Consensus of multiple double‐integrator agents with intermittent measurement

This paper is concerned with consensus problems in directed networks of multiple agents with double‐integrator dynamics. It is assumed that each agent adjusts its state based on the information of its states relative to its neighbors at discrete times and the interaction topology among agents is time‐varying. Both synchronous and asynchronous cases are considered. The synchrony means that each agent's update times, at which it obtains new control signals, are the same as the others', and the asynchrony implies that each agent's update times are independent of the others'. In the synchronous case, the consensus problem is proved to be equivalent to the asymptotic stability problem of a discrete‐time switched system. By analyzing the asymptotic stability of the discrete‐time switched system, it is shown that consensus can be reached if the update time intervals are small sufficiently, and an allowable upper bound of update time intervals is obtained. In the asynchronous case, the consensus problem is transformed into the global asymptotic stability problem of a continuous‐time switched system with time‐varying delays. In virtue of a linear matrix inequality method, it is proved that consensus can be reached if the delays are small enough, and an admissible upper bound of delays is derived. Simulations are provided to illustrate the effectiveness of the theoretical results. Copyright © 2009 John Wiley & Sons, Ltd.     

Group consensus control for double‐integrator dynamic multiagent systems with fixed communication topology

The problem of group consensus is investigated in this paper, where all agents possess double‐integrator dynamics. Two different kinds of consensus protocols are proposed for networks with fixed communication topology to reach group consensus for the agents’ positions and velocities. Convergence analysis is discussed, and necessary and/or sufficient conditions are presented for multiagent systems to achieve group consensus. The first protocol leads to dynamic consensus where positions of all agents reach time‐varying consensus values. By applying the second protocol, both the agents’ positions and their velocities reach constant consensus values. That is, static consensus is achieved. Simulation examples are given to show the effectiveness of the theoretical results.Copyright © 2012 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 for multi‐agent systems under double integrator dynamics with time‐varying communication delays

In this paper, the consensus control problems for multi‐agent systems under double integrator dynamics with time‐varying communication delays are investigated. We assume that the interaction graphs among agents are directed. Two kinds of protocols are considered. One is an absolute damping protocol, and the other is a relative damping protocol. For the first protocol, Lyapunov–Razumikhin functional techniques are used. We derive sufficient conditions that guarantee that all agents asymptotically reach consensus under fixed topology and switching topology, respectively. Moreover, the allowable upper bound for communication delays is given. For the second protocol, Lyapunov–Krasovskii functional techniques are used. Linear matrix inequality (LMI)‐form sufficient conditions are obtained to guarantee the consensus problems to be solved under fixed topology and switching topology, respectively. The allowable upper bound for communication delays is given as well. The feasibilities of the demanded LMIs are also discussed. Finally, numerical simulations are provided to illustrate the effectiveness of our theoretical results. Copyright © 2011 John Wiley & Sons, Ltd.     

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.     

Leaderless and leader‐following fixed‐time consensus for multiagent systems via impulsive control

This article addresses the leaderless fixed‐time consensus (LLFTC) and leader‐following fixed‐time consensus (LFFTC) problems for multiagent systems (MASs) via impulsive control. First, a novel fixed‐time stability for impulsive dynamical system is developed. Then the novel fixed‐time impulsive control protocols are designed to achieve leaderless and leader‐following consensus for MASs. Based on the impulsive control theory, fixed‐time stability theory and algebraic graph theory, some sufficient conditions are derived for each agent to achieve LLFTC and LFFTC under the proposed control protocols. Finally, numerical simulations are put forward to validate the theoretical results.     

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.     

Observer‐based leader‐following consensus of uncertain nonlinear multi‐agent systems

In this paper, the leader‐following consensus problem of uncertain high‐order nonlinear multi‐agent systems on directed graph with a fixed topology is studied, where it is assumed that the relative states of a follower and its neighbors are immeasurable and only the relative outputs are available. Nonlinear adaptive observers are firstly proposed for each follower to estimate the states of it and its neighbors, and an observer‐based distributed adaptive control scheme is constructed to guarantee that all followers asymptotically synchronize to a leader with tracking errors being semi‐globally uniform ultimate bounded. On the basis of algebraic graph theory and Lyapunov theory, the closed‐loop system stability analysis is conducted. Finally, numerical simulations are presented to illustrate the effectiveness and potential of the proposed new design techniques. Copyright © 2017 John Wiley & Sons, Ltd.     

On the general consensus protocol in multi‐agent networks with second‐order dynamics and sampled data

This paper considers the problem of the convergence of the consensus for multiple agents in a directed network. A general distributed consensus protocol is designed, the advantage of this protocol is that almost all the existing linear local interaction consensus protocols can be considered as special cases of the present paper. Necessary and sufficient conditions are established for reaching consensus of the system by choosing the appropriate sampling period, the control parameters and the spectra of the Laplacian matrix. It is found that second‐order consensus cannot be reached for a sufficiently large sampling period while it can be reached for a sufficiently small one. Furthermore, the coupling gains can be carefully designed under the given network structure and the sampling period. Finally, a simulation example is given to verify and illustrate the theoretical analysis.     

Robust consensus tracking of double‐integrator dynamics by bounded distributed control

This paper studies the robust consensus tracking problem of multiple second‐order systems with additive disturbances and a direct communication topology. We design a continuous, bounded and distributed controller that is composed of a tracker and an uncertainty and disturbance estimator. The tracker makes the nominal closed‐loop system globally asymptotically stable, while the output of uncertainty and disturbance estimator attenuates the effect of disturbances. We show that if the disturbances converge to constants, the tracking error converges asymptotically to zero, whereas for other types of disturbances, the obtained error system is small‐signal L_∞ stable. Some inequalities are developed to show the relationship between the ultimate bounds of tracking errors and the design parameters. Finally, simulation results for four cases are presented to demonstrate the performance of the controller. Copyright © 2015 John Wiley & Sons, Ltd.     

Output‐feedback adaptive consensus tracking control for a class of high‐order nonlinear multi‐agent systems

In this paper, an output‐feedback adaptive consensus tracking control scheme is proposed for a class of high‐order nonlinear multi‐agent systems. The agents are allowed to have unknown parameters, unknown nonlinearities, and input quantization simultaneously. The desired trajectory to be tracked is available for only a subset of agents, and only the relative outputs and the quantized inputs need to be measured or transmitted as signal exchange among neighbors regardless of the system order. By introducing a kind of high‐gain K‐filters and a smooth function, the effect among agents caused by the unknown nonlinearities is successfully counteracted, and all closed‐loop signals are proved to be globally uniformly bounded. Moreover, it is shown that the tracking errors converge to a residual set that can be made arbitrarily small. Simulation results on robot manipulators are presented to illustrate the effectiveness of the proposed scheme. Copyright © 2017 John Wiley & Sons, Ltd.     

Event‐triggered distributed constrained consensus

We consider a distributed consensus problem for continuous‐time multi‐agent systems with set constraints on the final states. To save communication costs, an event‐triggered communication‐based protocol is proposed. By comparing its own instantaneous state with the one previously broadcasted to neighbours, each agent determines the next communication time. Based on this event‐triggered communication, each agent is not required to continuously monitor its neighbours' state and the communication only happens at discrete time instants. We show that, under some mild conditions, the constrained consensus of the multi‐agent system with the proposed protocol can be achieved with an exponential convergence rate. A lower bound of the transmission time intervals is provided that can be adjusted by choosing different values of parameters. Numerical examples illustrate the results. Copyright © 2016 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.     

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.     

Necessary and sufficient conditions for bounded distributed mean square tracking of multi‐agent systems with noises

This paper is concerned with the distributed control problem of second‐order agents under directed network topology. The control input of each agent only depends on its own state and the states of its neighbors corrupted by white noises. By using the algebraic graph theory and stochastic analysis method, necessary and sufficient conditions are presented for mean square bounded tracking. Finally, several simulation examples are given to illustrate the results. Copyright © 2015 John Wiley & Sons, Ltd.     

Consensus of heterogeneous first‐ and second‐order multi‐agent systems with directed communication topologies

In this paper, we consider the consensus problem for heterogeneous multi‐agent systems composed of some first‐order and some second‐order dynamic agents in directed communication graphs. Consensus protocols are proposed for the second‐ and first‐order dynamic agents, respectively. Under certain assumptions on the control parameters, for fixed communication topologies, necessary and sufficient conditions for consensus are given, and the consensus values of all agents are established. For switching topologies, sufficient conditions are given for all agents to reach consensus. Finally, simulation examples are presented to demonstrate the effectiveness of the proposed methods. Copyright © 2013 John Wiley & Sons, Ltd.     

Multi‐surface sliding control for fast finite‐time leader–follower consensus with high order SISO uncertain nonlinear agents

In this paper, multi surface sliding cooperative control scheme is presented and new multiple sliding surfaces are proposed. It is proven that, for the setup that each agent is described by a chain of integrators, where the last integrator is perturbed by a bounded disturbance, leader–follower consensus can be achieved on these sliding surfaces if the communication graph has a directed spanning tree. Also, sliding variables can be driven to the sliding surfaces in fast finite time by the nonsmooth control law. The fast finite‐time Lyapunov stability theorem, the terminal sliding control technique, and the adding a power integrator design approach are used in our proposed control. Simulation results demonstrate the effectiveness of the proposed scheme. Copyright © 2013 John Wiley & Sons, Ltd.     

Fixed‐time output‐feedback consensus tracking control for second‐order multiagent systems

This paper is concerned with the problem of fixed‐time consensus tracking control for a class of second‐order multiagent systems under an undirected communication graph. A distributed output‐feedback fixed‐time consensus tracking control scheme is proposed to make the states of all individual agents simultaneously track a time‐varying reference state even when the reference state is available only to a subset of the group members and only output measurements are available for feedback. Homogeneous Lyapunov function and homogeneity property are employed to show that the control scheme can guarantee the consensus tracking errors converging the origin in finite time which is bounded by a fixed constant independent of initial conditions. Numerical simulations are carried out to demonstrate the effectiveness of the proposed control law.     

Consensus Control in Linear Multi‐Agent Systems with Current and Sampled Partial Relative States

This paper studies consensus in linear multi‐agent systems with current and sampled partial relative states. A distributed linear consensus protocol is designed, where both current and sampled relative states are utilized. A necessary and sufficient condition for consensus in this setting is established. The notion of the consensus region is then introduced and analyzed for third‐order systems, provided that each agent can only know its relative positions and velocities. It is shown that the consensus regions are stable to control gains and sampling period. Additionally, how to choose the control gains and the sampling period is given for consensus in third‐order systems. Finally, an example is given to verify and illustrate the analysis.     

Two fault‐tolerant control problems for multiple‐integrator networks

The paper considers a network of agents with multiple‐integrator internal dynamics, which share partial information on their states according to an arbitrary topology. For this system, two control problems are addressed and solved. The first consists in assigning the dominant closed‐loop poles. The second consists in achieving a specified consensus with arbitrary dominant dynamics. In both cases, the regulator is required to be decentralized, and the controlled network has to result tolerant with respect to faults in the communication apparatuses of the agents. Copyright © 2015 John Wiley & Sons, Ltd.