synchronization of identical linear dynamic systems subject to input saturation abstract this paper investigates the synchronization problem for a group of agents with identical linear dynamics subject to input saturation two classes of linear systems asymptotically null controllable with bounded control ancbc systems and double integrator systems are studied for ancbc systems it is shown that a linear protocol with the control gain obtained via parametric lyapunov equations can semiglobally synchronize the undirected topology provided that its augmented directed topology has a spanning tree for a special case of ancbc the double integrator systems it is established that if the augmented directed topology has a spanning tree then in the presence of input saturation using linear protocols with positive control gains can achieve global synchronization two numerical examples are given to demonstrate the effectiveness of the theoretical results

distributed formation control of multi agent systems using complex laplacian the paper concentrates on the fundamental coordination problem that requires a network of agents to achieve a specific but arbitrary formation shape a new technique based on complex laplacian is introduced to address the problems of which formation shapes specified by inter agent relative positions can be formed and how they can be achieved with distributed control ensuring global stability concerning the first question we show that all similar formations subject to only shape constraints are those that lie in the null space of a complex laplacian satisfying certain rank condition and that a formation shape can be realized almost surely if and only if the graph modeling the inter agent specification of the formation shape is 2 rooted concerning the second question a distributed and linear control law is developed based on the complex laplacian specifying the target formation shape and provable existence conditions of stabilizing gains to assign the eigenvalues of the closed loop system at desired locations are given moreover we show how the formation shape control law is extended to achieve a rigid formation if a subset of knowledgable agents knowing the desired formation size scales the formation while the rest agents do not need to re design and change their control laws

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

brief paper formation control using range only measurements this paper proposes algorithms to coordinate a formation of mobile agents when the agents are not able to measure the relative positions of their neighbors but only the distances to their respective neighbors in this sense less information is available to agents than is normally assumed in formation stabilization or station keeping problems to control the shape of the formation the solution advanced in the paper involves subsets of non neighbor agents cyclically localizing the relative positions of their respective neighbor agents while these are held stationary and then moving to reduce the value of a cost function which is nonnegative and assumes the zero value precisely when the formation has correct distances the movement schedule is obtained by a novel vertex coloring algorithm whose computation time is linear in the number of agents when implemented on the graphs of minimally rigid formations since in some formations it may be that an agent is never allowed to be stationary e g it is a fixed wing aircraft or because formations may be required to move as a whole in a certain direction the results are extended to allow for cyclic localization of agents in this case the tool used is the cayley menger determinant

strong invariance principles for mixing random fields given a random field z q indexed by q tuples of positive integers and satisfying a strong mixing condition we study the approximation of the partial sum field sn n z q by brownian sheet setting g alpha n 1 n q in z q n k underset raise0 3em hbox smash scriptscriptstyle geqslant mathop pi limits 1 underset raise0 3em hbox smash scriptscriptstyle leqslant i underset raise0 3em hbox smash scriptscriptstyle leqslant q i pm k n i alpha k 1 q for 0 0 we also construct an example showing that in a somewhat larger similar type domain the above approximation is generally impossible even with 0

flocking with connectivity preservation for disturbed nonlinear multi agent systems by output feedback abstractthis paper considers the problem of flocking with connectivity preservation for a class of disturbed nonlinear multi agent systems in order to deal with the nonlinearities in the dynamic of all agents some auxiliary variables are introduced into the state observer for stability analysis by proposing a bounded potential function and using adaptive theory a novel output feedback consensus algorithm is developed to guarantee that the states of all agents achieve flocking with connectivity preservation

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

leader follower formation via complex laplacian the paper introduces complex valued laplacians for graphs whose edges are attributed with complex weights and studies the leader follower formation problem based on complex laplacians the main goal is to control the shape of a planar formation of point agents in the plane using simple and linear interaction rules related to complex laplacians we present a characterization of complex laplacians that preserve a specific planar formation as an equilibrium solution for both single integrator kinematics and double integrator dynamics planar formations under study are subject to translation rotation and scaling in the plane but can be determined by two co leaders in leader follower networks furthermore when a complex laplacian does not result in an asymptotically stable behavior of the multi agent system we show that a stabilizing matrix which updates the complex weights exists to asymptotically stabilize the system while preserving the equilibrium formation also algorithms are provided to find stabilizing matrices finally simulations are presented to illustrate our results

global bounded synchronization of general dynamical networks with nonidentical nodes this note addresses the problem of synchronization for general dynamical networks with nonidentical nodes the coupling strength outer coupling configuration and inner connection in such networks are all time varying neither an equilibrium for each node nor a synchronization manifold is assumed to exist an estimate of the convergence domain for a general class of time varying nonlinear systems is given by introducing the average dynamics of all nodes and based on this estimate a criterion of global synchronization in the sense of boundedness of the maximum state deviation between nodes is developed an explicit bound of the maximum state deviation between nodes is obtained by the maximum difference between each node dynamics and the average dynamics the proposed criterion is an extension of several related synchronization criteria for the case of identical nodes to the case of nonidentical nodes

invariance principles for von mises and u statistics the almost sure approximation of von mises statistics and u statistics by appropriate stochastic integrals with respect to kiefer processes is obtained in general these integrals are non gaussian processes as applications we get almost sure versions for the estimator of the variance and for the 2 test of goodness of fit

an almost sure invariance principle for hilbert space valued martingales we obtain an almost sure approximation of a martingale with values in a real separable hilbert space h by a suitable h valued brownian motion

sparse stable systems abstract in the design of decentralized networked systems it is important to know whether a given network topology can sustain stable dynamics we consider a basic version of this problem here given a vector space of sparse real matrices does it contain a stable hurwitz matrix said differently is a feedback channel corresponding to a non zero entry necessary for stabilization or can it be done without we provide in this paper a set of necessary conditions and a set of sufficient conditions for the existence of stable matrices in a vector space of sparse matrices we further prove some properties of the set of sparse matrix spaces that contain hurwitz matrices the conditions we exhibit are most easily stated in the language of graph theory which we thus adopt in this paper

distributed coordination of multi agent systems with quantized observer based encoding decoding integrative design of communication mechanism and coordinated control law is an interesting and important problem for multi agent networks in this paper we consider distributed coordination of discrete time second order multi agent systems with partially measurable state and a limited communication data rate a quantized observer based encoding decoding scheme is designed which integrates the state observation with encoding decoding a distributed coordinated control law is proposed for each agent which is given in terms of the states of its encoder and decoders it is shown that for a connected network 2 bit quantizers suffice for the exponential asymptotic synchronization of the states of the agents the selection of controller parameters and the performance limit are discussed it is shown that the algebraic connectivity and the spectral radius of the laplacian matrix of the communication graph play key roles in the closed loop performance the spectral radius of the laplacian matrix is related to the selection of control gains while the algebraic connectivity is related to the spectral radius of the closed loop state matrix furthermore it is shown that as the number of agents increases the asymptotic convergence rate can be approximated as a function of the number of agents the number of quantization levels communication data rate and the ratio of the algebraic connectivity to the spectral radius of the laplacian matrix of the communication graph

consensus tracking for higher order multi agent systems with switching directed topologies and occasionally missing control inputs abstract this paper studies the distributed consensus tracking problem of linear higher order multi agent systems with switching directed topologies and occasionally missing control inputs in this framework the underlying topology of dynamic agents may switch among several directed graphs each having a directed spanning tree rooted at the leader furthermore the control inputs to the followers may be temporally missed due to actuator failures and network induced packet loss to guarantee asymptotic consensus tracking in such a multi agent system several distributed controllers are constructed based only on the relative state information of neighboring agents by appropriately constructing a switching lyapunov function and using tools from the m matrix theory some sufficient conditions for achieving distributed consensus tracking are provided finally some numerical simulations are given to illustrate the theoretical analysis

global and robust formation shape stabilization of relative sensing networks this paper proposes a simple distributed algorithm that achieves global stabilization of formations for relative sensing networks in arbitrary dimensions with fixed topology assuming the network runs an initialization procedure to equally orient all agent reference frames convergence to the desired formation shape is guaranteed even in partially asynchronous settings we characterize the algorithm robustness against several sources of errors link failures measurement errors and frame initialization errors the technical approach combines algebraic graph theory multidimensional scaling and distributed linear iterations

control of minimally persistent formations in the plane this paper studies the problem of controlling the shape of a formation of point agents in the plane a model is considered where the distance between certain agent pairs is maintained by one of the agents making up the pair if enough appropriately chosen distances are maintained with the number growing linearly with the number of agents then the shape of the formation will be maintained the detailed question examined in the paper is how one may construct decentralized nonlinear control laws to be operated at each agent that will restore the shape of the formation in the presence of small distortions from the nominal shape using the theory of rigid and persistent graphs the question is answered as it turns out a certain submatrix of a matrix known as the rigidity matrix can be proved to have nonzero leading principal minors which allows the determination of a stabilizing control law

coordination of multiagents interacting under independent position and velocity topologies we consider the coordination control for multiagent systems in a very general framework where the position and velocity interactions among agents are modeled by independent graphs different algorithms are proposed and analyzed for different settings including the case without leaders and the case with a virtual leader under fixed position and velocity interaction topologies as well as the case with a group velocity reference signal under switching velocity interaction it is finally shown that the proposed algorithms are feasible in achieving the desired coordination behavior provided the interaction topologies satisfy the weakest possible connectivity conditions such conditions relate only to the structure of the interactions among agents while irrelevant to their magnitudes and thus are easy to verify rigorous convergence analysis is preformed based on a combined use of tools from algebraic graph theory matrix analysis as well as the lyapunov stability theory

geometric analysis of the formation problem for autonomous robots in the formation control problem for autonomous robots a distributed control law steers the robots to the desired target formation a local stability result of the target formation can be derived by methods of linearization and center manifold theory or via a lyapunov based approach besides the target formation the closed loop dynamics of the robots feature various other undesired invariant sets such as nonrigid formations this note addresses a global stability analysis of the closed loop formation control dynamics we pursue a differential geometric approach and derive purely algebraic conditions for local stability of invariant embedded submanifolds these theoretical results are then applied to the well known example of a cyclic triangular formation and result in instability of all invariant sets other than the target formation

control of minimally persistent leader remote follower and coleader formations in the plane this paper solves an n agent formation shape control problem in the plane the objective is to design decentralized control laws so that the agents cooperatively restore a prescribed formation shape in the presence of small perturbations from the prescribed shape we consider two classes of directed cyclic information architectures associated with so called minimally persistent formations leader remote follower and coleader in our framework the formation shape is maintained by controlling certain interagent distances only one agent is responsible for maintaining each distance we propose a decentralized control law where each agent executes its control using only the relative position measurements of agents to which it must maintain its distance the resulting nonlinear closed loop system has a manifold of equilibria which implies that the linearized system is nonhyperbolic we apply center manifold theory to show local exponential stability of the desired formation shape the result circumvents the non compactness of the equilibrium manifold choosing stabilizing gains is possible if a certain submatrix of the rigidity matrix has all leading principal minors nonzero and we show that this condition holds for all minimally persistent leader remote follower and coleader formations with generic agent positions simulations are provided

distributed algorithms for reaching consensus on general functions this paper presents analysis and design results for distributed consensus algorithms in multi agent networks we consider continuous consensus functions of the initial state of the network agents under mild smoothness assumptions we obtain necessary and sufficient conditions characterizing any algorithm that asymptotically achieves consensus this characterization is the building block to obtain various design results for networks with weighted directed interconnection topologies we first identify a class of smooth functions for which one can synthesize in a systematic way distributed algorithms that achieve consensus we apply this result to the family of weighted power mean functions and characterize the exponential convergence properties of the resulting algorithms we establish the validity of these results for scenarios with switching interconnection topologies finally we conclude with two discontinuous distributed algorithms that achieve respectively max and min consensus in finite time

distributed control of angle constrained cyclic formations using bearing only measurements abstract this paper studies distributed control of multi vehicle formations with angle constraints using bearing only measurements it is assumed that each vehicle can only measure the local bearings of their neighbors and there are no wireless communications among the vehicles the desired formation is a cyclic one whose underlying information flow is described by an undirected cycle graph we propose a distributed bearing only formation control law that ensures local exponential or finite time stability collision avoidance between any vehicles can be locally guaranteed in the absence of inter vehicle distance measurements

on global stability of planar formations formation control is concerned with the design of control laws that stabilize agents at given distances from each other with the constraint that an agent s dynamics only depends on a subset of other agents we show in this technical note that a broad class of control laws fails to stabilize a simple formation with four agents the novelty of the approach used in this technical note lies in the use of bifurcation theory to show that for almost all control laws there exists a stable undesired equilibrium

on stably quasimonotone hemivariational inequalities abstract we establish some existence results for variational hemivariational inequalities of the hartman stampacchia type involving stably quasimonotone set valued mappings on bounded closed and convex subsets in reflexive banach spaces we also derive a sufficient condition for the existence and boundedness of solutions

formation shape control based on bearing rigidity distance measurements are not the only geometric quantities that can be used for multi agent formation shape control bearing measurements can be used in conjunction with distances this article employs bearing rigidity for mobile formations which was developed for robot and sensor network localisation so that bearings can be used for shape control in mobile formations the first part of this article examines graph theoretical models for formation network analysis and control law design that are needed to maintain the shape of a formation in two dimensional space while the formation moves as a cohesive whole bearing based shape control for a formation of mobile agents involves the design of distributed control laws that ensure the formation moves so that bearing constraints maintain some desired values the second part of this article focuses on the design of a distributed control scheme for nonholonomic agents to solve the bearing based formation shape control problem in particular a control law u