approach is proposed to design local consensus controllers in order to guarantee the consensus tracking between the followers and the leader the function approximation technique using neural networks is employed to compensate unknown nonlinear terms induced from the controller design procedure from the lyapunov stability theorem it is shown that the consensus errors are cooperatively semiglobally uniformly ultimately bounded and converge to an adjustable neighborhood of the origin

brief paper multi agent consensus with diverse time delays and jointly connected topologies this paper investigates consensus problems in networks of continuous time agents with diverse time delays and jointly connected topologies for convergence analysis of the networks a class of lyapunov krasovskii functions is constructed which contains two parts one describes the current disagreement dynamics and the other describes the integral impact of the dynamics of the whole network over the past by a contradiction approach sufficient conditions are derived under which all agents reach consensus even though the communication structures between agents dynamically change over time and the corresponding graphs may not be connected the obtained conditions are composed of a sum of decoupled parts corresponding to each possible connected component of the communication topology finally numerical examples are included to illustrate the obtained results

synchronizing nonlinear complex networks via switching disconnected topology the current theoretical study on the synchronization mechanism of complex networks mainly focuses on fixed connected topology or switching balanced topology which is heavily based on constructing common smooth lyapunov functions however for complex networks with nonlinear node dynamics it is still unknown whether such kind of networks can synchronize under the condition of switching directed and disconnected topology by employing the ideas of sequential connectivity and joint connectivity this paper finds that complex networks with one sided lipschitz node dynamics can realize synchronization even if the network topology is not connected at any time instant by iteratively estimating the maximal distance between different nodes this paper gives several sufficient conditions on synchronization of nonlinear complex networks under switching disconnected topology finally simulation examples validate the main results

controllability and stabilizability of the third order linear dispersion equation on a periodic domain in this paper solutions of the third order linear dispersion equations frac partial w partial t frac partial 3 w partial x 3 f x t qquad text and qquad frac partial w partial t frac partial 3 w partial x 3 0 are studied for t geqq 0 0 leqq x leqq 2 pi in the first case periodic boundary conditions are imposed at 0 and 2 pi and the distributed control f which may however have support smaller than 0 2 pi is assumed to be generated by a linear feedback law conserving the volume int 0 2 pi w x t dx while monotonically reducing int 0 2 pi w x t 2 dx for the second equation a feedback boundary control having the same properties is applied in both cases uniform exponential decay to a constant state is obtained related exact controllability questions are also studied and affirmative results are obtained

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

consensus seeking of high order dynamic multi agent systems with fixed and switching topologies this article studies a consensus problem for a group of high order dynamic agents with fixed and switching topologies two linear consensus protocols which only depend on the agent s own information and its neighbours partial information are proposed respectively for the group with and without communication time delays for the case of fixed topology and zero communication time delay a necessary and sufficient condition for the consensus is established the parameter design of the protocol is also discussed under switching topology the consensus is investigated for two cases the case of zero communication time delay and the case of nonuniform communication time delays for each case a sufficient condition for the consensus is provided moreover for a group of double triple integrator agents with fixed topology and uniform constant time delay some necessary and sufficient conditions for the consensus are given finally numerical simulations are worked out to illustrate the effectiveness of the

distributed velocity constrained consensus of discrete time multi agent systems with nonconvex constraints switching topologies and delays in this technical note a distributed velocity constrained consensus problem is studied for discrete time multi agent systems where each agent s velocity is constrained to lie in a nonconvex set a distributed constrained control algorithm is proposed to enable all agents to converge to a common point using only local information the gains of the algorithm for all agents need not to be the same or predesigned and can be adjusted by each agent itself based on its own and neighbors information it is shown that the algorithm is robust to arbitrarily bounded communication delays and arbitrarily switching communication graphs provided that the union of the graphs has directed spanning trees among each certain time interval the analysis approach is based on multiple novel model transformations proper control parameter selections boundedness analysis of state dependent stochastic matrices1 exploitation of the convexity of stochastic matrices and the joint connectivity of the communication graphs numerical examples are included to illustrate the theoretical results

exact controllability and stabilizability of the korteweg de vries equation in this paper we consider distributed control of the system described by the korteweg de vries equation i atu uaxu e3 u f on the interval 0 0 with periodic boundary conditions ii au 27r t ku o t k 0 1 2 where the distributed control f f x t is restricted so that the volume f u x t dx of the solution is conserved both exact controllability and stabilizibility questions are studied for the system in the case of open loop control if the control f is allowed to act on the whole spatial domain 0 27r it is shown that the system is globally exactly controllable i e for given t 0 and functions q x x with the same volume one can alway find a control f so that the system i ii has a solution u x t satisfying u x 0 0 x u x t x if the control f is allowed to act on only a small subset of the domain 0 27r then the same result still holds if the initial and terminal states b and 0 have small amplitude in a certain sense in the case of closed loop control the distributed control f is assumed to be generated by a linear feedback law conserving the volume while monotonically reducing f u x t 2dx the solutions of the resulting closed loop system are shown to have uniform exponential decay to a constant state as in the open loop control case a small amplitude assumption is needed if the control is allowed to act on only a small subdomain the smoothing property of the periodic linear kdv equation discovered recently by bourgain has played an important role in establishing the exact controllability and stabilizability results presented in this paper

distributed h constrained consensus problem abstract this paper is concerned with the distributed h constrained consensus problem for multi agent systems the objective is to use local information to make all agents reach a consensus in a given convex set while satisfying a desired h performance index in the presence of external disturbances a nonlinear distributed algorithm is adopted to solve this constrained consensus problem to measure the effects of the disturbance on the consensus of all agents and the convergence of all agents to the convex set a nonlinear function is constructed as the h output function by analyzing the convexity of the convex set a sufficient condition is given to solve the constrained consensus problem with the desired h performance finally a numerical simulation example is provided to show the effectiveness of our theoretical results

synchronization of complex dynamical networks with switching topology a switched system point of view in this paper we study the synchronization problem for complex dynamical networks with switching topology from a switched system point of view the synchronization problem is transformed into the stability problem for time varying switched systems we address two basic problems synchronization under arbitrary switching topology and synchronization via design of switching within a pre given collection of topologies when synchronization cannot be achieved by using any topology alone in this collection for the both problems we first establish synchronization criteria for general connection topology then under the condition of simultaneous triangularization of the connection matrices a common lyapunov function for the first problem and a single lyapunov and multiple lyapunov functions for the second problem are systematically constructed respectively by those of several lower dimensional dynamic systems in order to achieve synchronization using multiple lyapunov functions a stability condition and switching law design method for time varying switched systems are also presented which avoid the usual non increasing condition

a novel alignment repulsion algorithm for flocking of multi agent systems based on the number of neighbours per agent in this paper an energy based control methodology is proposed to satisfy the reynolds three rules in a flock of multiple agents first a control law is provided that is directly derived from the passivity theorem in the next step the number of neighbours alignment repulsion algorithm is introduced for a flock of agents which loses the cohesion ability and uniformly joint connectivity condition with this method each agent tries to follow the agents which escape its neighbourhood by considering the velocity of escape time and number of neighbours it is mathematically proved that the motion of multiple agents converges to a rigid and uncrowded flock if the group is jointly connected just for an instant moreover the conditions for collision avoidance are guaranteed during the entire process finally simulation results are presented to show the effectiveness of the proposed methodology

distributed consensus of second order multiagent systems with nonconvex velocity and control input constraints this paper is devoted to a distributed consensus problem for second order multiagent systems with nonconvex velocity and control input constraints a distributed control algorithm is introduced using local information it is shown that consensus can be achieved as long as the union of the communication graphs has directed spanning trees among each time interval of certain bounded length in the presence of arbitrarily bounded communication delays finally a numerical example is included to illustrate the theoretical results

lyapunov based approach to multiagent systems with switching jointly connected interconnection this note addresses a coordination problem of a multiagent system with jointly connected interconnection topologies neighbor based rules are adopted to realize local control strategies for these continuous time autonomous agents described by double integrators although the interagent connection structures vary over time and related graphs may not be connected a sufficient condition to make all the agents converge to a common value is given for the problem by a proposed lyapunov based approach and related space decomposition technique

reaching an optimal consensus dynamical systems that compute intersections of convex sets in this paper multi agent systems minimizing a sum of objective functions where each component is only known to a particular node is considered for continuous time dynamics with time varying interconnection topologies assuming that each node can observe a convex solution set of its optimization component and the intersection of all such sets is nonempty the considered optimization problem is converted to an intersection computation problem by a simple distributed control rule the considered multi agent system with continuous time dynamics achieves not only a consensus but also an optimal agreement within the optimal solution set of the overall optimization objective directed and bidirectional communications are studied respectively and connectivity conditions are given to ensure a global optimal consensus in this way the corresponding intersection computation problem is solved by the proposed decentralized continuous time algorithm we establish several important properties of the distance functions with respect to the global optimal solution set and a class of invariant sets with the help of convex and non smooth analysis

energy and fan in of logic circuits computing symmetric boolean functions in this paper we consider a logic circuit i e a combinatorial circuit consisting of gates each of which computes a boolean function c computing a symmetric boolean function f and investigate a relationship between two complexity measures energy e and fan in l of c where the energy e is the maximum number of gates outputting 1 over all inputs to c and the fan in l is the maximum number of inputs of every gate in c we first prove that any symmetric boolean function f of n variables can be computed by a logic circuit of energy e o n l and fan in l and then provide an almost tight lower bound e email protected n m f email protected where m f is the maximum numbers of consecutive 0 s or 1 s in the value vector of f our results imply that there exists a tradeoff between the energy and fan in of logic circuits computing a symmetric boolean function

extensions of weak invariance principle for nonlinear switched systems with time invariant and time varying subsystems abstract this paper addresses the stability problem for nonlinear switched systems with both time invariant and time varying subsystems given that lyapunov like functions are difficult to construct for nonlinear switched systems generalized invariance principles are established based on observer functions for nonlinear switched systems where the subsystems share lyapunov like functions the generalized invariance principles can be specialized to lyapunov based invariance principles where accurate convergent region can be obtained in addition to the above efforts the definitions of p limit system and limit system set are presented under which the proposed invariance principles are extended to nonlinear switched systems with time varying subsystems illustrative examples show the effectiveness of the theoretical results

energy and depth of threshold circuits in this paper we show that there is a close relationship between the energy complexity and the depth of threshold circuits computing any boolean function although they have completely different physical meanings suppose that a boolean function f can be computed by a threshold circuit c of energy complexity e and hence at most e threshold gates in c output 1 for any input to c we prove that the function f can also be computed by a threshold circuit c of the depth 2e 1 and hence the parallel computation time of c is 2e 1 if the size of c is s that is there are s threshold gates in c then the size s of c is s 2es 1 thus if the size s of c is polynomial in the number n of input variables then the size s of c is polynomial in n too

stability of multiagent systems with time dependent communication links we study a simple but compelling model of network of agents interacting via time dependent communication links the model finds application in a variety of fields including synchronization swarming and distributed decision making in the model each agent updates his current state based upon the current information received from neighboring agents necessary and or sufficient conditions for the convergence of the individual agents states to a common value are presented thereby extending recent results reported in the literature the stability analysis is based upon a blend of graph theoretic and system theoretic tools with the notion of convexity playing a central role the analysis is integrated within a formal framework of set valued lyapunov theory which may be of independent interest among others it is observed that more communication does not necessarily lead to faster convergence and may eventually even lead to a loss of convergence even for the simple models discussed in the present paper