on the stability margin of networked dynamical systems this paper is concerned with the stability gain and phase margin of networked dynamical systems e g vehicles in formation each of which has access to the state of its neighbors and subsequently uses a state feedback gain f for a certain global objective such as attitude synchronization here the network topology is directed and described by a generalized laplacian matrix l an individual dynamical system can adopt its own state feedback control law such as a linear quadratic regulator controller for an ample stability margin but it may lose the stability margin to a great extent when the same control strategy utilizing relative state information is used after being interconnected with other dynamical systems this paper reveals and elaborates upon the following four facts first the stability margin after interconnection is quantified via the minimum singular value of a frequency dependent matrix made up of f and l second the stability margin of a networked dynamical system having a pole at the origin is at most the inverse of the zero eigenvalue sensitivity of l third there exists an upper bound of the stability margin that has a computational merit and asymptotically converges to the exact margin with respect to network size probability of link existence and control gain in a random network setting and finally l can be designed to maximize the stability margin numerical examples are provided to demonstrate the elaboration

distributed rotating formation control of multi agent systems this paper investigates collective rotating motions of second order multi agent systems we first consider rotating consensus problems using local relative information we propose a protocol and give a necessary and sufficient condition for rotating consensus of the system then we consider rotating formation control problems with the help of lyapunov theory for complex systems we propose rotating formation protocols and give sufficient conditions to make all agents move with a specific structure in a circular channel finally simulation results are provided to demonstrate the effectiveness of our 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

probabilistic synchronisation of pinning control this paper is concerned with synchronization of complex stochastic dynamical networks in the presence of noise and functional uncertainty a probabilistic control method for adaptive synchronization is presented all required probabilistic models of the network are assumed to be unknown therefore estimated to be dependent on the connectivity strength the state and control values robustness of the probabilistic controller is proved via the liapunov method furthermore based on the residual error of the network states we introduce the definition of stochastic pinning controllability a coupled map lattice with spatiotemporal chaos is taken as an example to illustrate all theoretical developments the theoretical derivation is complemented by its validation on two representative examples

laplacian graph eigenvectors abstract if g is a graph its laplacian is the difference of the diagonal matrix of its vertex degrees and its adjacency matrix the main thrust of the present article is to prove several laplacian eigenvector principles which in certain cases can be used to deduce the effect on the spectrum of contracting adding or deleting edges and or of coalescing vertices one application is the construction of two isospectral graphs on 11 vertices having different degree sequences only one of which is bipartite and only one of which is decomposable

leaders in multi agent controllability under consensus algorithm and tree topology abstract by controllability of multi agent systems we mean the property that all agents can be driven to arbitrary configurations only through regulating a few leaders externally while the rest of the agents are subject to the nearest neighbor law it is known that the controllability of multi agent systems depends not only on the communication topologies among agents but also on the selection of leaders the main objective of this paper aims to characterize the virtue that leaders should have from the perspective of algebraic and graphical conditions we begin with a heuristic observation for tree graph to gain more insights necessary and sufficient conditions are then proposed in terms of downer branch and subgraphs respectively in particular it is shown for path topologies that controllability completely depends on the leaders location the obtained results may help us to pave the way towards a new method of formation and reconfiguration control in swarming robots

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

matrix weighted consensus and its applications abstract this paper proposes the matrix weighted consensus algorithm which is a generalization of the consensus algorithm given a networked dynamical system where the interconnections between agents are weighted by nonnegative definite matrices it is shown that consensus and clustering phenomena naturally exist we examine algebraic and algebraic graph conditions for achieving a consensus

containment control for second order multi agent systems with time varying delays abstract this paper considers the containment control problem for second order multi agent systems with time varying delays both the containment control problem with multiple stationary leaders and the problem with multiple dynamic leaders are investigated sufficient conditions on the communication digraph the feedback gains and the allowed upper bound of the delays to ensure containment control are given in the case that the leaders are stationary the lyapunov razumikhin function method is used in the case that the leaders are dynamic the lyapunov krasovskii functional method and the linear matrix inequality lmi method are jointly used a novel discretized lyapunov functional method is introduced to utilize the upper bound of the derivative of the delays no matter how large it is which leads to a better result on the allowed upper bound of the delays to ensure containment control finally numerical simulations are provided to illustrate the effectiveness of the obtained theoretical results

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

sampled data discrete time coordination algorithms for double integrator dynamics under dynamic directed interaction in this article we study two sampled data based discrete time coordination algorithms for multi vehicle systems with double integrator dynamics under dynamic directed interaction for both algorithms we derive sufficient conditions on the interaction graph the damping gain and the sampling period to guarantee coordination by using the property of infinity products of stochastic matrices when the conditions on the damping gain and the sampling period are satisfied the first algorithm guarantees coordination on positions with a zero final velocity if the interaction graph has a directed spanning tree jointly while the second algorithm guarantees coordination on positions with a constant final velocity if the interaction graph has a directed spanning tree at each time interval simulation results are presented to show the effectiveness of the theoretical results

collective motion from consensus with cartesian coordinate coupling collective motions including rendezvous circular patterns and logarithmic spiral patterns can be achieved by introducing cartesian coordinate coupling to existing consensus algorithms we study the collective motions of a team of vehicles in 3d by introducing a rotation matrix to an existing consensus algorithm for double integrator dynamics it is shown that the network topology the damping gain and the value of the euler angle all affect the resulting collective motions we show that when the nonsymmetric laplacian matrix has certain properties the damping gain is above a certain bound and the euler angle is below equal or above a critical value the vehicles will eventually rendezvous move on circular orbits or follow logarithmic spiral curves lying on a plane perpendicular to the euler axis in particular when the vehicles eventually move on circular orbits the relative radii of the orbits respectively the relative phases of the vehicles on their orbits are equal to the relative magnitudes respectively the relative phases of the components of a right eigenvector associated with a critical eigenvalue of the nonsymmetric laplacian matrix simulation results are presented to demonstrate the theoretical results

leader enabled deployment onto planar curves a pde based approach we introduce an approach for stable deployment of agents onto families of planar curves namely 1 d formations in 2 d space the agents collective dynamics are modeled by the reaction advection diffusion class of partial differential equations pdes which is a broader class than the standard heat equation and generates a rich geometric family of deployment curves the pde models whose state is the position of the agents incorporate the agents feedback laws which are designed based on a spatial internal model principle namely the agents feedback laws allow the agents to deploy to a family of geometric curves that correspond to the model s equilibrium curves parameterized by the continuous agent identity 0 1 however many of these curves are open loop unstable stable deployment is ensured by leader feedback designed in a manner similar to the boundary control of pdes by discretizing the pde model with respect to we impose a fixed communication topology specifically a chain graph on the agents and obtain control laws that require communication with only an agent s nearest neighbors on the graph a pde based approach is also used to design observers to estimate the positions of all the agents which are needed in the leader s feedback by measuring only the position of the leader s nearest neighbor hence the leader uses only local information when employing output feedback

a finite element method for surface diffusion the parametric case surface diffusion is a fourth order highly nonlinear geometric driven motion of a surface with normal velocity proportional to the surface laplacian of mean curvature we present a novel variational formulation for parametric surfaces with or without boundaries the method is semi implicit requires no explicit parametrization and yields a linear system of elliptic pde to solve at each time step we next develop a finite element method propose a schur complement approach to solve the resulting linear systems and show several significant simulations some with pinch off in finite time we introduce a mesh regularization algorithm which helps prevent mesh distortion and discuss the use of time and space adaptivity to increase accuracy while reducing complexity

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

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

flocking for multi agent systems with unknown nonlinear time varying uncertainties under a fixed undirected graph this paper presents a flocking algorithm for networked multi agent systems with unknown nonlinear time varying uncertainties by integrating cooperative control and l1 adaptive control methods an ideal multi agent system without uncertainties is introduced first the cooperative control law based on an artificial potential function is designed to make the ideal multi agent system achieve flocking under a fixed and connected undirected graph information of ideal states instead of real states is exchanged among agents through a communication network the presence of uncertainties will lead to the degeneration of the performance or even destabilize the entire multi agent system the l1 adaptive control law is therefore introduced to handle unknown nonlinear time varying uncertainties by integrating the cooperative control law with the adaptive control law the real multi agent system stays close to the ideal multi agent system which achieves flocking asymptotically under a connected graph simulati

multi vehicle consensus with a time varying reference state in this paper we study the consensus problem in multi vehicle systems where the information states of all vehicles approach a time varying reference state under the condition that only a portion of the vehicles e g the unique team leader have access to the reference state and the portion of the vehicles might not have a directed path to all of the other vehicles in the team we first analyze a consensus algorithm with a constant reference state using graph theoretical tools we then propose consensus algorithms with a time varying reference state and show necessary and sufficient conditions under which consensus is reached on the time varying reference state the time varying reference state can be an exogenous signal or evolve according to a nonlinear model these consensus algorithms are also extended to achieve relative state deviations among the vehicles an application example to multi vehicle formation control is given as a proof of concept

l 1 group consensus of multi agent systems with stochastic inputs under directed interaction topology we address l 1 group consensus problems of networked multi agent systems with fixed directed information exchange in this article a discrete time protocol is designed to solve the l 1 group consensus problems via general stochastic inputs under some mild assumptions we derive sufficient conditions to guarantee the l 1 group consensus based on algebraic graph theory and ergodicity theory for finite markov chains moreover the boundedness of the expected infinite sum of the inputs ensures the boundedness of the expected trajectory numerical simulations instantiating the inputs as varied independent and identically distributed random processes as well as autoregressive processes are presented to demonstrate the effectiveness of our theoretical results

cooperative output regulation of heterogeneous multi agent systems an h_ infty criterion in this note the cooperative output regulation problem of heterogeneous linear multi agent systems is investigated our approach is based on internal model and dynamic error feedback among the agents under some standard assumptions the problem is solved by an internal model and a stabilizing h controller we showed that the exo signal free system is stabilized if each controlled agent is robust in the sense of h norm to resist the disturbance measured by the second largest eigenvalue of the graph adjacency matrix then the synthesis problem is solved using algebraic riccati equation furthermore we showed that this condition is a generalization of existing results

network topology and communication data rate for consensusability of discrete time multi agent systems this paper investigates the joint effect of agent dynamic network topology and communication data rate on consensusability of linear discrete time multi agent systems neglecting the finite communication data rate constraint and under undirected graphs a necessary and sufficient condition for consensusability under a common control protocol is given which explicitly reveals how the intrinsic entropy rate of the agent dynamic and the communication graph jointly affect consensusability the result is established by solving a discrete time simultaneous stabilization problem a lower bound of the optimal convergence rate to consensus which is shown to be tight for some special cases is provided as well moreover a necessary and sufficient condition for formationability of multi agent systems is obtained as a special case the discrete time second order consensus is discussed where an optimal control gain is designed to achieve the fastest convergence the effects of undirected graphs on consensability formationability and optimal convergence rate are exactly quantified by the ratio of the second smallest to the largest eigenvalues of the graph laplacian matrix an extension to directed graphs is also made the consensus problem under a finite communication data rate is finally investigated

brief paper distributed discrete time coordinated tracking with a time varying reference state and limited communication this paper studies a distributed discrete time coordinated tracking problem where a team of vehicles communicating with their local neighbors at discrete time instants tracks a time varying reference state available to only a subset of the team members we propose a pd like discrete time consensus algorithm to address the problem under a fixed communication graph we then study the condition on the communication graph the sampling period and the control gain to ensure stability and give the quantitative bound of the tracking errors it is shown that the ultimate bound of the tracking errors is proportional to the sampling period the benefit of the proposed pd like discrete time consensus algorithm is also demonstrated through comparison with an existing p like discrete time consensus algorithm simulation results are presented as a proof of concept

a sufficient condition for convergence of sampled data consensus for double integrator dynamics with nonuniform and time varying communication delays this technical note investigates a discrete time second order consensus algorithm for networks of agents with nonuniform and time varying communication delays under dynamically changing communication topologies in a sampled data setting some new proof techniques are proposed to perform the convergence analysis it is finally shown that under certain assumptions upon the velocity damping gain and the sampling period consensus is achieved for arbitrary bounded time varying communication delays if the union of the associated digraphs of the interaction matrices in the presence of delays has a directed spanning tree frequently enough

automated traffic and the finite size resonance we investigate in detail what one might call the canonical automated traffic problem a long string of n 1 cars numbered from 0 to n moves along a one lane road in formation at a constant velocity and with a unit distance between successive cars each car monitors the relative velocity and position of only its neighboring cars this information is then fed back to its own engine which decelerates brakes or accelerates according to the information it receives the question is what happens when due to an external influence a traffic light turning green the zero th car the leader accelerates

nonsmooth leader following formation control of nonidentical multi agent systems with directed communication topologies this paper presents two nonsmooth leader following formation protocols for nonidentical lipschitz nonlinear multi agent systems with directed communication network topologies one protocol is used to achieve finite time formation for first order systems and the other to achieve asymptotic formation for second order systems in these protocols the states of all the agents including the leader and the followers are available only locally within their neighborhoods some sufficient conditions for reaching formations are derived for nonidentical nonlinear systems satisfying locally lipschitz conditions to prove the stability a new nonsmooth lyapunov function is constructed with stability conditions derived under a nonsmooth analysis framework the proposed formation protocols are applied to multi spacecraft systems in deep space exploration with numerical simulations demonstrating the effectiveness of the theoretical results

extension of the herglotz algorithm to nonautonomous canonical transformations the herglotz algorithm for constructing autonomous canonical transformations that was presented by guenther gottsch and kramer in siam rev 38 1996 pp 287 293 is extended to include nonautonomous canonical transformations and a remainder function cal r that is related to a generating function by cal r partial f partial t

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

lq control for coordinated linear systems coordinated linear systems are a special class of hierarchical linear systems with a strict top to bottom information structure the lq problem over all structure preserving static state feedbacks is discussed the overall control problem separates into conditionally independent subproblems a numerical approach to their solution is derived and the behavior and performance of the resulting control law are illustrated in examples

criteria for global pinning controllability of complex networks in this paper we study pinning controllability of networks of coupled dynamical systems in particular we study the problem of asymptotically driving a network of coupled identical oscillators onto some desired common reference trajectory by actively controlling only a limited subset of the whole network the reference trajectory is generated by an exogenous independent oscillator and pinned nodes are coupled to it through a linear state feedback we describe the time evolution of the complex dynamical system in terms of the error dynamics thereby we reformulate the pinning controllability problem as a global asymptotic stability problem by using lyapunov stability theory and algebraic graph theory we establish tractable sufficient conditions for global pinning controllability in terms of the network topology the oscillator dynamics and the linear state feedback

a bounded distributed connectivity preserving aggregation strategy with collision avoidance property abstract this paper presents a bounded connectivity preserving control strategy for the aggregation of multi agent systems the problem is investigated for two cases of single integrator agents and unicycles under the proposed control strategy if two agents are in the connectivity range at some point in time they will stay connected thereafter the agents finally aggregate while avoiding collision in such a way that the average of the distances between every pair of neighboring agents is bounded by a pre specified positive real number which can be chosen arbitrarily small the results are developed based on some important characteristics of the positive limit set of the closed loop system under the proposed control strategy and a fundamental property of convex real functions the theoretical results are verified by simulation

static output feedback stabilization of interconnected systems abstract this paper is concerned with the celebrated static output feedback control problem sofp subject to linear constraints on control input k e g bounds on control magnitude zeros in some elements of k etc these constraints typically arise in the control of resource limited systems interconnected to each other where the local control for each system makes use of its own and neighboring systems outputs only and its magnitude is bounded this control problem can be approached by a spectral norm minimization technique q snm whose preliminary version was previously introduced with little mathematical justification but shown to be promising for the regular sofp without control constraints this paper mathematically justifies q snm by showing its explicit relationship with spectral radius and extends q snm to accommodate various linear control constraints this paper also discusses the practical application of q snm to vehicle formation control which demonstrates the merit of q snm

a synthesis approach of distributed model predictive control for homogeneous multi agent system with collision avoidance for the tracking and formation problem of multi agent systems with collision avoidance a synchronous distributed model predictive control dmpc algorithm is proposed we consider the deterministic linear time invariant and homogeneous dynamics for all agents in the synchronous dmpc all the agents solve their optimisation problems synchronously taking advantage of their neighbours assumed predictive information to obtain the current optimal inputs considering the uncertain deviation existing between the assumed and actual predictive information of each agent we contribute to design a deviation dependent collision avoidance constraint which is imposed in the individual optimisation problem to guarantee the safety of each agent we constrain the uncertain deviation by designing a time varying compatibility constraint in the two norm form which is imposed in the individual optimisation problem to play an important role in both the collision avoidance and exponential stability by applying the pr

consensus problems in networks of agents with double integrator dynamics and time varying delays in this article we consider consensus problems in networks of agents with double integrator dynamics and non uniform time varying delays the agent dynamics is adopted as a typical point mass model based on newton s law without assuming that the weighting factors in the information update schemes are non negative we propose two protocols such that both the state and the velocity of agents achieve consensus an equivalent reduced order system is introduced to analyse the convergence of the protocols some necessary and or sufficient conditions for consensus are established in terms of linear matrix inequalities simulation results are provided that demonstrate the effectiveness of our theoretical results

flocks and formations given a large number the flock of moving physical objects we investigate physically reasonable mechanisms of influencing their orbits in such a way that they move along a prescribed course and in a prescribed and fixed configuration or in formation each agent is programmed to see the position and velocity of a certain number of others this flow of information from one agent to another defines a fixed directed loopless graph in which the agents are represented by the vertices this graph is called the communication graph to be able to fly in formation an agent tries to match the mean position and velocity of his neighbors his direct antecedents on the communication graph to his own this operation defines a directed laplacian on the communication graph a linear feedback is used to ensure stability of the coherent flight patterns we analyze in detail how the connectedness of the communication graph affects the coherence of the stable flight patterns and give a characterization of these stable flight patterns we do the same if in addition the flight of the flock is guided by one or more leaders finally we use this theory to develop some applications examples of these are flight guided by external controls flocks of flocks and some results about flocks whose formation is always oriented along the line of flight such as geese

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 formation control for fractional order systems dynamic interaction and absolute relative damping abstract this paper studies the distributed formation control problem for multiple fractional order systems under dynamic interaction and with absolute relative damping in the context of this paper formation control means that a group of systems reaches the desired state deviations via a local interaction we first study a formation control algorithm in the case of a directed dynamic network topology the convergence conditions on both the network topology and the fractional orders are presented when the fractional order satisfies 0 1 1 2 n sufficient conditions on the network topology are given to ensure the formation control we then propose fractional order formation control algorithms with absolute relative damping and study the conditions on the network topology and the control gains such that the formation control will be achieved under a directed fixed network topology the final equilibria are also given explicitly finally several simulation examples are presented as a proof of concept

distributed centroid estimation from noisy relative measurements a b s t r a c t we propose an anchorless distributed technique for estimating the centroid of a network of agents from noisy relative measurements the positions of the agents are then obtained relative to the estimated centroid the usual approach to multi agent localization assumes instead that one anchor agent exists in the network and the other agents positions are estimated with respect to the anchor we show that our centroid based algorithm converges to the optimal solution and such a centroid based representation produces results that are more accurate than anchor based ones irrespective of the selected anchor