First-order Nonlinear Multi-agent Systems Research Articles

Design of consensus and cluster consensus controller for first-order nonlinear multi-agent systems based on subgroup structure

It is well known that nonlinear multi-agent systems (MASs) with a directed topology can reach a consensus if the global coupling coefficient is strong enough. In this paper, we propose a novel distributed protocol based on the subgroup structure. Our results demonstrate that the MAS design can follow a part-to-whole approach, starting with subgroups and gradually building up to a more complex system. We firstly consider two cases for the MASs: one with a single leader and one with a leader group, where agents within the leader group can communicate with each other, but cannot receive the information of other group. We show that followers can track the leader or group leaders if intra-coupling within the subgroup and information strength received by the root node are above a certain threshold. Next, we investigate cluster consensus and practical cluster consensus for the Laplacian matrix with unequal row sum, equal row sum, and mixing of partitioned matrices. Our results reveal that row sum and community structure of the partitioned matrix are crucial in determining the final state of each agent. Our proposed control protocol is highly flexible and relies only on the cluster structure and information received by the root node, rather than global information. Moreover, our method is not limited to tracking problems, cooperative control, or multi-objective control, and can accommodate new group agents joining the system, making it highly adaptable. We provide illustrative examples to demonstrate the effectiveness of our approach.

Leader-following cluster-delay consensus control for first-order nonlinear multi-agent systems based on event-triggered mechanism

In this paper, the event-triggered-based cluster-delay consensus control problem is investigated for leader-following nonlinear multi-agent systems (MASs). In control design, both state triggering in the agents’ network and constant time-delay in the leaders’ communication network are considered. Under the framework of Lyapunov function stability theory, the Lipschitz condition is used to overcome the influence caused by time-delay. In order to further effectively utilize data transmission resources, and reduce the communication load of the topology network between each agent, an event-triggered mechanism is established. Subsequently, a robust cluster consensus control strategy is proposed based on event-triggered mechanism, which can ensure all signals of the controlled system are bounded, and the tracking errors converge to zero. In addition, it can also effectively avoid the Zeno behavior. Finally, the effectiveness of the presented control method and theory is verified by a simulation example.

The fixed-time consensus of leader-following nonlinear multi-agent systems under event-triggered impulsive control

This paper studies the leader-following fixed-time consensus problem for a class of first-order nonlinear multi-agent systems via event-triggered impulsive control where the communication topologies are general undirected. For each agent, the controller is updated only when some state-dependent errors exceed a tolerable bound, and the impulsive control time sequence is produced by the event triggered mechanism. This original control protocol can substantially improve the convergence speed, obtain the lower energy consumption and reduce the update times of the controller. Also, it is shown that continuous communication of neighboring agents can be avoided and there is no Zeno-behavior. The results are verified by a numerical simulation.

Distributed Fast Finite-Time Tracking Consensus of Multi-Agent Systems With a Dynamic Leader

Distributed fast finite-time tracking consensus (FTTC) is investigated for first-order nonlinear multi-agent systems (MASs), where the leader has an external input unknown to all followers. Based on global finite-time stability and Lyapunov stability, two distributed tracking protocols are proposed to guarantee fast FTTC. First, a basic distributed non-smooth protocol for solving this problem is proposed and analyzed. A limitation of the designed protocol is that the control gains should depend on some global information like the spectrum of Laplacian matrix. To remove this limitation, a fully distributed protocol is further designed and analyzed. Theoretical studies imply that the states of the considered MASs will also achieve fast FTTC. Finally, two simulation examples are performed on Chua’s circuit system to verify the theoretical results.

Event-Triggered Fixed-Time Integral Sliding Mode Control for Nonlinear Multi-Agent Systems with Disturbances.

In this paper, the leader-following consensus problem of first-order nonlinear multi-agent systems (FONMASs) with external disturbances is studied. Firstly, a novel distributed fixed-time sliding mode manifold is designed and a new static event-triggered protocol over general directed graph is proposed which can well suppress the external disturbances and make the FONMASs achieve leader-following consensus in fixed-time. Based on fixed-time stability theory and inequality technique, the conditions to be satisfied by the control parameters are obtained and the Zeno behavior can be avoided. In addition, we improve the proposed protocol and propose a new event-triggering strategy for the FONMASs with multiple leaders. The systems can reach the sliding mode surface and achieve containment control in fixed-time if the control parameters are designed carefully. Finally, several numerical simulations are given to show the effectiveness of the proposed protocols.

Fixed-time consensus of first-order multi-agent systems over signed directed graphs

This paper studies the fixed-time consensus problems of first-order multi-agent systems over signed directed graphs. Fixed-time consensus protocols are designed for first-order multi-agent systems without/with disturbances and first-order nonlinear multi-agent systems with disturbances, respectively. With proposed protocols, it is proved that multi-agent systems with strongly connected topologies will achieve consensus in a fixed time if the control parameters satisfy certain conditions. Finally, simulation examples are provided to verify the effectiveness of the theoretical results.

Consensus of Multiagent Systems With Relative State Saturations

Within the multiagent systems framework, the relative states between neighbors can be acquired by some on-board sensors, and then the relative state saturations inevitably occur due to the limited sensing capabilities. This paper investigates the consensus problem of nonlinear multiagent systems subject to the relative state saturations. Utilizing the incidence matrix and the edge Laplacian, the consensus problem of nonlinear multiagent systems with the relative state saturations can be cast into the stabilization problem of edge dynamics operating on the constrained set. Three types of protocols, namely continuous, intermittent, and adaptive state feedback protocols are, respectively, proposed for achieving the constrained consensus, and meanwhile yielding consensus values. A consensus analysis is provided by virtue of state saturation theory, switched system theory, adaptive theory, and Lyapunov stability theory. Output feedback protocol is also designed. Finally, the obtained results are applied to connectivity preservation for first-order nonlinear multiagent systems, despite the presence of limited communication range and input constraints. The theoretical results are validated by two simulation examples.

Event-triggered Consensus Control of Nonlinear Multi-agent Systems based on First-order Hold

In this paper, consensus problem is studied for the first-order nonlinear multi-agent systems under directed topology, and a novel event-triggered consensus protocol is proposed. Different from the existing results with general zero-order hold, the first-order hold is adopted to construct the event-triggered control signal so as to reduce the triggering rate. By using Lyapunov stability method and matrix theory, a sufficient consensus condition is derived for the agents to reach the asymptotic consensus, and Zeno-behavior can be avoided. Finally, a numerical example is presented to demonstrate the effectiveness of our proposed protocol.

Fixed-Time Consensus of Nonlinear Multi-Agent Systems With General Directed Topologies

In this brief, the authors study the fixed-time consensus problem for a class of first-order nonlinear multi-agent systems where the communication topologies are general directed. Both fixed-time tracking consensus and fixed-time leaderless consensus problems are investigated. For the leader–follower situation, the communication topology is only required to contain a directed spanning tree. As for the leaderless situation, the topology is required strongly connected. Simulations are finally provided to verify the effectiveness of the proposed algorithms.

Consensus in first-order nonlinear multi-agent systems with state time delays using adaptive fuzzy wavelet networks

In this paper, a consensus problem is addressed for first-order multi-agent systems with unknown nonlinear dynamics under undirected graphs. Adaptive fuzzy wavelet networks are used to design two n...

Leader-following Cluster Consensus in Multi-agent Systems with Intermittence

In this paper, the cluster consensus problem of first-order nonlinear multi-agent systems with aperiodic intermittent communication is studied through pinning leader-following approach. The pinning consensus algorithm based on the relative local intermittent information is designed according to the varies linking ways of clustered network structure. New notions of leading intermittence and inter-cluster intermittence which related to the intermittent linking ways of leader-following clustered structure are developed, and several new systems with intermittence are established due to the new notions. Besides, dynamics with inherent delay are also considered to extend our results to a more general framework. The original communication graph without intermittent pattern is supposed to be directed and weakly connected. Some consensus criteria are derived to guarantee that the cluster consensus problem for the systems with intermittent communication can be solved. Finally, numerical simulations are given to illustrate the effectiveness of the theoretical results.

Cluster-delay consensus in multi-agent systems via pinning leader-following approach with intermittent effect

ABSTRACTIn this paper, the cluster consensus problem with delays of first-order nonlinear multi-agent systems is studied through pinning leader-following approach with periodic intermittent effect. The graph of the networked system is assumed to be directed and weakly connected. A new type of pinning consensus protocol with intermittent effect is designed according to the ways in which the agents link, specifically, the agents in each cluster are divided into three subsets due to the orientation of their topological degree, and each subset of agents is controlled by an individual law. A redefined notion on cluster consensus with two sorts of time delays is proposed in this article. Some consensus criteria are derived to guarantee that the agents in the same cluster asymptotically follow the virtual leader with a delay, while agents in different clusters reach consensus with delays via following their leaders. Some numerical simulations are given to illustrate the effectiveness of the theoretical results.

Distributed Adaptive Consensus of Nonlinear Multi-agent Systems with Unknown Control Coefficients

This paper is devoted to the leader-follower consensus problem for nonlinear multi-agent systems. Remarkably, the control coefficients in the systems are unknown which makes the problem rather difficult to solve. By employing the distributed adaptive protocols, the consensus is achieved under undirected connected graph for the first-order nonlinear multi-agent systems. Furthermore, similar results for the general case are obtained for the second-order nonlinear multi-agent systems. At last, two simulation examples are given to show the effectiveness of the protocols.