Second‐order consensus for directed multi‐agent systems with sampled data

This paper deals with the consensus problem of second‐order multi‐agent systems with sampled data. Because of the unavailable velocity information, consensus problem is studied only by using the sampled position information. The final consensus states of multi‐agent system are given. And a necessary and sufficient consensus condition is provided, which depends on the parameters of sampling interval, eigenvalues of Laplacian matrix, and coupling strengths. Then, the case that both the sampled position and velocity information can be obtained is discussed. On the basis of introducing a time‐varying piecewise‐continuous delay and proposing a novel time‐dependent Lyapunov functional, the sufficient consensus condition is presented, and the upper bound of sampling interval can be estimated. Simulation examples are provided finally to demonstrate the effectiveness of the proposed design methods. Copyright © 2013 John Wiley & Sons, Ltd.     

Observer‐based consensus of second‐order multi‐agent system with fixed and stochastically switching topology via sampled data

This paper addresses the distributed observer‐based consensus problem of second‐order multi‐agent systems via sampled data. Firstly, for the case of fixed topology, a velocity‐independent distributed control law is proposed by designing a distributed observer to estimate the unavailable velocity, then a sufficient and necessary condition of consensus on design parameters and sampling period is obtained by using the matrix analysis method. Secondly, for the case of stochastically switching topology, a sufficient and necessary condition of mean square consensus is also proposed and proven, and an algorithm is provided to design the parameters in the consensus protocol. Two simulation examples are given to illustrate the effectiveness of the proposed consensus algorithms. Copyright © 2012 John Wiley & Sons, Ltd.     

Consensus analysis for leader‐following multi‐agent systems with second‐order individual dynamics and arbitrary sampling

This paper performs a consensus analysis of leader‐following multi‐agent systems with multiple double integrators in the framework of sampled‐data control. Both single‐leader and multiple‐leader scenarios are considered under the assumption of networks with detectable position‐like state information. The coordination tasks are accomplished by a given protocol with the robustness against the change of sampling periods. The sampling periods can be chosen to be of an arbitrary fixed length or large time‐varying length. Under the proposed protocol, we achieve two objectives: (i) in the single leader‐subgroup case, all followers reach an agreement with leaders on states asymptotically and (ii) in the multiple leader‐subgroup case, each follower converges to some convex combination of the final states of all leaders. It is shown that the final state configuration of the convex combination is uniquely determined by the underlying interaction topology, which can be any weakly connected graph. Compared with the existing results on leader‐following networks, the consensus problem and the containment problem are solved in a unified framework with large sampling periods. Some numerical experiments are conducted to illustrate the dynamic behavior of all agents with this protocol. Copyright © 2017 John Wiley & Sons, Ltd.     

r‐consensus control for higher‐order multi‐agent systems with digraph

This paper studies a consensus problem for lth (l ≥ 2) order multi‐agent systems with digraph, namely, for a fixed r (0 ≤ r ≤ l ? 1), the rth derivative of the states x_i of agents are convergent to a constant value and, for every k (0 ≤ k ≤ l ? 1), are convergent to zeros. A new concept of r‐consensus is introduced and new consensus protocols are proposed for solving such an r‐consensus problem. A sufficient and necessary condition for r‐consensus is obtained. As special cases, criteria for third‐order systems are given, in which the exact relationship between feedback gains is established. Finally, an illustrative example is given to demonstrate the effectiveness of these protocols.     

A novel consensus algorithm for second‐order multi‐agent systems without velocity measurements

In this paper, a novel consensus protocol for second‐order multi‐agent systems is elegantly designed, and it relaxes the common requirement of the velocity information of the agents. An interesting consensus criterion is explicitly derived in terms of the proposed cooperation law provided that the dynamical equation for each agent is linear. As an extension, the proposed cooperation rule is further extended to a general scenario, where the coupling weights characterizing the relationships among the neighboring agents are time‐varying. Accordingly, two distributed cooperative algorithms (node/edge‐based scheme) are explicitly designed. Moreover, we study the case of network with switching communication setting. It shows that edge‐based law is capable with the time‐varying topology, while the node‐based scheme is not. In addition, the proposed coordination strategies are applied to the tracking problem as well. Finally, these obtained consensus results are well supported in the light of the pendulum models. Copyright © 2016 John Wiley & Sons, Ltd.     

Bounded consensus tracking for sampled‐data second‐order multi‐agent systems with fixed and Markovian switching topology

This paper studies the bounded consensus tracking problems of second‐order multi‐agent systems with fixed and Markovian switching topology in a sampling setting. It is assumed that all the agents can only obtain the approximative value of the leader's acceleration instead of the actual value. Moreover, only a portion of agents can have the access to the leader and obtain the leader's position and velocity directly. By virtue of matrix analysis and perturbation theory, we present necessary and sufficient conditions for boundedness of tracking error system and show the ultimate bound of tracking errors under fixed and Markovian switching topology, respectively. Finally, a simulation example is given to illustrate the effectiveness of the results. Copyright © 2013 John Wiley & Sons, Ltd.     

Consensus of second‐order multi‐agent systems with exogenous disturbances

In this paper, the consensus of second‐order multi‐agent dynamical systems with exogenous disturbances is studied. A pinning control strategy is designed for a part of agents of the multi‐agent systems without disturbances, and this pinning control can bring multiple agents' states to reaching an expected consensus track. Under the influence of the disturbances, disturbance observers‐based control (DOBC) is developed for disturbances generated by an exogenous system to estimate the disturbances. Asymptotical consensus of the multi‐agent systems with disturbances under the composite controller can be achieved for fixed and switching topologies. Finally, by applying an example of multi‐agent systems with switching topologies and exogenous disturbances, the consensus of multi‐agent systems is reached under the DOBC with the designed parameters. Copyright © 2010 John Wiley & Sons, Ltd.     

Consensus in second‐order Markovian jump multi‐agent systems via impulsive control using sampled information with heterogenous delays

This paper investigates the consensus problem of second‐order Markovian jump multi‐agent systems with delays. Both network‐induced random delay and node‐induced state delay are considered, where the network‐induced random delay, subjected to a Markov chain, exists in the switching signal and the node‐induced state delay, related to switching topologies, is heterogeneous between any two linked agents. In order to reduce communication and control energy, an impulsive protocol is proposed, where each agent only can get delayed relative positions to neighbors and the velocity of itself at impulsive instants. By performing three steps of model transformation and introducing a mapping for two independent Markov chains, the consensus problem of the original continuous‐time system is equivalent to the stability problem of a discrete‐time expand error system with two Markovian jumping parameters and a necessary and sufficient criterion is derived. A numerical example is given to illustrate the effectiveness of the theoretical result.@@@@This work is supported by the National Natural Science Foundation of China under Grants 61374171, 61572210, and 51537003, the Fundamental Research Funds for the Central Universities (2015TS030), and the Program for Changjiang Scholars and Innovative Research Team in University (IRT1245).     

Distributed model predictive control for consensus of nonlinear second‐order multi‐agent systems

This paper proposes a distributed model predictive control algorithm for the consensus of nonlinear second‐order multi‐agent systems. At each update time, all the agents are permitted to optimize. A positively invariant terminal region and a corresponding auxiliary controller are developed for each agent. Furthermore, time‐varying compatibility constraint is presented to denote a degree of consistency between the assumed trajectories and the actual trajectories of each agent. Given the designed terminal ingredients (terminal region, auxiliary controller, and terminal cost) and compatibility constraints, the recursive feasibility and closed‐loop stability of the whole system are guaranteed. The simulation results are given to illustrate the effectiveness of the proposed approach. Copyright © 2016 John Wiley & Sons, Ltd.     

Consensus strategy for a class of multi‐agents with discrete second‐order dynamics

This paper investigates consensus strategies for a group of agents with discrete second‐order dynamics under directed communication topology. Consensus analysis for both the fixed topology and time‐varying topology cases is systematically performed by employing a novel graph theoretic methodology as well as the classical nonnegative matrix theory. Furthermore, it is shown that the necessary and sufficient condition for the agents under fixed communication topology to reach consensus is that the communication topology has a spanning tree; and sufficient conditions for the agents to reach consensus when allowing for the dynamically changing communication topologies are also given. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed results. Copyright © 2011 John Wiley & Sons, Ltd.     

Semi‐global and global containment control of multi‐agent systems with second‐order dynamics and input saturation

This paper considers both semi‐global and global containment control for a second‐order multi‐agent system that is composed by a network of identical harmonic oscillators or double integrators with multiple leaders and input saturation. A distributed low gain feedback algorithm is proposed to solve the semi‐global containment control problem for the network whose topology is directed and initial condition is taken from any a priori given bounded set. In particular, by using a parametric Lyapunov equation approach, M‐matrix properties and algebraic graph theory, an upper bound of the low gain parameter is estimated such that the low gain feedback matrix can be analytically determined without involving numerical computation. Furthermore, under the assumption that the induced subgraph formed by the followers is strongly connected and detail balanced, two linear feedback protocols are designed for coupled harmonic oscillators and coupled double integrators, respectively, to asymptotically achieve the global containment control of the network with any initial condition. Finally, numerical examples are given to illustrate the effectiveness of the theoretical results. Copyright © 2016 John Wiley & Sons, Ltd.     

Distributed consensus and tracking control of second‐order time‐varying nonlinear multi‐agent systems

In this paper, the distributed consensus and tracking protocols are developed for the second‐order time‐varying nonlinear multi‐agent systems under general directed graph. Firstly, the consensus and tracking problems can be converted into a conventional stabilization control problem. Then a state transformation is employed to deal with the time‐varying nonlinearities. By choosing an appropriate time‐varying parameter and coupling strengths, exponential consensus and tracking of second‐order nonlinear multi‐agent systems can be achieved. Finally, a simulation is given to illustrate the effectiveness of the proposed consensus and tracking protocols. Copyright © 2017 John Wiley & Sons, Ltd.     

Further results on finite‐time consensus of second‐order multi‐agent systems without velocity measurements

This paper investigates the problem of finite‐time consensus (FTC) for second‐order nonlinear multi‐agent systems when the velocity information is unavailable. Based on the global finite‐time stability theory and homogeneity with dilation, a class of novel finite‐time consensus protocols are proposed for the multi‐agent systems. The protocol design is divided into two parts. First, when all the state information of the agents are measurable, a new continuous state feedback is designed to achieve FTC. Then, when the velocity information is unmeasurable, two finite‐time convergent discontinuous observers are presented to estimate the velocities of the followers and the leader, respectively, which further ensure the final FTC for the multi‐agent systems. Finally, one example is given to demonstrate the efficiency of the proposed method. Copyright © 2015 John Wiley & Sons, Ltd.     

Consensus of multi‐agent systems with nonlinear dynamics and sampled‐data information: a delayed‐input approach

This paper is concerned with the problem of consensus in directed networks of multiple agents with intrinsic nonlinear dynamics and sampled‐data information. A new protocol is induced from a class of continuous‐time linear consensus protocols by implementing data‐sampling technique and a zero‐order hold circuit. On the basis of a delayed‐input approach, the sampled‐data multi‐agent system is converted to an equivalent nonlinear system with a time‐varying delay. Theoretical analysis on this time‐delayed system shows that consensus with asymptotic time‐varying velocities in a strongly connected network can be achieved over some suitable sampled‐data intervals. A multi‐step procedure is further presented to estimate the upper bound of the maximal allowable sampling intervals. The results are then extended to a network topology with a directed spanning tree. For the case of the topology without a directed spanning tree, it is shown that the new protocol can still guarantee the system to achieve consensus by appropriately informing a fraction of agents. Finally, some numerical simulations are presented to demonstrate the effectiveness of the theoretical results and the dependence of the upper bound of maximal allowable sampling interval on the coupling strength. Copyright © 2012 John Wiley & Sons, Ltd.     

Consensus of data‐sampled multi‐agent systems with Markovian switching topologies

This paper studies the consensus problem of data‐sampled multi‐agent systems with Markovian switching topologies. Two different consensus algorithms are considered. By a system transformation, the mean‐square consensus problem of multi‐agent systems is converted into the mean‐square stability problem of Markov jump systems. Necessary and sufficient conditions of mean‐square consensus are obtained. The cone complementary linearization algorithm is used to get the allowable control gain. Simulation examples are given to show the effectiveness of the results. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Distributed consensus of multi‐agent systems with general linear node dynamics and intermittent communications

Without assuming that the mobile agents can communicate with their neighbors all the time, the consensus problem of multi‐agent systems with general linear node dynamics and a fixed directed topology is investigated. To achieve consensus, a new class of distributed protocols designed based only on the intermittent relative information are presented. By using tools from matrix analysis and switching systems theory, it is theoretically shown that the consensus in multi‐agent systems with a periodic intermittent communication and directed topology containing a spanning tree can be cast into the stability of a set of low‐dimensional switching systems. It is proved that there exists a protocol guaranteeing consensus if each agent is stabilizable and the communication rate is larger than a threshold value. Furthermore, a multi‐step intermittent consensus protocol design procedure is provided. The consensus algorithm is then extended to solve the formation control problem of linear multi‐agent systems with intermittent communication constraints as well as the consensus tracking problem with switching directed topologies. Finally, some numerical simulations are provided to verify the effectiveness of the theoretical results. Copyright © 2013 John Wiley & Sons, Ltd.     

Consensus in multi‐agent systems with communication constraints

The problem of second‐order consensus is investigated in this paper for a class of multi‐agent systems with a fixed directed topology and communication constraints where each agent is assumed to share information only with its neighbors on some disconnected time intervals. A novel consensus protocol designed based on synchronous intermittent local information feedback is proposed to coordinate the states of agents to converge to second‐order consensus under a fixed strongly connected topology, which is then extended to the case where the communication topology contains a directed spanning tree. By using tools from algebraic graph theory and Lyapunov control approach, it is proved that second‐order consensus can be reached if the general algebraic connectivity of the communication topology is larger than a threshold value and the mobile agents communicate with their neighbors frequently enough as the network evolves. Finally, a numerical example is simulated to verify the theoretical analysis. Copyright © 2011 John Wiley & Sons, Ltd.     

Robust consensus tracking for a class of heterogeneous second‐order nonlinear multi‐agent systems

This paper deals with the robust consensus tracking problem for a class of heterogeneous second‐order nonlinear multi‐agent systems with bounded external disturbances. First, a distributed adaptive control law is proposed based on the relative position and velocity information. It is shown that for any connected undirected communication graph, the proposed control law solves the robust consensus tracking problem. Then, by introducing a novel distributed observer and employing backstepping design techniques, a distributed adaptive control law is constructed based only on the relative position information. Compared with the existing results, the proposed adaptive consensus protocols are in a distributed fashion, and the nonlinear functions are not required to satisfy any globally Lipschitz or Lipschitz‐like condition. Numerical examples are given to verify our proposed protocols. Copyright © 2014 John Wiley & Sons, Ltd.     

Adaptive robust consensus tracking for nonlinear second‐order multi‐agent systems with heterogeneous uncertainties

This paper addresses the consensus tracking problem for a class of heterogeneous nonlinear second‐order multi‐agent systems with parametric uncertainties, unmodeled dynamics, and bounded external disturbances. By linearly parameterizing the control input of the leader, two distributed adaptive robust consensus tracking control protocols with dynamic and fixed coupling gains are constructed based on the relative information from neighboring agents. The global tracking errors are shown to be guaranteed to exponentially converge to a ball with a constant radius at a prescribed rate of convergence under external disturbances. Finally, a numerical example is provided to verify the theoretical results. Copyright © 2017 John Wiley & Sons, Ltd.     

Finite time agreement protocol design of multi‐agent systems with communication delays

In this paper, the finite‐time agreement problem of continuous‐time multi‐agent systems with communication delays is considered. First, the multi‐agent system researched in the paper is described. Second, some notations and lemmas used in the paper are given. Then, agreement protocols for continuous (but non‐smooth) multi‐agent systems are proposed, which ensure that the states of agents reach agreement in finite time. The stability analysis and simulations are presented to show the effectiveness of the method. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society