M-matrix strategies for pinning-controlled leader-following consensus in multiagent systems with nonlinear dynamics

Leader-Following Consensus of Nonlinear Multiagent Systems With Stochastic Sampling

This paper is concerned with sampled-data leader-following consensus of a group of agents with nonlinear characteristic. A distributed consensus protocol with probabilistic sampling in two sampling periods is proposed. First, a general consensus criterion is derived for multiagent systems under a directed graph. A number of results in several special cases without transmittal delays or with the deterministic sampling are obtained. Second, a dimension-reduced condition is obtained for multiagent systems under an undirected graph. It is shown that the leader-following consensus problem with stochastic sampling can be transferred into a master-slave synchronization problem with only one master system and two slave systems. The problem solving is independent of the number of agents, which greatly facilitates its application to large-scale networked agents. Third, the network design issue is further addressed, demonstrating the positive and active roles of the network structure in reaching consensus. Finally, two examples are given to verify the theoretical results.

Event-Triggered Schemes on Leader-Following Consensus of General Linear Multiagent Systems Under Different Topologies

This paper investigates the leader-following consensus for multiagent systems with general linear dynamics by means of event-triggered scheme (ETS). We propose three types of schemes, namely, distributed ETS (distributed-ETS), centralized ETS (centralized-ETS), and clustered ETS (clustered-ETS) for different network topologies. All these schemes guarantee that all followers can track the leader eventually. It should be emphasized that all event-triggered protocols in this paper depend on local information and their executions are distributed. Moreover, it is shown that such event-triggered mechanism can significantly reduce the frequency of control's update. Further, positive inner-event time intervals are assured for those cases of distributed-ETS, centralized-ETS, and clustered-ETS. In addition, two methods are proposed to avoid continuous communication between agents for event detection. Finally, numerical examples are provided to illustrate the effectiveness of the ETSs.

Event-Triggered Distributed Average Consensus Over Directed Digital Networks With Limited Communication Bandwidth

In this paper, we consider the event-triggered distributed average-consensus of discrete-time first-order multiagent systems with limited communication data rate and general directed network topology. In the framework of digital communication network, each agent has a real-valued state but can only exchange finite-bit binary symbolic data sequence with its neighborhood agents at each time step due to the digital communication channels with energy constraints. Novel event-triggered dynamic encoder and decoder for each agent are designed, based on which a distributed control algorithm is proposed. A scheme that selects the number of channel quantization level (number of bits) at each time step is developed, under which all the quantizers in the network are never saturated. The convergence rate of consensus is explicitly characterized, which is related to the scale of network, the maximum degree of nodes, the network structure, the scaling function, the quantization interval, the initial states of agents, the control gain and the event gain. It is also found that under the designed event-triggered protocol, by selecting suitable parameters, for any directed digital network containing a spanning tree, the distributed average consensus can be always achieved with an exponential convergence rate based on merely one bit information exchange between each pair of adjacent agents at each time step. Two simulation examples are provided to illustrate the feasibility of presented protocol and the correctness of the theoretical results.

Leader-follower consensus and synchronization in numerosity-constrained networks with dynamic leadership

In this work, we study leader-follower consensus and synchronization protocols over a stochastically switching network. The agents representing the followers can communicate with any other agent, whereas the agents serving as leaders are restricted to interact only with the other leaders. The model incorporates the phenomenon of numerosity, which limits the perceptual capacity of the agents while allowing for shuffling with whom each individual interacts at each time step. We derive closed form expressions for necessary and sufficient conditions for consensus, the rate of convergence to consensus, and conditions for stochastic synchronization in terms of the asymptotic convergence factor. We provide simulation results to validate the theoretical findings and to illustrate the dependence of this factor on system parameters. The closed form results enable us to study the factors affecting the feasibility of consensus. We show that agents' traits can be chosen for an engineered system to maximize the convergence speed and that protocol speed is enhanced as the proportion of the leaders increases in certain cases. These results may find application in the design and control of an engineered leader-follower system, where consensus or synchronization at the fastest possible rate is desired.

Consensus of Multiagent Systems Using Aperiodic Sampled-Data Control

This paper is concerned with the consensus of multiagent systems with nonlinear dynamics through the use of aperiodic sampled-data controllers, which are more flexible than classical periodic sampled-data controllers. By input delay approach, the resulting sampled-data system is reformulated as a continuous system with time-varying delay in the control input. A continuous Lyapunov functional, which captures the information on sampling pattern, together with the free-weighting matrix method, is then used to establish a sufficient condition for consensusability. For a more general case that the sampled-data controllers are subject to constant input delays, a novel discontinuous Lyapunov functional is introduced on the basis of the vector extension of Wirtinger's inequality. This functional can lead to simplified and efficient stability conditions for computation and optimization. Further results on the estimate of maximal allowable sampling interval upper bound is given as well. Numerical example is provided to show the effectiveness and merits of the proposed protocol.

Reaching Synchronization in Networked Harmonic Oscillators With Outdated Position Data

This paper studies the synchronization problem for a network of coupled harmonic oscillators by proposing a distributed control algorithm based only on delayed position states, i.e., outdated position states stored in memory. The coupling strength of the network is conveniently designed according to the absolute values and the principal arguments of the nonzero eigenvalues of the network Laplacian matrix. By analyzing a finite number of stability switches of the network with respect to the variation in the time delay, some necessary and sufficient conditions are derived for reaching synchronization in networked harmonic oscillators with positive and negative coupling strengths, respectively, and it is shown that the time delay should be taken from a set of intervals bounded by some critical values. Simulation examples are given to illustrate the effectiveness of the theoretical analysis.

Robust Consensus of Nonlinear Multiagent Systems With Switching Topology and Bounded Noises

Consensus of multiagent systems (MASs) is an intriguing topic in recent years due to its widely used application in robotics, biology, computer, and social science. In the real world, the evolution of MAS is inevitably involved in dynamical environments and the recent development of MAS calls for novel tools for the analysis of MAS with dynamic topology. In addition, the interactions between agents are generally nonlinear and environmental noises are ubiquitous in the communication channels between agents. However, the existing investigation on MAS places little attention on nonlinear models and the inner relationship between external disturbance and consensus is still unclear. Facing these problems, this paper considers an MAS in which the interactions between agents are nonlinear and the communication between agents are infected by environmental noises. By using a novel method of nonsmooth Lyapunov candidate, it has been demonstrated that such an MAS can realize robust consensus under the conditions of jointly (sequentially) connected topology and bounded noises. Finally, simulation results validate the effectiveness of these criteria.

Velocity synchronization of multi-agent systems with mismatched parameters via sampled position data

Power systems are special multi-agent systems with nonlinear coupling function and symmetric structures. This paper extends these systems to a class of multi-agent systems with mismatched parameters, linear coupling function, and asymmetric structures and investigates their velocity synchronization via sampled position data. The dynamics of the agents is adopted as that of generators with mismatched parameters, while the system structures are supposed to be complex. Two distributed linear consensus protocols are designed, respectively, for multi-agent systems without or with communication delay. Necessary and sufficient conditions based on the sampling period, the mismatched parameters, the delay, and the nonzero eigenvalues of the Laplacian matrix are established. It is shown that velocity synchronization of multi-agent systems with mismatched parameters can be achieved if the sampled period is chosen appropriately. Simulations are given to illustrate the effectiveness of the theoretical results.

Distributed Synchronization Control of Multiagent Systems With Unknown Nonlinearities

This paper revisits the distributed adaptive control problem for synchronization of multiagent systems where the dynamics of the agents are nonlinear, nonidentical, unknown, and subject to external disturbances. Two communication topologies, represented, respectively, by a fixed strongly-connected directed graph and by a switching connected undirected graph, are considered. Under both of these communication topologies, we use distributed neural networks to approximate the uncertain dynamics. Decentralized adaptive control protocols are then constructed to solve the cooperative tracker problem, the problem of synchronization of all follower agents to a leader agent. In particular, we show that, under the proposed decentralized control protocols, the synchronization errors are ultimately bounded, and their ultimate bounds can be reduced arbitrarily by choosing the control parameter appropriately. Simulation study verifies the effectiveness of our proposed protocols.

Fault-Tolerant Consensus of Multi-Agent System With Distributed Adaptive Protocol

In this paper, fault-tolerant consensus in multi-agent system using distributed adaptive protocol is investigated. Firstly, distributed adaptive online updating strategies for some parameters are proposed based on local information of the network structure. Then, under the online updating parameters, a distributed adaptive protocol is developed to compensate the fault effects and the uncertainty effects in the leaderless multi-agent system. Based on the local state information of neighboring agents, a distributed updating protocol gain is developed which leads to a fully distributed continuous adaptive fault-tolerant consensus protocol design for the leaderless multi-agent system. Furthermore, a distributed fault-tolerant leader-follower consensus protocol for multi-agent system is constructed by the proposed adaptive method. Finally, a simulation example is given to illustrate the effectiveness of the theoretical analysis.

Consensus of Euler-Lagrange systems networked by sampled-data information with probabilistic time delays

This paper investigates the consensus problem of multiple Euler-Lagrange systems under directed topology. Unlike the common assumptions on continuous-time information exchanges, a more realistic sampled-data communication strategy is proposed with probabilistic occurrence of time-varying delays. Both of the sampling period and the delays are assumed to be time-varying, which is more general in some practical situations. In addition, the relative coordinate derivative information is not required in the distributed controllers such that the communication network burden can be further reduced. In particular, a distinct feature of the proposed scheme lies in the fact that it can effectively reduce the energy consumption. By employing the stochastic analysis techniques, sufficient conditions are established to guarantee that the consensus can be achieved. Finally, a numerical example is provided to illustrate the applicability and benefits of the theoretical results.

ISS method for coordination control of nonlinear dynamical agents under directed topology

The problems of coordination of multiagent systems with second-order locally Lipschitz continuous nonlinear dynamics under directed interaction topology are investigated in this paper. A completely nonlinear input-to-state stability (ISS)-based framework, drawing on ISS methods, with the aid of results from graph theory, matrix theory, and the ISS cyclic-small-gain theorem, is proposed for the coordination problem under directed topology, which can effectively tackle the technical challenges caused by locally Lipschitz continuous dynamics. Two coordination problems, i.e., flocking with a virtual leader and containment control, are considered. For both problems, it is assumed that only a portion of the agents can obtain the information from the leader(s). For the first problem, the proposed strategy is shown effective in driving a group of nonlinear dynamical agents reach the prespecified geometric pattern under the condition that at least one agent in each strongly connected component of the information-interconnection digraph with zero in-degree has access to the state information of the virtual leader; and the strategy proposed for the second problem can guarantee the nonlinear dynamical agents moving to the convex hull spanned by the positions of multiple leaders under the condition that for each agent there exists at least one leader that has a directed path to this agent.