Consensus Of Second-order Multi-agent Systems Research Articles

Reverse Group Consensus of Second-Order Multi-Agent Systems With Delayed Nonlinear Dynamics in the Cooperation–Competition Networks

This paper studies the reverse group consensus problem for second-order multi-agent systems with delayed nonlinear dynamics and intermittent communication in the cooperation-competition networks. It is assumed that each agent is assumed to share information only with its neighbors on some disconnected time intervals, a new kind of adaptive intermittent control protocol is proposed without in-degree balance condition, the results show the reverse group consensus can be achieved if the mirror graph is connected, and the communication time duration is larger than their corresponding threshold values, respectively. Finally, the two simulation examples are provided to demonstrate the effectiveness of the obtained theoretical results.

Consensus of Second-order Multi-agent Systems with Directed Networks Using Relative Position Measurements Only

This brief paper studies the consensus problem of second-order multi-agent systems when the agents’ velocity measurements are unavailable. Firstly, two simple consensus protocols which do not need velocity measurements of the agents are derived to guarantee that the multi-agent systems achieve consensus in directed networks. Secondly, a key constant which is determined by the complex eigenvalue of the nonsymmetric Laplacian matrix and an explicit expression of the consensus state are respectively developed based on matrix theory. The obtained results show that all the agents can reach consensus if the feedback parameter is bigger than the key constant. Thirdly, the theoretical analysis shows that the followers can track the position and velocity of the leader provided that the leader has a directed path to all other followers and the feedback parameter is bigger enough. Finally, numerical simulations are given to illustrate the effectiveness of the proposed protocols.

Observer-based consensus for second-order multi-agent systems with arbitrary asynchronous and aperiodic sampling periods

A novel distributed consensus protocol, where only sampled position information is exchanged between neighboring agents, is designed for second-order multi-agent systems under a directed communication topology. This protocol allows to reach the consensus for asynchronous and aperiodic sampling periods, which means that every agent can send its measurements independently from its neighbors. Furthermore, the upper bound on the sampling periods can be chosen arbitrarily long by adapting the tuning parameters. This result is obtained by using a continuous–discrete time observer which allows to reconstruct the system state in real time from only discrete-time measurements. The feedback control gain is set according to the observer gain which is itself set according to the maximum sampling period.

Fully distributed consensus of second-order multi-agent systems using adaptive event-based control

Fully distributed consensus of second-order multi-agent systems using adaptive event-based control

Second-Order Consensus for Multiagent Systems via Intermittent Sampled Data Control

In this paper, a periodic intermittent sampled data control strategy, which both reduces the load of updating rate of the controller and cuts down the working time of the controller in each sampling interval, is proposed to investigate the second-order consensus of multiagent systems. In order to reach consensus, a necessary and sufficient condition depending on the coupling gains, the communication width, the sampling period, and the spectrum of the Laplacian matrix, is established. Furthermore, the feasible region of communication width is derived for given coupling gains and structure of network. Besides, the coupling gains are also carefully designed. On the other hand, when the time delay exists in the sampling process, a time delayed protocol is proposed. A necessary and sufficient condition based on the communication width, the sampling period, the coupling gains, the time delay, and the network structure is also derived for achieving consensus. It is amazing found that the sampling period should have both lower and upper bounds for given time delay and communication width for the sake of reaching consensus. Finally, several numerical simulations are presented to demonstrate the effectiveness of the theoretical results.

Finite-Time Consensus for Second-Order Multi-Agent Systems With Input Saturation

In this brief, a new class of finite-time consensus controller is designed for second-order multi-agent systems subject to input saturation. Only a single saturation function is involved in the proposed controller, which distinguishes it from the previous ones. The proposed controllers achieve finite-time consensus using only relative state measurements. Both leaderless and leader-following consensus problems are studied. Comparisons of the proposed controllers with other existing controllers are shown through simulation examples.

Robust Second-Order Consensus Using a Fixed-Time Convergent Sliding Surface in Multiagent Systems.

Faster convergence is always sought in many applications. Designing fixed-time control has recently gained much attention since, for this type of control structure, the convergence time of the states does not depend on initial conditions, unlike other control methods providing faster convergence. This paper proposes a new distributed algorithm for second-order consensus in multiagent systems by using a full-order fixed-time convergent sliding surface. The stability analysis is performed using the Lyapunov function and bi-homogenous property. Moreover, the proposed control is smooth and free from any singularity. The robustness of the proposed scheme is verified both in the presence of Lipschitz disturbances and uncertainties in the network. The proposed method is compared with a state-of-the-art method to show the effectiveness.

Leader-following fixed-time output feedback consensus for second-order multi-agent systems with input saturation

ABSTRACTThis paper investigates the leader-following fixed-time output feedback consensus problem for second-order multi-agent systems with input saturation. By combing fixed-time control technique and bi-limit homogeneous systems theory, a class of bounded fixed-time consensus protocols are developed for leader-following multi-agent systems. The protocol design is divided into two parts. First, when all the state information of the followers are measurable, a state feedback consensus protocol is designed to achieve fixed-time consensus. Then, when the velocity information is unmeasurable, an observer-based fixed-time consensus protocol is proposed. With the help of Lyapunov stability theorem and the property of a homogeneous function, it is theoretically shown that the states of all followers can track that of the leader in fixed-time in the presence of input saturation. Finally, numerical simulation is carried out to illustrate the effectiveness of theoretical results.

Leader-Follower Consensus of Second-Order Multiagent Systems with Absent Velocity Measurement and Time Delay

The leader-follower consensus problem of second-order multiagent systems with both absent velocity measurement and time delay is considered. First of all, the consensus protocol is designed by introducing an auxiliary system to compensate for the unavailability of the velocity information. Then, time delay is incorporated into the consensus protocol and two cases with, respectively, constant time delay and time-varying delay are investigated. For the case of constant time delay, Lyapunov-Razumikhin theorem is deployed to obtain the sufficient conditions that guarantee the stability of the consensus algorithm. For the case of time-varying delay, the sufficient conditions are also derived by resorting to the Lyapunov-Razumkhin theorem and linear matrix inequalities (LMIs). Various numerical simulations demonstrate the correctness of the theoretical results.

The group-delay consensus for second-order multi-agent systems by piecewise adaptive pinning control in part of time interval

This paper addresses the group-delay consensus of second-order nonlinear multi-agent systems by piecewise adaptive pinning control in part of time interval. The topology of the networked system is assumed to be directed and weakly connected. The agents in each group can be classified into three subsets, which are inter-act agent, intra-act agent with zero in-degree and the other agents. According to the agents’ property and intrinsic dynamics, the protocol is designed to guarantee that agents in the same group reach consensus, and the agents in different groups reach group-delay consensus. By using Lyapunov stability theory, graph theory and matrix theory, some consensus criteria are derived in the form of matrix inequalities. At last, a numerical simulation is also given to verify the correctness of theoretical analysis.

Guaranteed cost consensus for second-order multi-agent systems with heterogeneous inertias

In this paper, the guaranteed cost consensus problem for second-order multi-agent systems with directed topology is considered, in which each agent has a heterogeneous inertia and control gain. The distributed control protocols with the absolute and relative velocity dampings are proposed, respectively. In each kind of protocol, both the communications with and without the input time delay are also considered. By introducing the auxiliary variables and using Lyapunov stability theory, some sufficient conditions are given to achieve the consensus. Moreover, the upper bounds of the guaranteed cost functions are obtained. Finally, some simulation examples are presented to show the effectiveness of the proposed approaches.

Distributed rotating consensus of second-order multi-agent systems with nonuniform delays

In this paper, we study a distributed rotating consensus problem of second-order multi-agent systems with nonuniform delays. A distributed algorithm is adopted to drive all agents to reach consensus while moving around a common point. Based on a frequency domain approach, an upper bound on the maximum delay is given for the consensus stability of the system. Finally, a numerical simulation result is included to illustrate the obtained results.

Second-order consensus of multi-agent systems with noises via intermittent control

ABSTRACTSecond-order consensus of multi-agent systems with noises via intermittent control is investigated in this paper. First, we study the mean-square consensus problem with communication noises by intermittent control. In order to reach consensus, under the strong directed interacted topology, by using the tools of graph theory and Lyapunov method, a distributed control protocol is proposed based on the noises and periodical intermittent information. The upper bound of noise strength in the sense of matrix norm and the lower bound of communication time duration are obtained. Second, a class of coupled system models which include delay-terms in their nonlinearities in the noisy environment is discussed. Under the balanced strongly connected topology, the sufficient conditions to achieve the mean-square average-consensus are obtained. Finally, simulations are given to illustrate the effectiveness of our results.

Distributed Consensus of Second-Order Multiagent Systems With Nonconvex Velocity and Control Input Constraints

This paper is devoted to a distributed consensus problem for second-order multiagent systems with nonconvex velocity and control input constraints. A distributed control algorithm is introduced using local information. It is shown that consensus can be achieved as long as the union of the communication graphs has directed spanning trees among each time interval of certain bounded length in the presence of arbitrarily bounded communication delays. Finally, a numerical example is included to illustrate the theoretical results.

Asynchronous sampling-based leader-following consensus in second-order multi-agent systems

Asynchronous sampling-based leader-following consensus in second-order multi-agent systems

Fixed-Time Leader-Follower Output Feedback Consensus for Second-Order Multiagent Systems.

This paper addresses the fixed-time leader-follower consensus problem for second-order multiagent systems without velocity measurement. A new continuous fixed-time distributed observer-based consensus protocol is developed to achieve consensus in a bounded finite time fully independent of initial condition. A rigorous stability proof of the multiagent systems by output feedback control is presented based on the bi-limit homogeneity and the Lyapunov technique. Finally, the efficiency of the proposed methodology is illustrated by numerical simulation.

Second-order consensus of discrete-time multi-agent systems in directed networks with nonlinear dynamics via impulsive protocols

Abstract In this paper, we discuss the second-order consensus problem of discrete-time multi-agent systems with fixed and switching topology. Impulsive protocols are introduced for such multi-agent systems with nonlinear dynamics. The consensus problem of multi-agent systems is analyzed by algebraic graph theory and matrix theory, where a connection of impulsive control methods and network topologies is established. Our main results indicate that the second-order consensus of multi-agent systems can be achieved if the graphs of the topology are balanced and strongly connected under suitable conditions. Numerical simulations are presented to support the theoretical results.

Quantized consensus in second-order multi-agent systems via event-trigger control with sampled data

This paper addresses the quantized consensus problem of second-order multi-agent systems (MASs) where the topology has a directed spanning tree. An event-trigger control protocol (ETCP) is proposed by designing a combined threshold. The combined threshold not only reduces more event triggers than the state-dependent threshold, but also is more practical than the time-dependent threshold. For further reducing computation resources and transmission cost, the sampled data, self-trigger scheme and data quantization are employed together. Under the proposed ETCP, the sufficient condition is derived to guarantee the quantized consensus of second-order MASs. Finally, the comparison experiments are conducted to demonstrate the superiority of ETCP based on the combined threshold.

Distributed Finite Time Consensus of Secondorder Multi-agent Systems via Pinning Control (August 2018).

The robust distributed finite time consensus of second-order multi-agent systems via pinning control has been investigated in this paper. A new nonsingular finite time TSM control method is proposed for second-order single system with disturbances. Based on the pinning error function vector, robust distributed finite time consensus of second-order multi-agent systems via pinning control method is given. Simulations results are performed to validate the effectiveness of the theoretical results.

Bipartite Consensus for Second-Order Multi-Agent Systems over Nonidentical Signed Graphs

In this paper, second-order multi-agent systems are considered with nonidentical topologies that are described by different signed graphs. Sign-consistency of signed graph pairs is defined and a frequency-domain approach is proposed to analyse the convergence of multi-agent systems. It is shown that given the sign-consistency of nonidentical signed graphs and the connectivity of their union, the multi-agent systems will reach bipartite consensus (respectively, stability) if and only if the union is structurally balanced (respectively, unbalanced). Simulation examples are involved to demonstrate the validity of the obtained results.