Consensus Of Second-order Multi-agent Systems Research Articles

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.

Fixed-Time Leader-Following Consensus for Second-Order Multiagent Systems With Input Delay

This paper studies fixed-time leader-following lag consensus problem of second-order multiagent systems with input delay. Using fixed-time distributed observer, we obtain the leader's states for each followers. An extension of the Artstein's reducing transformation is employed to transform the delayed error system into a second-order system without time delay and a novel nonsingular terminal sliding mode protocol is proposed to achieve fixed-time consensus. The presented sliding mode controller can avoid singularity, eliminate chattering, and achieve exact convergence. It is mathematically proved that the presented protocol can achieve exact fixed-time leader-following lag consensus. Moreover, the upper bound of convergence time only depends on observer parameters, controller parameters, network parameters, and delay time, which makes it possible to determine the convergence time offline regardless of initial condition. The presented protocol is applied to coordinated lag tracking control of single-link robotic manipulators and the results validate the effectiveness of the proposed fixed-time protocol.

Asynchronous consensus of second-order multi-agent systems with impulsive control and measurement time-delays

Abstract This paper investigates the asynchronous consensus of second-order multi-agent systems with directed networks and measurement time-delays via impulsive control. It is assumed that each agent receives the measurements of the information from its neighboring agents and itself according to its own sampling clock, and different agents can have independent sampling times. The controller of agent is designed in impulsive framework and changes agent’s state instantaneously. By transforming the consensus problem into static consensus and using common Lyapunov function, it is proved that there exist protocol parameters ensuring consensus. Also, the design of the parameters is given in a specific form. Finally, simulation examples are drawn to illustrate the effectiveness of the theoretical results.

Stochastic bounded consensus of second-order multi-agent systems in noisy environment**Project supported by the National Natural Science Foundation of China (Grant Nos. 61573156, 61273126, 61503142, 61272382, and 61573154) and the Fundamental Research Funds for the Central Universities (Grant No. x2zdD2153620).

This paper investigates the stochastic bounded consensus of leader-following second-order multi-agent systems in a noisy environment. It is assumed that each agent received the information of its neighbors corrupted by noises and time delays. Based on the graph theory, stochastic tools, and the Lyapunov function method, we derive the sufficient conditions under which the systems would reach stochastic bounded consensus in mean square with the protocol we designed. Finally, a numerical simulation is illustrated to check the effectiveness of the proposed algorithms.

Consensus analysis for multi-agent systems via periodic event-triggered algorithms with quantized information

In this article, a novel distributed event-triggered control protocol for the consensus of second-order multi-agent systems with undirected topology is studied. Based on the proposed control protocol, the event-triggered condition is evaluated only at every sampling instant. The control input for each agent will be updated with local information if and only if its condition is violated. Both ideal and quantized relative state measurements are considered under this framework. Some sufficient conditions for achieving consensus are derived using spectral properties of edge Laplacian matrix and the discrete-time Lyapunov function method. Finally, numerical examples are given to demonstrate the effectiveness of our theoretical results.

Event-based consensus for second-order multi-agent systems with actuator saturation under fixed and Markovian switching topologies

This paper studies the event-based consensus problem of second-order multi-agent systems with actuator saturation under fixed topology and Markovian switching topologies. By a model transformation, the consensus problem is first converted into the stability problem of the error system. Using discontinuous Lyapunov functional approach, two sufficient conditions on the consensus are derived for second-order multi-agent systems with fixed topology and Markovian switching topologies, respectively. The discontinuous Lyapunov functions take full account of the characteristics of the sawtooth delay, and thus lead to a less conservative consensus criterion. It is shown that the consensus condition depends on the parameters of sampling period, Laplacian matrix, and event-triggered parameter. In addition, this paper provides an effective method to co-design both the consensus controller and the event-triggered parameter. Finally, two numerical examples are provided to illustrate the effectiveness and feasibility of the proposed algorithm.

Event-Triggered Communication for Leader-Following Consensus of Second-Order Multiagent Systems.

This paper is concerned with leader-following consensus of second-order multiagent systems with nonlinear dynamics. First, to save the limited communication resources, a new event-triggered control protocol is delicately developed without requiring continuous communication among the follower agents. Then, by employing the Lyapunov functional method and the Kronecker product technique, a novel sufficient criterion with less conservation is derived to guarantee the leader-following consensus while excluding the Zeno behavior. Furthermore, for the first time, an algorithm to actively adjust the leader adjacency matrix is presented, which efficiently expands the application range of some existing criteria. An example is finally given to illustrate the effectiveness of theoretical results.

Distributed robust H∞ composite-rotating consensus of second-order multi-agent systems

In this article, the distributed [Formula: see text] composite-rotating consensus problem is concerned for a class of second-order multi-agent systems. First, based on local state feedback and communication feedback, a distributed control algorithm is proposed. Then, sufficient conditions are derived in order to make all agents reach a composite-rotating consensus with the desired [Formula: see text] performance. Finally, the simulations are given to show the effectiveness of the theoretical results.

Quantized consensus of second-order multi-agent systems via impulsive control

This paper studies the consensus of second-order continuous-time multi-agent systems with quantized interaction. For static consensus, a hybrid impulsive protocol is proposed using the quantized relative position information. We prove that for any quantizer accuracy, the multi-agent systems can reach consensus if impulsive intervals are less than a given value. For dynamical consensus, an impulsive protocol is presented using both the quantized relative position and velocity information. It is shown that for any given impulsive interval, the multi-agent system can achieve consensus by selecting appropriate control gains and sufficiently small quantizer accuracy. The simulation results are given to verify the effectiveness of the theoretical results.

Distributed Position-Based Consensus of Second-Order Multiagent Systems With Continuous/Intermittent Communication.

This paper considers the position-based consensus in a network of agents with double-integrator dynamics and directed topology. Two types of distributed observer algorithms are proposed to solve the consensus problem by utilizing continuous and intermittent position measurements, respectively, where each observer does not interact with any other observers. For the case of continuous communication between network agents, some convergence conditions are derived for reaching consensus in the network with a single constant delay or multiple time-varying delays on the basis of the eigenvalue analysis and the descriptor method. When the network agents can only obtain intermittent position data from local neighbors at discrete time instants, the consensus in the network without time delay or with nonuniform delays is investigated by using the Wirtinger's inequality and the delayed-input approach. Numerical examples are given to illustrate the theoretical analysis.

Event-based consensus of second-order multi-agent systems with discrete time

Event-based control has received considerable attention due to its irreplaceable advantage in resource-limited systems. In this paper, event-based consensus of second-order discrete-time multi-agent systems is investigated. The event-based controller is designed for each agent, which is based on the state measurement error among neighborhood agents at its own triggering time instants. Some sufficient conditions are obtained for achieving consensus. To avoid observing the current states of its neighbor agents as well as its own state at every discrete-time, a self-triggered approach is presented to determine the triggering time sequence. Furthermore, certain conditions are given to avoid controller update at every discrete time. Finally, a simulation example is given to illustrate the efficiency of the proposed control strategy.

Couple-group consensus for second-order multi-agent systems with the effect of second-order neighbours’ information

This paper investigates a couple-group consensus problem of second-order multi-agent systems with the impact of second-order neighbours’ information. For systems with/without time delays, couple-group consensus criteria are established in the form of linear matrix inequalities by utilizing both model transformation and stability theories. The main results indicate that the group consensus for multi-agent systems under the effect of second-order neighbours’ information can be achieved based on the premise of a generalized balanced couple. Finally, illustrative examples are presented to demonstrate the effectiveness of the theoretical results.

Adaptive finite-time bipartite consensus for second-order multi-agent systems with antagonistic interactions

This paper is concerned with the adaptive finite-time bipartite consensus problems for networked second-order multi-agent systems with antagonistic interactions and unknown external disturbances. A signed undirected graph is used to describe the interactions among agents. For the leaderless case, continuous nonlinear distributed protocols with adaptive update laws are given, which can not only guarantee the bipartite steady-state errors of any two agents converge to a small region in finite time, but also eliminate the chattering problem. Then, the proposed algorithm is extended to solve the adaptive finite-time bipartite consensus tracking problem for leader–follower case by designing distributed finite-time estimator. Simulation example is included to show the effectiveness of the presented methods.

Observer Design for Tracking Consensus in Second-Order Multi-Agent Systems: Fractional Order Less Than Two

This technical note studies the leader-following tracking consensus problem of a class of multi-agent systems where the dynamics of the leader is described by second-order systems. In order to track the states of the leader, observers for the followers are designed by fractional-order multi-agent systems where the relative velocity information is unavailable. It is interestingly found that the followers can track the leader with second-order dynamics even if the fractional order is less than two by only using the position information of the local neighbors, which is different from the existing results. A novel fractional-order observer is first proposed, whose order is surprisingly less than the original leader system. It is also shown that leader-following consensus can be ensured if some carefully selected followers are informed and the relative position-based protocols are appropriately designed with fractional order being between one and two. A necessary and sufficient condition for the leader-following consensus in multi-agent systems without control-input delay is proposed. The results are then extended to the case with constant control-input delay. It is found that, in both cases, the real and imaginary parts of the eigenvalues of the augmented Laplacian matrix of the topology play an important role in achieving consensus.

Second-Order Consensus in Multiagent Systems via Distributed Sliding Mode Control.

In this paper, the new decoupled distributed sliding-mode control (DSMC) is first proposed for second-order consensus in multiagent systems, which finally solves the fundamental unknown problem for sliding-mode control (SMC) design of coupled networked systems. A distributed full-order sliding-mode surface is designed based on the homogeneity with dilation for reaching second-order consensus in multiagent systems, under which the sliding-mode states are decoupled. Then, the SMC is applied to the decoupled sliding-mode states to reach their origin in finite time, which is the sliding-mode surface. The states of agents can first reach the designed sliding-mode surface in finite time and then move to the second-order consensus state along the surface in finite time as well. The DSMC designed in this paper can eliminate the influence of singularity problems and weaken the influence of chattering, which is still very difficult in the SMC systems. In addition, DSMC proposes a general decoupling framework for designing SMC in networked multiagent systems. Simulations are presented to verify the theoretical results in this paper.

Static consensus of second-order multi-agent systems with impulsive algorithm and time-delays

This paper studies the consensus problem of second-order multi-agent systems with constant time-delay, fixed topology and impulsive algorithm based on periodic sampling. First, by theory of impulsive differential equations, it is proved that the consensus is achieved if and only if some matrix has a simple 1 eigenvalue and all the other eigenvalues are in the unit circle. Meanwhile, the consensus state of the system is obtained, which indicates that the positions and the velocities of all agents reach, respectively, a constant state and zero. Hence we say a static consensus is achieved for multiple second-order agents. Then, by stability of polynomials, we establish a necessary and sufficient condition from the perspective of topology and protocol parameters, which provides the range of allowable time-delay and the choice of impulse period. Finally, simulation examples are given to illustrate the effectiveness of the theoretical results.

Necessary and Sufficient Conditions for Consensus of Second-Order Multiagent Systems Under Directed Topologies Without Global Gain Dependency.

The consensus problem for second-order multiagent systems with absolute velocity damping under directed topologies is investigated. In contrast to the existing results, which rely on a sufficiently large common absolute velocity damping gain above a lower bound dependent on global information, this paper focuses on novel algorithms to overcome this limitation. A novel consensus algorithm, where different agents use different absolute velocity damping gains, is first proposed. In the absence of delays, based on a system transformation method, the consensus problem for second-order multiagent systems is converted into that for first-order multiagent systems with the agent number doubled. Necessary and sufficient conditions are then derived under directed topologies by relating the topologies associated with the doubled number of agents and the original team of agents. In the presence of multiple constant delays, based on a further system transformation method, the consensus problem for second-order multiagent systems is converted into the stability problem for corresponding systems. Necessary and sufficient conditions are presented to guarantee consensus under a directed fixed topology. For systems with a uniform constant delay, more concrete necessary and sufficient conditions on how large the delay can be to guarantee consensus is given. Numerical simulations are provided to illustrate the effectiveness of the obtained theoretical results.

Consensus of second-order multi-agent systems with nonlinear dynamics via edge-based distributed adaptive protocols

This paper investigates the distributed consensus problem of second-order multi-agent systems with nonlinear dynamics for both the cases leaderless and with a leader. First, based only on local information of the network structure, a new type of distributed adaptive consensus protocol is proposed, namely, the edge-based adaptive protocol which assigns a time-varying coupling weight to each edge in the communication. The coupling gains can be chosen randomly in the protocol and the consensus of second-order multi-agent systems can be reached without satisfying any additional conditions. Moreover, the leader–follower consensus problem in multi-agent systems with updated control gains is studied. To remove the limitation of coupling gains, a fully distributed adaptive protocol is designed. Under the proposed protocol, the leader–follower consensus can be also achieved without satisfying any additional conditions. Finally, two examples are presented to illustrate the theoretical analysis.

Consensus for second-order multi-agent systems with position sampled data**Project supported by the Natural Science Foundation of Zhejiang Province, China (Grant No. LY13F030005) and the National Natural Science Foundation of China (Grant No. 61501331).

In this paper, the consensus problem with position sampled data for second-order multi-agent systems is investigated. The interaction topology among the agents is depicted by a directed graph. The full-order and reduced-order observers with position sampled data are proposed, by which two kinds of sampled data-based consensus protocols are constructed. With the provided sampled protocols, the consensus convergence analysis of a continuous-time multi-agent system is equivalently transformed into that of a discrete-time system. Then, by using matrix theory and a sampled control analysis method, some sufficient and necessary consensus conditions based on the coupling parameters, spectrum of the Laplacian matrix and sampling period are obtained. While the sampling period tends to zero, our established necessary and sufficient conditions are degenerated to the continuous-time protocol case, which are consistent with the existing result for the continuous-time case. Finally, the effectiveness of our established results is illustrated by a simple simulation example.

Consensus of second-order multi-agent systems using partial agents’ velocity measurements

This paper studies the consensus problems of multi-agent systems with different inertia and partial agents’ nonlinear velocity measurements. Firstly, based on one agent’s velocity measurements, two consensus protocols are developed to guarantee that all agents asymptotically achieve stationary consensus. Secondly, a new protocol, which needs $$n-1$$ agents’ velocity measurements, rather than n, is presented such that all agents achieve consensus. Thirdly, two new consensus states, which are dependent on not only the initial positions and velocities, but also the masses and velocity gains of all agents, are obtained analytically. Numerical examples are given for three network topologies to illustrate the effectiveness of the derived algorithms.