sampled data consensus over random networks this paper considers the consensus problem for a network of nodes with random interactions and sampled data control actions we first show that consensus in expectation in mean square and almost surely are equivalent for a general random network model when the inter sampling interval and maximum node degree satisfy a simple relation the three types of consensus are shown to be simultaneously achieved over an independent or a markovian random network defined on an underlying graph with a directed spanning tree for both independent and markovian random network models necessary and sufficient conditions for mean square consensus are derived in terms of the spectral radius of the corresponding state transition matrix these conditions are then interpreted as the existence of critical value on the intersampling interval below which a global mean square consensus is achieved and above which the system diverges in a mean square sense for some initial states finally we establish an upper bound on the intersampling interval below which almost sure consensus is reached and a lower bound on the intersampling interval above which almost sure divergence is reached some numerical simulations are given to validate the theoretical results and some discussions on the critical value of the inter sampling intervals for the mean square consensus are provided

sampled data consensus of linear multi agent systems with packet losses in this paper the consensus problem is studied for a class of multi agent systems with sampled data and packet losses where random and deterministic packet losses are considered respectively for random packet losses a bernoulli distributed white sequence is used to describe packet dropouts among agents in a stochastic way for deterministic packet losses a switched system with stable and unstable subsystems is employed to model packet dropouts in a deterministic way the purpose of this paper is to derive consensus criteria such that linear multi agent systems with sampled data and packet losses can reach consensus by means of the lyapunov function approach and the decomposition method the design problem of a distributed controller is solved in terms of convex optimization the interplay among the allowable bound of the sampling interval the probability of random packet losses and the rate of deterministic packet losses are explicitly derived to characterize consensus conditions the obtained criteria are closely related to the maximum eigenvalue of the laplacian matrix versus the second minimum eigenvalue of the laplacian matrix which reveals the intrinsic effect of communication topologies on consensus performance finally simulations are given to show the effectiveness of the proposed results

control of a three coleader formation in the plane this paper considers a formation of three point agents moving in the plane where the agents have a cyclic ordering with each one required to maintain a nominated distance from its neighbour further each agent is allowed to determine its movement strategy using local knowledge only of the direction of its neighbour and the current and desired distance from its neighbour the motion of the formation is studied when distances are initially incorrect a convergence result is established to the effect that provided agents never become collinear the correct distances will be approached exponentially fast and the formation as a whole will rotate by a finite angle and translate by a finite distance

couple group consensus for second order multi agent systems with fixed and stochastic switching topologies abstract this paper deals with the couple group consensus problem for second order discrete time multi agent systems both the fixed topology case and the stochastic switching topology case are considered the couple group consensus problem is converted into the stability problem of the error system by a linear transformation for the fixed topology case we obtain two different conditions of couple group consensus for the stochastic switching topology case we obtain a necessary and sufficient condition of mean square couple group consensus algorithms are provided to design the allowable control gains finally simulation examples are given to show the usefulness of the theoretical results

necessary and sufficient graphical conditions for formation control of unicycles the feasibility problem is studied of achieving a specified formation among a group of autonomous unicycles by local distributed control the directed graph defined by the information flow plays a key role it is proved that formation stabilization to a point is feasible if and only if the sensor digraph has a globally reachable node a similar result is given for formation stabilization to a line and to more general geometric arrangements

consensus of multi agent networks with aperiodic sampled communication via impulsive algorithms using position only measurements in this technical note an impulsive consensus algorithm is proposed for second order continuous time multi agent networks with switching topology the communication among agents occurs at sampling instants based on position only measurements by using the property of stochastic matrices and algebraic graph theory some sufficient conditions are obtained to ensure the consensus of the controlled multi agent network if the communication graph has a spanning tree jointly a numerical example is given to illustrate the effectiveness of the proposed algorithm

second order consensus of multi agent systems in the cooperation competition network with switching topologies a time delayed impulsive control approach abstract this paper investigates the consensus problem of second order multi agent systems with switching topologies by designing a time delayed impulsive consensus control scheme all the agents are governed by the same nonlinear intrinsic dynamics in this study agents can cooperate or compete with each other i e the elements in the weight matrix of the coupling graph can be either positive or negative by establishing a comparison system a new comparison principle method is successfully applied to study such consensus problem then several effective sufficient conditions are attained without assuming that the interaction topology is strongly connected or contains a directed spanning tree meanwhile the exponential consensus rate is also obtained finally simulation results are presented to validate the effectiveness of the theoretical analysis

three and higher dimensional autonomous formations rigidity persistence and structural persistence in this paper we generalize the notion of persistence which has been originally introduced for two dimensional formations to r d for d 3 seeking to provide a theoretical framework for real world applications which often are in three dimensional space as opposed to the plane persistence captures the desirable property that a formation moves as a cohesive whole when certain agents maintain their distances from certain other agents we verify that many of the properties of rigid and or persistent formations established in r 2 are also valid for higher dimensions analysing the closed subgraphs and directed paths in persistent graphs we derive some further properties of persistent formations we also provide an easily checkable necessary condition for persistence we then turn our attention to consider some practical issues raised in multi agent formation control in three dimensional space we display a new phenomenon not present in r 2 whereby subsets of agents can behave in a problematic way when this behaviour is precluded we say that the graph depicting the multi agent formation has structural persistence in real deployment of controlled multi agent systems formations with underlying structurally persistent graphs are of interest we analyse the characteristics of structurally persistent graphs and provide a streamlined test for structural persistence we study the connections between the allocation of degrees of freedom dofs across agents and the characteristics of persistence and or structural persistence of a directed graph we also show how to transfer dofs among agents when the formation changes with new agent s added to preserve persistence and or structural persistence

on implementing a primal dual interior point method for conic quadratic optimization based on the work of the nesterov and todd on self scaled cones an implementation of a primal dual interior point method for solving large scale sparse conic quadratic optimization problems is presented the main features of the implementation are it is based on a homogeneous and self dual model it handles rotated quadratic cones directly it employs a mehrotra type predictor corrector extension and sparse linear algebra to improve the computational efficiency finally the implementation exploits fixed variables which naturally occurs in many conic quadratic optimization problems this is a novel feature for our implementation computational results are also presented to document that the implementation can solve very large problems robustly and efficiently

weighted consensus protocols design based on network centrality for multi agent systems with sampled data this technical note aims at constructing and analyzing an efficient framework for the leader following consensus protocol in multi agent systems mass we propose two novel consensus protocols weighted by calculating the betweenness and eigenvector centralities for agent and link which are determined by the interconnection structure of mass the concepts of centrality were introduced in the field of social science ultimately the use of the proposed protocols can be described with regard to not only the number of each agent s neighbors which was utilized in the existing works but also more information about agents through considering two such centralities by utilizing the lyapunov method and some mathematical techniques the leader following guaranteed cost consensus conditions for mass with the proposed protocols and sampled data will be established in terms of linear matrix inequalities lmis based on the result of consensus criteria two new protocol design methods which utilize the betweenness and eigenvector centralities will be proposed finally some simulation results are given to illustrate the advantages of the proposed protocols in point of the robustness on sampling interval and the transient consensus performance

on iterative learning algorithms for the formation control of nonlinear multi agent systems this paper deals with formation control problems for multi agent systems with nonlinear dynamics and switching network topologies using the nearest neighbor knowledge a distributed algorithm is constructed by employing the iterative learning control approach sufficient conditions are given to obtain the desired relative formations of agents which benefits from the strict positiveness of products of stochastic matrices it is shown that the derived results can effectively work although the network topologies dynamically change along both time and iteration axes and the corresponding directed graphs may not have spanning trees such result is also illustrated via numerical simulations

distributed consensus for sampled data control multi agent systems with missing control inputs abstract this paper is concerned about the distributed consensus problem for general sampled data control multi agent systems without or with a leader under control inputs missing over some sampling intervals for these two cases a distributed adaptive dynamical consensus algorithm is proposed based only on the relative information of network structure under the assumption that the dynamical network contains a directed spanning tree some sufficient consensus conditions are induced under a switched model these obtained consensus criteria are independent of dynamical network topology namely they are valid for both undirected and directed topology besides they do not rely on the spectra and the eigenvalue of laplacian matrix furthermore some quantitative relations included in dynamical systems such as sampling period admissible control inputs missing rate and exponential reaching rate of the consensus performance are established finally simulation examples are given to show the effectiveness of the proposed results

observer design for tracking consensus in second order multi agent systems fractional order less than two this technical note studies the leader following tracking consensus problem of a class of multi agent systems where the dynamics of the leader is described by second order systems in order to track the states of the leader observers for the followers are designed by fractional order multi agent systems where the relative velocity information is unavailable it is interestingly found that the followers can track the leader with second order dynamics even if the fractional order is less than two by only using the position information of the local neighbors which is different from the existing results a novel fractional order observer is first proposed whose order is surprisingly less than the original leader system it is also shown that leader following consensus can be ensured if some carefully selected followers are informed and the relative position based protocols are appropriately designed with fractional order being between one and two a necessary and sufficient condition for the leader following consensus in multi agent systems without control input delay is proposed the results are then extended to the case with constant control input delay it is found that in both cases the real and imaginary parts of the eigenvalues of the augmented laplacian matrix of the topology play an important role in achieving consensus

first and second order methods for semidefinite programming in this paper we survey the most recent methods that have been developed for the solution of semidefinite programs we first concentrate on the methods that have been primarily motivated by the interior point ip algorithms for linear programming putting special emphasis in the class of primal dual path following algorithms we also survey methods that have been developed for solving large scale sdp problems these include first order nonlinear programming nlp methods and more specialized path following ip methods which use the preconditioned conjugate gradient or residual scheme to compute the newton direction and the notion of matrix completion to exploit data sparsity

edge consensus on complex networks a structural analysis abstractthis paper investigates the consensus taking place on the edges of networks by defining dynamics to edges discrete time and continuous time edge consensus protocols are proposed in which each edge regulates itself according to the information of itself and its neighbouring edges by mapping the original graph to its corresponding line graph conditions guarantee the reaching of edge consensus are presented furthermore the influence of network structure on the speed of reaching edge consensus is analysed by considering a scale free network with a tunable exponent between 2 and it is found that the convergence speed increases as the network becomes more heterogeneous in addition as original network becomes more homogeneous i e as the exponent increases from 2 the corresponding line graph becomes more heterogeneous till reaches 2 5 after that the line graph becomes more homogeneous

sampled measurement output feedback control of multi agent systems with jointly connected topologies this note studies the consensus problem of a class of multi agent systems mass with linear dynamics where each agent is able to use the specified measurement output e g position relative to its neighbors at certain sampling instants it is assumed that the network has switching but jointly connected topologies in the sense that the union of the associated graphs over a certain time interval always has a spanning tree under this assumption a linear sampled measurement output feedback controller is proposed to achieve full state consensus for a sufficiently small sampling period

comments on global stabilization of rigid formations in the plane automatica 49 2013 14361441 this paper shows that the modified gradient control law proposed in tian and wang 2013 does not globally stabilize rigid formation shapes also further analysis on the control law and a numerical example showing that the control law cannot drive the agents out from a stable incorrect equilibrium of the corresponding gradient control system are provided

formation tracking of the second order multi agent systems using position only information via impulsive control with input delays in this paper the formation tracking problem for the second order multi agent system with and without input delay are investigated respectively the objective is to design the formation tracking algorithm such that a certain follower follows the trajectory of the leader while also maintains a certain desired geometric formation with other agents simultaneously the impulsive algorithms are designed by using only the relative position information of the neighbors for both the cases with and without the input delay by using properties of the laplacian matrix and combining the stability theory of impulsive systems necessary and sufficient conditions are derived to achieve the formation tracking of the second order multi agent system with and without the input delay respectively the numerical examples are given to illustrate the effectiveness of our theoretical results

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

distributed leader follower flocking control for multi agent dynamical systems with time varying velocities abstract using tools from algebraic graph theory and nonsmooth analysis in combination with ideas of collective potential functions velocity consensus and navigation feedback a distributed leader follower flocking algorithm for multi agent dynamical systems with time varying velocities is developed where each agent is governed by second order dynamics the distributed leader follower algorithm considers the case in which the group has one virtual leader with time varying velocity for each agent i this algorithm consists of four terms the first term is the self nonlinear dynamics which determines the final time varying velocity the second term is determined by the gradient of the collective potential between agent i and all of its neighbors the third term is the velocity consensus term and the fourth term is the navigation feedback from the leader to avoid an impractical assumption that the informed agents sense all the states of the leader the new designed distributed algorithm is developed by making use of observer based pinning navigation feedback in this case each informed agent only has partial information about the leader yet the velocity of the whole group can still converge to that of the leader and the centroid of those informed agents having the leader s position information follows the trajectory of the leader asymptotically finally simulation results are presented to demonstrate the validity and effectiveness of the theoretical analysis surprisingly it is found that the local minimum of the potential function may not form a commonly believed lattice

great expectations part ii generalized expected utility as a universal decision rule many different rules for decision making have been introduced in the literature we show that a notion of generalized expected utility proposed in f chu j y halpern great expectation part i on the customizability of generalized expected utility in proc ijcai 03 acapulco mexico 2003 is a universal decision rule in the sense that it can essentially all other decision rules this approach gives us a general technique for designing new decision rules as well as providing a framework for comparing decision rules to each other

mean square consensus of stochastic multi agent systems with nonlinear dynamics by distributed event triggered strategy abstractthis paper is concerned with the problem of mean square consensus for nonlinear multi agent systems with state dependent noise perturbations a distributed event triggered mechanism which can be used to reduce the number of controller updates and communication load is developed to apply in stochastic dynamical systems by combining the tools of graph theory and stochastic analysis the sufficient conditions are given to ensure that mean square consensus in the multi agent systems can be achieved exponentially the convergence rate is also analytically derived moreover the feasibility of the proposed distributed event triggered strategy is further verified by exclusion of zeno behaviour finally some numerical examples are given to demonstrate the effectiveness of the obtained results

impulsive multiconsensus of second order multiagent networks using sampled position data a multiconsensus problem of multiagent networks is solved in this paper where multiconsensus refers to that the states of multiple agents in each subnetwork asymptotically converge to an individual consistent value when there exist information exchanges among subnetworks a distributed impulsive protocol is proposed to achieve multiconsensus of second order multiagent networks in terms of three categories 1 stationary multiconsensus 2 the first dynamic multiconsensus and 3 the second dynamic multiconsensus this impulsive protocol utilizes only sampled position data and is implemented at sampling instants for those three categories of multiconsensus the control parameters in the impulsive protocol are designed respectively moreover necessary and sufficient conditions are derived under which each multiconsensus can be reached asymptotically several simulations are finally provided to demonstrate the effectiveness of the obtained theoretical results

synchronization of sampled data coupled harmonic oscillators with control inputs missing abstract this paper is concerned with the synchronization problem of sampled data coupled harmonic oscillators with control inputs missing a distributed algorithm for synchronization in undirected networks of coupled harmonic oscillators is proposed based on the sampled data measurement with controller failures some generic criteria for such algorithm over respectively undirected fixed and switching network topologies are derived analytically compared with some existing works a distinctive feature of this work is to solve synchronization problem in undirected networks even if each oscillator intermittently exchanges the velocity information with its neighbors in terms of sampled data setting only at discrete moments subsequently numerical examples illustrate and visualize the effectiveness and feasibility of the theoretical results

the dual theory of choice under risk in this essay a new theory of choice under risk is being proposed it is a theory which in a sense that will become clear is dual to expected utility theory hence the title dual theory risky prospects are evaluated in this theory by a cardinal numerical scale which resembles an expected utility except that the roles of payments and probabilities are reversed this theme the reversal of the roles of probabilities and payments will recur throughout the paper i should emphasize that playing games with probabilities masquerading as payments and payments masquerading as probabilities is not my object rather i hope to convince the reader that the dual theory has intrinsic economic significance and that in some areas its predictions are superior to those of expected utility theory while in other areas the reverse will be the case two reasons have prompted me to look for an alternative to expected utility theory the first reason is methodological in expected utility theory the agent s attitude towards risk and the agent s attitude towards wealth are forever bonded together at the level of fundamental principles risk aversion and diminishing marginal utility of wealth which are synonymous under expected utility theory are horses of different colors the former expresses an attitute towards risk increased uncertainty hurts while the latter expresses an attitude towards wealth the loss of a sheep hurts more when the agent is poor than when the agent is rich a question arises therefore as to whether these two notions can be kept separate from each other in a full fledged theory of cardinal utility the dual theory will have this property the second reason that leads me to look for an alternative to expected utility theory is empirical behavior patterns which are systematic yet inconsistent with expected utility theory have often been observed two prominent references among many others are allais 1953 and kahneman tversky 1979 so deeply

disconnected synchronized regions of complex dynamical networks this technical note addresses the synchronized region problem which is converted to a more convenient matrix stability problem for complex dynamical networks for any natural number n the existence of a network with n disconnected synchronized regions is theoretically proved and numerically demonstrated this shows the intrinsic complexity of the network synchronization problem convexity characteristic of stability for relevant matrix pencils is further discussed a smooth chua s circuit network is finally discussed as an example for illustration

polynomial convergence of primal dual algorithms for the second order cone program based on the mz family of directions in this paper we study primal dual path following algorithms for the second order cone programming socp based on a family of directions that is a natural extension of the monteiro zhang mz family for semidefinite programming we show that the polynomial iteration complexity bounds of two well known algorithms for linear programming namely the short step path following algorithm of kojima et al and monteiro and adler and the predictor corrector algorithm of mizuno et al carry over to the context of socp that is they have an o loge 1 iteration complexity to reduce the duality gap by a factor of e where n is the number of second order cones since the mz type family studied in this paper includes an analogue of the alizadeh haeberly and overton pure newton direction we establish for the first time the polynomial convergence of primal dual algorithms for socp based on this search direction

leader following formation control of multi agent systems under fixed and switching topologies in this article two kinds of leader following formation control problems for second order nonlinear multi agent systems are investigated that is the cases with fixed topology and with switching topology for the former by constructing an appropriate lyapunov functional and utilising linear matrix inequality lmi method we propose a formation control algorithm which makes the nonlinear multi agent systems converge to a desired formation in addition a formation control algorithm is also developed for coupled double integrators with a constant reference velocity then we extend these results to the case when the interaction topology is switching numerical simulations are presented finally to demonstrate the effectiveness of the proposed results

smoothing functions for second order cone complementarity problems smoothing functions have been much studied in the solution of optimization and complementarity problems with nonnegativity constraints in this paper we extend smoothing functions to problems in which the nonnegative orthant is replaced by the direct product of second order cones these smoothing functions include the chen mangasarian class and the smoothed fischer burmeister function we study the lipschitzian and differential properties of these functions and in particular we derive computable formulas for these functions and their jacobians these properties and formulas can then be used to develop and analyze noninterior continuation methods for solving the corresponding optimization and complementarity problems in particular we establish the existence and uniqueness of the newton direction when the underlying mapping is monotone

characterizing and reasoning about probabilistic and non probabilistic expectation expectation is a central notion in probability theory the notion of expectation also makes sense for other notions of uncertainty we introduce a propositional logic for reasoning about expectation where the semantics depends on the underlying representation of uncertainty we give sound and complete axiomatizations for the logic in the case that the underlying representation is a probability b sets of probability measures c belief functions and d possibility measures we show that this logic is more expressive than the corresponding logic for reasoning about likelihood in the case of sets of probability measures but equi expressive in the case of probability belief and possibility finally we show that satisfiability for these logics is np complete no harder than satisfiability for propositional logic

sampled data synchronization of complex networks with partial couplings and t s fuzzy nodes this paper is concerned with the synchronization of complex networks subject to partial couplings and takagi sugeno t s fuzzy nodes by adopting the aperiodic sampled data strategy a decoupling method is utilized to handle the partial couplings among connected nodes which enables us to investigate each channel of complex networks independently on the basis of the input delay approach the hybrid system about each channel is reformulated to a continuous time varying delay system then the free weighting matrix approach and a novel continuous lyapunov functional are adopted to capture the information of sampling pattern sufficient conditions are obtained to ensure that the complex networks achieves synchronization with the target node furthermore the proposed strategy is extended to more general case in which there exist constant transmission time delays in the local interactions of connected nodes based on wirtinger s inequality a simplified and efficient synchronization strategy is proposed moreover the corresponding optimization problem about the maximal sampling interval upper bound is addressed as well finally the communication frequency reduction potential of the proposed synchronization strategy is well demonstrated via a numerical example

impulsive consensus algorithms for second order multi agent networks with sampled information in this paper the distributed consensus problem for second order continuous time multi agent networks with sampled data communication is investigated motivated by impulsive control strategy two kinds of impulsive distributed consensus algorithm are proposed these algorithms only utilize the sampled information and are implemented at sampled times by using the stability theory of impulsive systems and properties of the laplacian matrix necessary and sufficient conditions are obtained to ensure the consensus of the controlled networks it is shown that the control gains the sampling period and the eigenvalues of the laplacian matrix of the communication graph play key roles in achieving the consensus a numerical example is given to illustrate the results

optimal magnetic shield design with second order cone programming in this paper we consider a continuous version of the convex network flow problem which involves the integral of the euclidean norm of the flow and its square in the objective function a discretized version of this problem can be cast as a secondorder cone program for which efficient primal dual interior point algorithms have been developed recently an optimal magnetic shielding design problem of the maglev train a new bullet train under development in japan is formulated as the continuous convex network flow problem and is solved with the primal dual interiorpoint algorithm taking advantage of its efficiency and stability the algorithm is further applied to robust design of the magnetic shielding

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

brief paper second order consensus in multi agent dynamical systems with sampled position data this paper studies second order consensus in multi agent dynamical systems with sampled position data a distributed linear consensus protocol with second order dynamics is designed where both the current and some sampled past position data are utilized it is found that second order consensus in such a multi agent system cannot be reached without any sampled position data under the given protocol while it can be achieved by appropriately choosing the sampling period a necessary and sufficient condition for reaching consensus of the system in this setting is established based on which consensus regions are then characterized it is shown that if all the eigenvalues of the laplacian matrix are real then second order consensus in the multi agent system can be reached for any sampling period except at some critical points depending on the spectrum of the laplacian matrix however if there exists at least one eigenvalue of the laplacian matrix with a nonzero imaginary part second order consensus cannot be reached for sufficiently small or sufficiently large sampling periods in such cases one nevertheless may be able to find some disconnected stable consensus regions determined by choosing appropriate sampling periods finally simulation examples are given to verify and illustrate the theoretical analysis

stability analysis of swarms in this note we specify an individual based continuous time model for swarm aggregation in n dimensional space and study its stability properties we show that the individuals autonomous agents or biological creatures will form a cohesive swarm in a finite time moreover we obtain an explicit bound on the swarm size which depends only on the parameters of the swarm model

a time varying complex dynamical network model and its controlled synchronization criteria today complex networks have attracted increasing attention from various fields of science and engineering it has been demonstrated that many complex networks display various synchronization phenomena in this note we introduce a time varying complex dynamical network model we then further investigate its synchronization phenomenon and prove several network synchronization theorems especially we show that synchronization of such a time varying dynamical network is completely determined by the inner coupling matrix and by the eigenvalues and the corresponding eigenvectors of the coupling configuration matrix of the network

analyzing and controlling the network synchronization regions abstract in this paper the commonly concerned issue of synchronization regions of complex dynamical networks is investigated for the case when the synchronous state is an equilibrium point some simple sufficient conditions for a network to have or have no unbounded synchronization regions of the form 1 are established where 1 is a constant in addition a sufficient condition for the existence of a bounded synchronization region of the form 2 3 is derived where 2 and 3 are constants by using the parameter dependent lyapunov function method furthermore some effective controller design methods are presented that can change the synchronization regions thereby managing the synchronizability of the network finally some numerical examples are given to show that a dynamical network may have disconnected synchronization regions particularly it may have the coexistence of unbounded and bounded synchronization regions in the form of 1 2 3

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

continuous time and sampled data based average consensus with logarithmic quantizers this paper considers the average consensus problem for multi agent systems with continuous time first order dynamics logarithmic quantization is considered in the communication channels and continuous time and sampled data based protocols are proposed for the continuous time protocol we give an explicit upper bound of the consensus error in terms of the initial states the quantization density and the parameters of the network graph it is shown that in contrast with the case with uniform quantization the consensus error in the logarithmic quantization case is always uniformly bounded independent of the quantization density and the b asymptotic average consensus is ensured under the proposed protocol i e the asymptotic consensus error converges to zero as the sector bound b of the logarithmic quantizer approaches zero for the sampled data based protocol we give sufficient conditions on the sampling interval to ensure the b asymptotic average consensus numerical examples are given to demonstrate the effectiveness of the protocols

reaching a consensus in a dynamically changing environment a graphical approach this paper presents new graph theoretic results appropriate for the analysis of a variety of consensus problems cast in dynamically changing environments the concepts of rooted strongly rooted and neighbor shared are defined and conditions are derived for compositions of sequences of directed graphs to be of these types the graph of a stochastic matrix is defined and it is shown that under certain conditions the graph of a sarymsakov matrix and a rooted graph are one and the same as an illustration of the use of the concepts developed in this paper graph theoretic conditions are obtained which address the convergence question for the leaderless version of the widely studied vicsek consensus problem

distributed formation stabilization using relative position measurements in local coordinates in this paper we present a novel distributed method to stabilize a set of agents moving in a two dimensional environment to a desired rigid formation in our approach each agent computes its control input using the relative positions of a set of formation neighbors but contrary to most existing works this information is expressed in the agent s own independent local coordinate frame without requiring any common reference the controller is based on the minimization of a lyapunov function that includes locally computed rotation matrices which are required due to the absence of a common orientation our contribution is that the proposed distributed coordinate free method achieves global stabilization to a rigid formation with the agents using only partial information of the team does not require any leader units and is applicable to both single integrator or unicycle agents to guarantee global stability we require that the network induced by the agent interactions belongs to a certain class of undirected rigid graphs in two dimensions which we explicitly characterize the performance of the proposed method is illustrated with numerical simulations

observer based distributed consensus for general nonlinear multi agent systems with interval control inputs in this paper observer based distributed consensus for general nonlinear multi agent systems with interval control inputs under strongly connected balanced topology is encountered when the relative states of agents are unavailable or undesirable theoretical analysis method is further extended to the case of general nonlinear multi agent systems under switching setting moreover tracking problem on the leader follower scenario is also explicitly investigated under a mutual assumption that the communication graph which represents the interaction among agents contains a directed spanning tree with the leader as its root it is shown that the consensus for underlying considered multi agent systems can be desirable as long as the data missing rate does not exceed a certain threshold finally simulation examples are presented to effectively corroborate the analytical findings

similarity and other spectral relations for symmetric cones abstract the similarity relations that are derived in this paper reduce to well known results in the special case of symmetric matrices in particular for two positive definite matrices x and y the square of the spectral geometric mean is known to be similar to the matrix product xy it is shown in this paper that this property carries over to symmetric cones more elementary similarity relations such as xy 2 x yx 2 y are generalized as well we also extend the result that the eigenvalues of a matrix product xy are less dispersed than the eigenvalues of the jordan product xy yx 2 the paper further contains a number of inequalities on norms and spectral values this type of inequality is often used in the analysis of interior point methods in optimization we also derive an extension of stein s theorem to symmetric cones

brief paper some necessary and sufficient conditions for second order consensus in multi agent dynamical systems this paper studies some necessary and sufficient conditions for second order consensus in multi agent dynamical systems first basic theoretical analysis is carried out for the case where for each agent the second order dynamics are governed by the position and velocity terms and the asymptotic velocity is constant a necessary and sufficient condition is given to ensure second order consensus and it is found that both the real and imaginary parts of the eigenvalues of the laplacian matrix of the corresponding network play key roles in reaching consensus based on this result a second order consensus algorithm is derived for the multi agent system facing communication delays a necessary and sufficient condition is provided which shows that consensus can be achieved in a multi agent system whose network topology contains a directed spanning tree if and only if the time delay is less than a critical value finally simulation examples are given to verify the theoretical analysis

formation control of mobile agents based on distributed position estimation we propose a formation control strategy based on distributed position estimation for single integrator modeled agents by using relative position measurements under the proposed strategy the estimated and the actual formations globally exponentially converge to the actual and the desired formations respectively up to translation if and only if the interaction graph for the agents has a spanning tree a sufficient condition is provided for the case that the edge weights of the interaction graph are time varying further the proposed strategy is applied to formation control of unicycle like agents

stabilisation of infinitesimally rigid formations of multi robot networks this article considers the design of a formation control for multivehicle systems that uses only local information the control is derived from a potential function based on an undirected infinitesimally rigid graph that specifies the target formation a potential function is obtained from the graph from which a gradient control is derived under this controller the target formation becomes a manifold of equilibria for the multivehicle system it is shown that infinitesimal rigidity is a sufficient condition for local asymptotical stability of the equilibrium manifold a complete study of the stability of the regular polygon formation is presented and results for directed graphs are presented as well finally the controller is validated experimentally

subjective probability and expected utility without additivity comonotic acts are defined and an axiom of comonotomic independence 19 introduced that weakens the von newmann morgenstern axiom of independence if a nondegenerate continuous and monotonic state independent weak order over acts satisfies comonotonic independence then it induces a unique non necessarily additive probability and a von neumann morgenstern utility an extension of theexpected utility theory covers situations as the ellsberg paradox which are inconsistent with additive expected utility the concept of uncertainty aversion and interpretation of comonotonic independence in the context of social welfare functions are included

consensus of second order multi agent systems via impulsive control using sampled hetero information in this paper the consensus problem for second order multi agent systems using impulsive control with sampled hetero information is investigated necessary and sufficient conditions for sampling interval to achieve consensus for the second order multi agent systems are obtained analysis for the upper bound of sampling interval convergence performance and communication cost of the proposed control protocols are also discussed some numerical examples are given to demonstrate the effectiveness of the proposed control protocols

ratio of distance rigidity theory with application to similar formation control this paper develops a ratio of distance rod rigidity theory to study when a framework can be uniquely determined by a set of rod constraints up to similar transformations translation rotation scaling and reflection in particular a framework is specified by a set of rod constraints the rod of a pair of edges joining a common vertex instead of distance bearing and angle constraints assumed in existing literature its relations to three existing rigidity theories distance bearing and angle rigidity theories are established the proposed rod rigidity theory is further applied to the rod based similar formation stabilization problem where the desired formation shape is expressed as a set of rod constraints finally numerical simulations are presented to illustrate the effectiveness of the theoretical results

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

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