Consensus Of Second-order Multi-agent Systems Research Articles

Novel Reference Trajectory-Based Finite-Time Consensus Protocols for Multiagent Systems With Non-Identical Nonlinear Dynamics

This paper investigates the finite-time consensus for second-order multiagent systems under directed networks, where each agent is described by a non-identical nonlinear system. By using the reference trajectory-based method, two novel protocols are developed for the leader-follower and leaderless cases, respectively. It is noted that the dynamical evolutions of each agent's state and the reference trajectory are coupled, and the information of reference trajectories is not allowed to transmit in the communication channels. By the developed protocols, the relative state errors among agents can converge to the origin (instead of a neighborhood of the origin) within a finite time, though there are unknown parameters in agents' dynamics. The nonlinear terms in agents' dynamics are not required to be bounded by known constants or functions, which invalidates many consensus schemes based on the sliding mode control. Using the graph theory, Lyapunov functional method and finite-time stability theory, sufficient conditions are established for the finite-time consensus of considered multiagent systems. Finally, simulation examples are given to validate the effectivity of the proposed protocols.

Resilient Bipartite Consensus of Second-Order Multiagent Systems With Event-Triggered Communication

This article investigates the resilient bipartite consensus problem for continuous-time second-order multiagent systems in the presence of totally bounded malicious nodes under signed digraphs. An event-based resilient impulsive algorithm is employed, which cannot only mitigate the malicious nodes’ influence on the convergence of normal ones but also reduce the communication loads of agents. A necessary and sufficient condition related to the network topology is established for solving resilient bipartite consensus by using system transformation. A numerical simulation illustrates the effectiveness of the result.

Distributed Predefined-Time Optimization for Second-Order Systems under Detail-Balanced Graphs

This paper studies the problem of distributed predefined-time optimization for leaderless consensus of second-order multi-agent systems under a class of weighted digraphs. The proposed framework has two main steps. In the first step, the agents communicate to perform a consensus-based distributed predefined-time optimization and to generate a constant optimal output reference for each agent. In the second step, each agent tracks its corresponding optimal output reference, using a sliding-mode controller to reach the global optimum in a predefined time, even under matched disturbances. The proposed algorithm relies explicitly on user-defined constant parameters. Numerical simulations are performed to validate the efficacy of the algorithm.

Fixed-time group consensus of second-order multi-agent systems based on event-triggered control

The problem of fixed-time group consensus for second-order multi-agent systems with disturbances is investigated. For cooperative-competitive network, two different control protocols, fixed-time group consensus and fixed-time event-triggered group consensus, are designed. It is demonstrated that there is no Zeno behavior under the designed event-triggered control. Meanwhile, it is proved that for an arbitrary initial state of the system, group consensus within the settling time could be obtained under the proposed control protocols by using matrix analysis and graph theory. Finally, a series of numerical examples are propounded to illustrate the performance of the proposed control protocol.

Stochastic Bipartite Consensus for Second-Order Multi-Agent Systems with Communication Noise and Antagonistic Information

In this paper, the bipartite consensus problem for second-order multi-agent systems with no leader, one leader and multiple leaders are investigated, where the information exchange is disturbed by measurement noise and antagonistic information. In order to attenuate the effect of communication noise, a time-varying gain c(t) is utilized and the stochastic approximation bipartite control protocol is proposed. It is given that the underlying protocol can solve the bipartite consensus problem for MASs with no leader/one leader/multiple leaders if the communication topology is strongly connected/has a spanning tree/has a spanning forest and the c(t) satisfies some mild condition. Meanwhile, for system with these three cases, a series of sufficient and necessary conditions are given. Especially, for the case with no leader, we obtain that the final state of agent is related with the initial position and initial velocity of each agent. For the case with one leader, we can get that the followers in one group can follow up the state of one leader, and the followers in another group tend to the opposite value. Additionally, for the case with multiple leaders, the containment control can be achieved where followers’ states in one group can converge to the quai-convex hull of leaders’ state and the ones in another group converge to the opposite convex hull. Finally, some numerical examples are given to support our new results.

Bipartite Consensus for Second-Order Multiagent Systems With Matrix-Weighted Signed Network

The second-order scalar-weighted consensus problem of multiagent systems has been well explored. However, in some practical antagonistic interaction networks, the interdependencies of multidimensional states of the agents must be described by matrix coupling. In order to highlight the influence of matrix coupling in the antagonistic interaction network, we investigate the second-order matrix-weighted bipartite consensus problem on undirected structurally balanced signed networks. Under the proposed bipartite consensus protocol, an algebraic condition is obtained for achieving second-order bipartite consensus via utilizing matrix-valued Gauge transformation and stability theory. Then, using the obtained criteria, a more direct algebraic graph condition is given for reaching bipartite consensus. Besides, because of the existence of negative (positive) semidefinite connections, the matrix-weighted network may have clustering phenomena, which means that matrix weights play a critical role in achieving consensus. An algebraic graph condition for admitting cluster bipartite consensus is provided. By designing matrix weights in practical scenarios, the required number of clusters can be obtained. Finally, the theoretical results are verified by five simulation examples.

Second-Order Consensus for Multi-Agent Systems With Various Intelligent Levels via Intermittent Sampled-Data Control

This brief is concerned with the second-order consensus problem of multi-agent systems (MASs) over directed communication topologies. Due to engineering applications, agents in the network may have nonidentical intelligent degrees in practical scenarios. A novel intermittent sampled-data control protocol with different intelligent levels is proposed. Necessary and sufficient conditions are derived to guarantee the desired consensus under the protocol. Nevertheless, since the velocity states of real agents may not be measured, a novel protocol only utilizing past sampled position data with distinct intelligent levels is presented, under which the conditions of realizing consensus can be attained via similar analysis. Finally, the asymptotic consensus of MASs can be verified by some numerical simulations. The states of agents with the same intelligent level can be validated to converge to the common value as well.

Intentional delay can benefit consensus of second-order multi-agent systems

In this paper, second-order multi-agent systems with intentionally induced delay are studied, which cannot achieve consensus with a non-delay position-based protocol. Under the proposed distributed protocol with the current and outdated position states, the crossing frequencies and crossing delays of the related quasipolynomial of the delayed systems are identified. By determining the crossing directions of the imaginary roots, the change of the number of the right half-plane roots can be obtained. Accordingly, consensus condition and consensus delay range are provided. Simulations illustrate the effectiveness of the theoretical analysis.

Event-triggered bipartite consensus of second-order multi-agent systems under DoS attacks

This paper is concerned with the secure bipartite consensus of second-order multi-agent systems under denial-of-service (DoS) attacks. The communication network is an antagonistic network, in which there is cooperative or competitive relationship between neighboring agents. Meanwhile, information cannot be transmitted when the system is attacked. A novel event-triggered control algorithm based on sampled data is proposed to save limited resources and exclude the Zeno behavior. By applying the convergence of monotone sequences, graph theory as well as the discrete-time Lyapunov function method, some sufficient conditions on threshold parameters, frequency and duration of DoS attacks, and sampling period are derived to ensure the bipartite consensus under DoS attacks. Finally, the correctness and advantages of theoretical results are demonstrated by a numerical simulation.

Event-triggered consensus for second-order multi-agent systems with sampled position data via impulsive control

In this paper, the sampled-data-based event-triggered (SDBET) consensus problem of second-order multi-agent systems (MASs) with sampled position data is studied via impulsive control. Firstly, two kinds of SDBET impulsive control protocols are proposed, both of which employ sampled position data only. Secondly, a novel SDBET transmission scheme is designed to ensure the maximum length of triggering intervals exists, which can be regulated by the parameters in the triggering function. Also, the Zeno behavior is naturally excluded under the SDBET transmission scheme. And by using the designed SDBET impulsive control scheme, consensus of second-order MASs can be achieved with lower transmission and control updating frequency than using the periodical impulsive control scheme. Thirdly, sufficient conditions on the communication topology, the length of triggering intervals and control gains are derived to achieve SDBET consensus. It is also shown that to achieve consensus, both the maximum and minimum lengths of triggering intervals should be restricted. Also, a practical method for calculating the sampling period and other triggering parameters is given to ensure that the length of the triggering interval does not exceed the given range, and the SDBET transmission scheme is truly realized. Finally, some numerical examples are given to demonstrate the effectiveness of the theoretical results.

Adaptive event-triggered group consensus of multi-agent systems with non-identical nonlinear dynamics

The paper is concerned with mean-square group consensus for second-order multi-agent systems with non-identical dynamics, where the agents in the same group have the identical dynamics, the agents in the different groups have non-identical nonlinear dynamics. To reduce the update frequency of event-triggered controller, a novel adaptive dynamic event-triggered communication scheme is presented based on the local stochastic sampled information. The proposed event-triggered conditions of the position state and velocity state have be given separately owe to their state ranges may be different, which lead to the position state and velocity state with different event-triggered instants and release intervals. The event-triggered matrices and time-varying event-triggered parameters are introduced into event-triggered conditions, the given event-triggered conditions are detected only at discrete sampled times, which means Zeno behavior can be excluded. A novel distributed protocol is designed based on the neighboring agents information of the position state and velocity state at event-triggered instants. The group consensus issue can be transformed into the convergence problem of the augmented error system. Then some mean-square group consensus criteria can be derived with the help of tools from graph theory and matrix analysis, and the event-triggered matrices can be obtained by solving some linear matrix inequalities. Finally, two numerical examples are employed to show the validity and advantage of the proposed transmission scheme.

Scaled consensus of second-order multi-agent systems based on edge-event driven control

In this paper, the scaled consensus of resource-limited multi-agent systems with second-order integrator dynamics and undirected topologies is investigated. In order to reduce bandwidth and computation requirements, a scaled consensus protocol based on periodic edge-event driven control is proposed. It is proven that all the agents could converge to a scaled consensus state while the interaction topology is connected. Moreover, a self-triggered scheme is proposed so as to further reduce communication times between agents. Notably, the event-detecting period is introduced so that Zeno behavior could be excluded in our model. Finally, simulations are given to demonstrate the effectiveness of our theoretical results.

Consensus for Second-Order Multiagent Systems Under Two Types of Sampling Mechanisms: A Time-Varying Gain Observer Method.

This article considers the consensus of second-order multiagent systems (MASs) under a directed communication topology. By introducing time-varying gains into observers, two types of novel continuous-discrete-time observers are presented to estimate state information of agents under two sampling mechanisms, respectively, namely: 1) a synchronous nonuniform sampling (SNS) mechanism and 2) an asynchronous nonuniform sampling (ANS) mechanism. A new design method of the time-varying gain observer is proposed, in that it can allow for one to select a consensus protocol with lower cost observers to attain the consensus task. Only sampled position information needs to be transmitted in designing consensus protocols for the MSAs, and neither velocity information nor control input information is required. Under the SNS mechanism, a consensus condition is obtained and it is shown that the introduction of time-varying gains in the observers indeed can improve their convergence. Under the ANS mechanism, the corresponding consensus protocol allows the sampling and transmission of different agents to be asynchronous and aperiodic, which means that each agent may sample and transmit its information in line with its own sampling requirements. Furthermore, each sampling period can be arbitrarily selected within a certain range while ensuring the consensus of the MASs. Finally, numerical examples are given to illustrate the effectiveness of the obtained results.

Second-Order Consensus for Multiagent Systems With Switched Dynamics and Sampled Position Data

This article studies the consensus control problem of second-order multiagent systems with switching dynamics, which consist of a continuous-time and a discrete-time subsystem. A novel control protocol is proposed for fixed digraphs by using the same control strategy for two subsystems so that the controller can keep the control strategy unchanged when systems switch. Moreover, this control strategy uses only sampled position data at the current sampling time and the previous sampling time to deal with this possible situation when speed information is difficult to be measured, which is also robustness and low cost. Some necessary and sufficient conditions to achieve consensus are derived about the network topology, structure and sampling period. At last, a few simulation examples are given.

Synchronous and asynchronous resilient impulsive control for group consensus of second-order multi-agent systems with communication delays

This paper studies the resilient group consensus of continuous-time second-order multi-agent systems (MASs) with malicious agents. Adopting the idea that each normal agent ignores the most extreme values from neighbors, synchronous resilient impulsive algorithm based on sampled data is proposed for normal agents with bounded communication delays to achieve group consensus. Meanwhile, asynchronous resilient impulsive algorithm is also proposed for MASs where each agent has its own time clock. Sufficient topological conditions are obtained for solving resilient group consensus under synchronous and asynchronous settings, respectively. Numerical examples are provided to illustrate the effectiveness of the theoretical results.

Intermittent event-triggered control for finite-time bipartite consensus of second-order multi-agent systems

This article discusses how second-order nonlinear multi-agent systems achieve bipartite consensus in finite-time using intermittent event-triggered control strategies. Due to the problem arising from antagonistic links between neighboring nodes of second-order multi-agents, the finite-time bipartite consensus analysis is investigated, which is more challenging than that with only cooperative communication links. Accounting for limitations of communication bandwidths, an intermittent framework is proposed first. By utilizing algebraic graph theories and gauge transformations, sufficient conditions are given to achieve finite-time consensus in signed second-order multi-agent systems. Second, a hybrid control mechanism combining intermittent control with event-triggered control is developed. Therefore, some finite-time synchronization conditions of second-order multi-agents on signed graphs are further studied. The proposed protocol reduces the updating frequency of the controller, which saves communication resources a lot. Finally, the Zeno behavior is excluded and some numerical examples are performed to show the effectiveness of the theoretical analysis.

Predefined-time bipartite tracking consensus for second-order multi-agent systems with cooperative and antagonistic networks

This paper addresses the predefined-time bipartite tracking problem for second-order Multi-Agent Systems (MASs) with undirected signed topologies. A group of observers, which can estimate the state tracking errors for each follower in a pre-specified time, is proposed based on the time-varying function. In order to deal with the uncertainties caused by the unknown disturbances and the unknown input signal of the leader, we propose a predefined-time distributed control protocol based on the sliding mode control method. In addition, an auxiliary dynamic sliding variable is designed to reduce system chattering. We theoretically prove that the two control protocols can drive the state trajectories of each follower to reach the corresponding sliding surface within a specified time, and finally ensure that the prescribed-time bipartite tracking consensus is achieved for the MASs. Simulations are provided to verify the proposed schemes, and the simulation results further confirm the superiority of the adaptive control protocol.

Finite-Time Group Consensus for Second-Order Multi-agent Systems with Input Saturation

Finite-Time Group Consensus for Second-Order Multi-agent Systems with Input Saturation

Bipartite consensus for second-order multi-agent systems with external disturbances via constraint data-sampled impulsive method

This paper is aimed to deal with bipartite consensus for nonlinear second-order multi-agent systems (MASs) with external disturbances. Due to the existence of nonlinearity and external disturbances (containing bounded disturbances and stochastic disturbances separately), the original MASs are not stable. In this paper, the impulse signal at each impulsive instant only happens between the leader and followers. In order to consume less energy in the limited operating range of actuator, the input saturation function is taken into consideration to implement data-sampled control with impulsive information. Constraint data-sampled method and leader-following impulsive protocol are combined together under signed topology to deal with the extended bipartite consensus. Results show that some sufficient conditions relying on impulsive gains and convex combination parameters can be derived to reach the goal. Two numerical examples of simple pendulums illustrate the availability of theoretical analyses.

New Conditions for Consensus of Second-Order Multi-agent Systems

New Conditions for Consensus of Second-Order Multi-agent Systems