stochastic bounded consensus tracking of second order multi agent systems with measurement noises based on sampled data with general sampling delay this paper is devoted to the stochastic bounded consensus tracking problems of second order multi agent systems where the control input of each agent can only use the information measured at the sampling instants from its neighbors or the virtual leader with a time varying reference state the measurements are corrupted by random noises and the signal sampling process induces the small sampling delay the augmented matrix method the probability limit theory and some other techniques are employed to derive the necessary and sufficient conditions guaranteeing the mean square bounded consensus tracking we show that the convergence of the proposed protocol simultaneously depends on the constant feedback gains the network topology the sampled period and the sampling delay and that the static consensus tracking error depends on not only the above mentioned factors but also the noise intensity and the upper bound of the velocity and the acceleration of the virtual leader the obtained results cover no sampling delay as its one special case simulations are provided to demonstrate the effectiveness of the theoretical results

distributed robust consensus control of multi agent systems with heterogeneous matching uncertainties this paper considers the distributed consensus problem of linear multi agent systems subject to different matching uncertainties for both the cases without and with a leader of bounded unknown control input due to the existence of nonidentical uncertainties the multi agent systems discussed in this paper are essentially heterogeneous for the case where the communication graph is undirected and connected based on the local state information of neighboring agents a fully distributed continuous adaptive consensus protocol is designed under which the consensus error is uniformly ultimately bounded and exponentially converges to a small adjustable bounded set for the case where there exists a leader whose control input is unknown and bounded a distributed adaptive consensus protocol is proposed to ensure the boundedness of the consensus error a sufficient condition for the existence of the proposed protocols is that each agent is stabilizable

adaptive finite time consensus in multi agent networks abstract this paper is concerned with the finite time consensus problem of distributed agents having non identical unknown nonlinear dynamics to a leader agent that also has unknown nonlinear control input signal by parameterization of unknown nonlinear dynamics a lyapunov technique in conjunction with homogeneity technique is presented for designing a decentralized adaptive finite time consensus control protocol in undirected networks homogeneous lyapunov functions and homogeneous vector fields are introduced in the stability analysis although the whole system is not homogeneous theoretical analysis shows that leader following consensus can be achieved in finite time meanwhile finite time parameter convergence can be also guaranteed under the proposed control scheme an example is given to validate the theoretical results

distributed output tracking of high order nonlinear multi agent systems with unstable linearization abstract this paper addresses the problem of distributed output tracking for a class of high order nonlinear multi agent systems whose linearization parts may have unstable modes for the case where the graph topology is directed and the leader is the neighbor of only a small portion of followers distributed tracking control laws are designed by using the algebra graph theory it is shown that all the states of the closed loop system are bounded and the tracking errors can be tuned to be arbitrarily small finally the design procedure is applied to underactuated unstable mechanical multi agent systems from which the efficiency of the tracking controllers is demonstrated

adaptive consensus of multi agents in networks with jointly connected topologies in this paper the consensus problem of multi agent following a leader is studied an adaptive design method is presented for multi agent systems with non identical unknown nonlinear dynamics and for a leader to be followed that is also nonlinear and unknown by parameterizations of unknown nonlinear dynamics of all agents a decentralized adaptive consensus algorithm is proposed in networks with jointly connected topologies by incorporating local consensus errors in addition to relative position feedback analysis of stability and parameter convergence of the proposed algorithm are conducted based on algebraic graph theory and lyapunov theory finally examples are provided to validate the theoretical results

on constructing lyapunov functions for multi agent systems lyapunov equations that depend on communication graph topologies provide building blocks of lyapunov functions which play an important role in controller design and stability analysis of multi agent systems however construction of such a lyapunov equation in some published works has a flaw or requires unnecessarily strong graph conditions this paper presents several choices of lyapunov equations over various graph topologies

distributed adaptive consensus output regulation of network connected heterogeneous unknown linear systems on directed graphs this technical note deals with output regulation of network connected linear systems under directed connection graphs the subsystem dynamics are unknown and heterogeneous the desired output signal generated by a linear exosystem is only available to some subsystems and the others will estimate the exosystem state through the network connections for obtaining regulation errors the exosystem is parametrised in a specific form such that it has a skew symmetric system matrix whose property is further explored in the estimation of exosystem state and in the estimation of the desired feed forward control inputs for output regulation the unknown subsystem parameters are dealt with by the adaptive laws driven by the estimated regulation errors the proposed adaptive control strategy is fully distributed in the sense that the control design only uses the information in the connected neighbourhood without reference to the eigenstructure of the associated laplacian matrix as long as the connection graph is strongly connected

coordination of multi agent systems on interacting physical and communication topologies abstract a new framework is given for coordination of multi agent systems that are interconnected by a physical coupling digraph the edges of this graph represent physical couplings between agents that are fixed due to dynamical interactions on top of the physical graph distributed control protocols are designed where the allowed communications between agents for control purposes are prescribed by a second fixed communication digraph the physical and communication digraphs are generally different and the combination of these two graphs forms a cyber physical system the interactions between physical and communication graphs are the focus of this paper we consider different interactions between two graphs including the case when their pinned laplacian commutes the case of the communication graph with diagonalizable pinned laplacian and the case of two general graphs moreover within each graph the relations between the agents can be either collaborative or antagonistic to capture this the theory of bipartite consensus is used coordination protocols for different cases are designed that are distributed with respect to the communication graph and overcome the detrimental effects of the signed physical graph the proposed control methods are illustrated by simulation examples

distributed robust control of linear multi agent systems with parameter uncertainties this article considers the distributed robust control problems of uncertain linear multi agent systems with undirected communication topologies it is assumed that the agents have identical nominal dynamics while subject to different norm bounded parameter uncertainties leading to weakly heterogeneous multi agent systems distributed controllers are designed for both continuous and discrete time multi agent systems based on the relative states of neighbouring agents and a subset of absolute states of the agents it is shown for both the continuous and discrete time cases that the distributed robust control problems under such controllers in the sense of quadratic stability are equivalent to the h control problems of a set of decoupled linear systems having the same dimensions as a single agent a two step algorithm is presented to construct the distributed controller for the continuous time case which does not involve any conservatism and meanwhile decouples the feedback gain design from the commun

distributed self tuning consensus and synchronization abstract the problem of self tuning of coupling parameters in multi agent systems is considered agent dynamics are described by a discrete time double integrator with unknown input gain each agent locally tunes the strength of interaction with neighboring agents by using a normalized gradient algorithm nga the tuning algorithm minimizes the square of the error between an individual agent s state velocity and the one step delayed average of its own state and the states of its neighbors assuming that the network graph is strongly connected it is proved that the sequence of coupling parameters is convergent and all velocities converge toward the same constant value

deviation bounds in multi agent systems described by undirected graphs the theory of port hamiltonian systems is used to derive upper bounds for the state deviations in multi agent systems described by undirected graphs pinned to a reference signal the upper bounds for the deviations in networks of first or second order agents respectively depend on the minimal eigenvalue of the extended laplacian of the system in networks of first order agents the deviations decay exponentially with a rate depending on the same minimal eigenvalue in case networks of second order systems meet specific design properties it can be shown that the deviations also decay exponentially with half the rate compared to first order systems

designing fully distributed consensus protocols for linear multi agent systems with directed graphs this technical note addresses the distributed consensus protocol design problem for multi agent systems with general linear dynamics and directed communication graphs existing works usually design consensus protocols using the smallest real part of the nonzero eigenvalues of the laplacian matrix associated with the communication graph which however is global information in this technical note based on only the agent dynamics and the relative states of neighboring agents a distributed adaptive consensus protocol is designed to achieve leader follower consensus in the presence of a leader with a zero input for any communication graph containing a directed spanning tree with the leader as the root node the proposed adaptive protocol is independent of any global information of the communication graph and thereby is fully distributed extensions to the case with multiple leaders are further studied

brief paper on the v stability of complex dynamical networks this paper introduces the concept of lyapunov v stability for complex dynamical networks under the new framework each dynamical node is associated with a passivity degree which indicates to what extent an effort is required for stabilizing the node from this approach the network stability problem is converted to measuring the negative definiteness of one simple matrix that characterizes the topology of the network pinning control is then suggested and investigated based on the new v stability formulation as an illustrative example a network with different node dynamics and non uniform coupling strengths is simulated to verify the analytic results moreover a comparison study for three different kinds of networks is provided to further illustrate the novelty and efficacy of the proposed v stability criterion and stabilization scheme

self similar exponential approximants an approach is suggested for defining effective sums of divergent series in the form of self similar exponential approximants the procedure of constructing these approximants from divergent series with arbitrary noninteger powers is developed the basis of this construction is the self similar approximation theory control functions governing the convergence of exponentially renormalized series are defined from stability and fixed point conditions and from additional asymptotic conditions when the latter are available the stability of the calculational procedure is checked by analyzing cascade multipliers a number of physical examples for different statistical systems illustrate the generality and high accuracy of the approach

output synchronization on strongly connected graphs in this technical note we study output synchronization of networked multiagent systems the agents modeled as nonlinear systems with relative degree one exchange information over a network described by an interagent communication graph inspired by the results of igarashi we extend our earlier results on output synchronization to include the case of strongly connected graphs we first demonstrate output synchronization for input output passive systems communicating over strongly connected graphs and include the practical case of constant time delays in communication it is well known byrnes that weakly minimum phase systems with relative degree one are feedback equivalent to a passive system with a positive definite storage function we exploit this feedback equivalence to develop control laws for output synchronization of such systems exchanging outputs on strongly connected graphs and in the presence of communication delays a numerical example is also presented to illustrate the proposed results

distributed adaptive consensus control of lipschitz nonlinear multi agent systems using output feedback abstractthis paper addresses output feedback based distributed adaptive consensus control of multi agent systems having lipschitz nonlinear dynamics distributed dynamic protocols are designed base

pinning control of scale free dynamical networks abstract recently it has been demonstrated that many large complex networks display a scale free feature that is their connectivity distributions have the power law form in the present work control of a scale free dynamical network by applying local feedback injections to a fraction of network nodes is investigated the specifically and randomly pinning schemes are considered the specifically pinning of the most highly connected nodes is shown to require a significantly smaller number of local controllers as compared to the randomly pinning scheme the method is applied to an array of chua s oscillators as an example

distributed containment control for multiple unknown second order nonlinear systems with application to networked lagrangian systems in this paper we consider the distributed containment control problem for multiagent systems with unknown nonlinear dynamics more specifically we focus on multiple second order nonlinear systems and networked lagrangian systems we first study the distributed containment control problem for multiple second order nonlinear systems with multiple dynamic leaders in the presence of unknown nonlinearities and external disturbances under a general directed graph that characterizes the interaction among the leaders and the followers a distributed adaptive control algorithm with an adaptive gain design based on the approximation capability of neural networks is proposed we present a necessary and sufficient condition on the directed graph such that the containment error can be reduced as small as desired as a byproduct the leaderless consensus problem is solved with asymptotical convergence because relative velocity measurements between neighbors are generally more difficult to obtain than relative position measurements we then propose a distributed containment control algorithm without using neighbors velocity information a two step lyapunov based method is used to study the convergence of the closed loop system next we apply the ideas to deal with the containment control problem for networked unknown lagrangian systems under a general directed graph all the proposed algorithms are distributed and can be implemented using only local measurements in the absence of communication finally simulation examples are provided to show the effectiveness of the proposed control algorithms

impulsive observer based consensus control for multi agent systems with time delay the paper deals with the distributed consensus problem of a class of general linear multi agent systems with time delay assuming that the state of the multi agent system cannot be measured and the output of the multi agent system is measured discontinuously a novel impulsive observer is constructed based on the impulsive observer a distributed consensus protocol is proposed for the multi agent system with a directed communication topology in view of the hybrid characteristic of the multi agent system with the impulsive observer a novel type of piecewise lyapunov functional which can overcome the jump phenomena at impulsive times is introduced based on this some sufficient conditions in terms of linear matrix inequalities are presented such that the consensus of the multi agent system can be achieved with an exponential convergence rate a numerical example under two cases is given to show the effectiveness of the theoretical results

adaptive leader following consensus for a class of higher order nonlinear multi agent systems with directed switching networks abstract in this paper we study the leader following consensus problem for a class of uncertain nonlinear multi agent systems under jointly connected directed switching networks the uncertainty includes constant unbounded parameters and external disturbances we first extend the recent result on the adaptive distributed observer from global asymptotical convergence to global exponential convergence then by integrating the conventional adaptive control technique with the adaptive distributed observer we present our solution by a distributed adaptive state feedback control law our result is illustrated by the leader following consensus problem for a group of van der pol oscillators

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

brief paper distributed adaptive control for synchronization of unknown nonlinear networked systems this paper is concerned with synchronization of distributed node dynamics to a prescribed target or control node dynamics a design method is presented for adaptive synchronization controllers for distributed systems having non identical unknown nonlinear dynamics and for a target dynamics to be tracked that is also nonlinear and unknown the development is for strongly connected digraph communication structures a lyapunov technique is presented for designing a robust adaptive synchronization control protocol the proper selection of the lyapunov function is the key to ensuring that the resulting control laws thus found are implementable in a distributed fashion lyapunov functions are defined in terms of a local neighborhood tracking synchronization error and the frobenius norm the resulting protocol consists of a linear protocol and a nonlinear control term with adaptive update law at each node singular value analysis is used it is shown that the singular values of certain key matrices are intimately related to structural properties of the graph

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

prescribed performance distributed consensus control for nonlinear multi agent systems with unknown dead zone input in this paper the problem of prescribed performance distributed output consensus for higher order non affine nonlinear multi agent systems with unknown dead zone input is investigated fuzzy logic

on exponential synchronization of kuramoto oscillators in this technical note we study the problem of exponential synchronization for one of the most popular models of coupled phase oscillators the kuramoto model we consider the special case of finite oscillators with distinct bounded natural frequencies our first result derives a lower bound on the coupling gain which is necessary for the onset of synchronization this bound improves the one derived by jadbabaie we then calculate a lower bound on the coupling gain that is sufficient to guarantee oscillator synchronization and derive further sufficient conditions to ensure exponential synchronization of the angular frequencies of all oscillators to the mean natural frequency of the group we also characterize the coupling gain that is sufficient for the oscillator phase differences to approach any desired compact set in finite time

brief paper global stabilization of complex networks with digraph topologies via a local pinning algorithm this paper concerns the global stability of controlling a complex network with digraph topology to a homogeneous trajectory of the uncoupled system by the local pinning control algorithm the derived stability condition indicates that the smallest real part of eigenvalues of the laplacian sub matrix corresponding to the unpinned vertices can be used to measure the stabilizability of a digraph with a given pinned vertex set a pinned vertex set can stabilize a directed network to some unstable trajectories for instance to a chaotic trajectory of the uncoupled systems if and only if the pinned vertex set can access all other vertices in the digraph furthermore in the bigraph case the analytical estimation of the stabilizability s lower bound suggests that an optimal pinning strategy should take not only the vertex degree but also the shortest path between pairs of vertices into considerations