Consensus protocol for multi-agent continuous systems

Bipartite hybrid formation tracking control for heterogeneous multi-agent systems in multi-group cooperative-competitive networks

In this paper, we investigate two classes of consensus protocols for networked multi-agent systems: linear time-invariant (LTI) systems and linear time-delay systems. Based on the topology of multi-agent systems, the first-order integrator model is developed. The digraph (directed graph) is employed to show the topology of networked systems, and then a consensus convergence criterion is established. For LTI systems, we prove that their consensus value will converge globally asymptotically to the convex hull of initial states. By solving a set of linear equations, we get the convex combinations of equilibria, and we obtain the convex value of continuous system. If the topology is fixed and time-invariant, the consensus value of the linear time-delay system is also the convex hull of the initial states and is identical to the LTI system. Finally, a network of six agents is presented to show the effectiveness of the results of this paper.

Nowadays, the efficiency of multiagent systems in wireless sensor networks prompts the researchers to use these emerging mobile software packets in different simulated approaches or real-world applications. Heterogeneous and distributed wireless sensor networks could be integrated with the multiagent systems to map the real-world challenges into the artificial intelligence world. The multiagent systems have been applied from simulated approaches like object detection/tracking, healthcare, control/assistant, and security systems to real-world applications, including medical/human-care systems and unmanned aerial vehicles. Furthermore, the integration of wireless sensor networks with multiagent systems have emerged novel application, which is known as mobile robots. However, the extensive use of mobile agents in wireless sensor networks has posed different challenges for researchers, including security, resource, and timing limitation. In this work, we review recent simulated approaches and real-world applications of multiagent systems in wireless sensor networks, in which a set of common factors about the things that have been studied are extracted and compared to analyze the performance of mobile agent–based systems in the wireless sensor networks, as well. This analysis provides new research directions about multiagent systems in wireless sensor networks for interested researchers. Finally, a novel framework for dealing with the challenges of multiagent-based applications in the wireless sensor networks which have been mentioned is suggested.

The paper deals with the consensus convergence analysis of discrete-time single-integrator multi-agent systems (MASs) in switching networks. Here, we suppose that the switching network is composed of strongly connected digraphs. By adopting a time-varying quadratic Lyapunov function, we give the rigorous proof that the consensus of the single-integrator MASs can be achieved by either a constant-gain protocol or a decaying-gain protocol. This Lyapunov function based consensus analysis method is different from some existed ones for unbalanced switching networks (e.g., the property of products of indecomposable and aperiodic matrices) and provides a new perspective to study the consensus problem of MASs in unbalanced switching networks with uncertainties (e.g., additive noises).

An information consensus algorithm for high-order multi-agent systems is proposed based on algebraic graph theory. Sufficient and necessary conditions are given for each information to converge to common values. The network topology of multi-agent systems has a directed spanning tree and each weight of different derivatives is positive, then consensus is achieved.

Sampled-data leader-following consensus of nonlinear multi-agent systems subject to impulsive perturbations

In this paper, the leader-following consensus problem of a class of fractional-order nonlinear multi-agent systems is considered. By using the algebraic graph theory, Lyapunov theory and LMI method of fractional-order systems, the control gain matrix is designed to achieve leader-following consensus under fixed and switching topologies respectively. Furthermore, the convergence rate of the controlled multi-agent systems is studied based on the sense of Mittag-Leffler stability of fractional-order systems. Simulations indicate the effectiveness of the theoretical results.

This paper investigates the periodic event-triggered asymmetric bipartite consensus problem of multi-agent systems (MASs) under structurally balanced undirected signed graphs. In order to reduce the consumption of communication resources and continuous detection in the control process of MASs, a novel periodic detection event-triggered asymmetric bipartite consensus control protocol is proposed. In particular, each agent samples only in a fixed period. For each agent, two event conditions are given, and only when state error satisfies this event condition can the event be triggered. A new type of Laplacian matrix is constructed to achieve asymmetric bipartite consensus. The control method can guarantee the performance of MASs and have less communication resources. Based on the Lyapunov stability theorem and algebraic graph theory, the proposed periodic event-triggered control strategy is able to implement the asymmetric bipartite consensus when the topology is structurally balanced undirected signed graphs. The proposed method in this paper can reduce the restriction on the sampling period and automatically exclude Zeno behavior. Finally, the validity of the conclusion is verified by numerical simulation.

The consensus problem of multi-agent nonlinear systems with or without uncertain parameters is studied in this paper. Based on the theory of impulsive differential equations, Lyapunov stability theory and algebraic graph theory, some impulsive consensus conditions are given to realize the consensus of a class of multi-agent nonlinear systems. Compared with the existing investigations of impulsive consensus of multi-agent systems, the proposed impulsive control protocol with uncertain parameters is more rigorous and effective in practical systems. Two numerical simulations are verified to confirm the effectiveness of the proposed methods.

The consensus of fractional-order multi-agent nonlinear systems via distributed impulsive control method is studied in this paper. Based on the theory of impulsive differential equations, algebraic graph theory, Lyapunov stability theory and Mittag-Leffler function, a novel sufficient condition for achieving the consensus of a class of fractional-order multi-agent nonlinear systems are derived. Finally, one numerical simulation is given to illustrate the effectiveness of the proposed methods.

This paper investigates the leaderless and leader-following consensus problem for a second-order multi-agent systems with input saturation, i.e., the control input is required to be priori bounded. Moreover, the control coefficients are unknown and cannot be lower or upper bounded by known constants. By virtue of adaptive control technique, Lyapunov theory, algebraic graph theory and Barbalat's lemma, it is proved that the states of the multi-agent systems can achieve consensus under the assumption that the interconnection topology is undirected and connected. Finally, two simulation examples are provided to illustrate the effectiveness of the theoretical results.

With the development of swarm intelligence in last decades, consensus problem of multi-agent systems has been attracting much attention. To reveal the inherent mechanism of leader-following consensus in multi-agent systems with stochastic dynamics, PI control protocols are designed in this paper. Owing to the stochastic analysis techniques, algebraic graph theory, and constructing appropriate Lyapunov function, it is proved that the leader-following consensus of nonlinear stochastic dynamical multi-agent systems can be reached in mean square. Sufficient condition are deduced to select the PI control protocol parameters. Finally, the theoretical results are demonstrated through a simulation example.

In this manuscript, the stability and consensus problem of the leader-following multi-agent system is studied. The state information of the leader is only available to the dynamics of all the followers, while the communication among the agents occurs at sampling instant. The innovative part of this paper is to reach the consensus and attain the stability for prescribed MASs with interval time varying delay using impulsive control in the presence of leader. The interaction between the agent is illustrated by an undirected graph. A class of distributed impulsive protocol relying on sampling information is suggested to reach the leader following consensus. The consensus is critically relying on the sampling period, control gains. By performing the similar procedures, the consensus problem of multi-agent system is converted to stability problem of the error system. By utilizing the stability theory of impulsive systems, algebraic graph theory, sufficient conditions are derived to guarantee the leader-following consensus of the multi-agent system. Terminally, a numerical example is given to show an efficacy of this presented approach and the sureness of theoretical analysis.

Impulsive synchronization of networked nonlinear dynamical systems

This paper investigates an observer-based control strategy for networked multi-agent systems with general linear dynamics and time-varying communication delays in a sampling setting. The communication topology is assumed to be directed fixed. Different from a traditional observer-based controller for a single system, the objects that need to be observed here are the state differences between an agent and its neighbours. Using a system transformation method, some equivalent conditions concerning the consensus of multi-agent systems are established. Moreover, we prove that both the connection weights and the communication topology play an important role in the study of multi-agent systems, and establish a linear matrix inequality based observer design method.