Global Leader-following Consensus Research Articles

Comments on “Global leader-following consensus in finite time for fractional-order multi-agent systems with discontinuous inherent dynamics subject to nonlinear growth”

Despite the proposed results on the non-existing of finite time stable equilibria for fractional order systems (Shen and Lam, 2014), the commented paper (Wang et al., 2020) has shown finite time convergence of fractional order control systems via a couple of theorems. This comment demonstrates that the proofs of the given theorems in Wang et al. (2020) are incorrect.

Global Leader-Following Consensus of Double-Integrator Multiagent Systems by Fully Distributed Bounded Linear Protocols

This article is concerned with the global leader-following consensus problem of the input-constrained double-integrator multiagent systems. By utilizing a Lyapunov-like function consisting of a positive semidefinite term and an integral term, a class of bounded static linear protocols are proposed to ensure that the global leader-following consensus problem for homogeneous multiagent systems is solved in a fully distributed manner for all undirected communication graphs. As a further result, the global consensus problem for heterogeneous multiagent systems under directed communication graphs is also considered and two different distributed observer-based bounded linear protocols are proposed to solve such a problem also in a fully distributed manner. The most significant advantages of this article are that the system under consideration is more general, the designed protocols are linear, and the global consensus in a fully distributed manner can be guaranteed. A numerical example shows the effectiveness of the proposed approaches.

Global leader-following consensus in finite time for fractional-order multi-agent systems with discontinuous inherent dynamics subject to nonlinear growth

This paper considers the global leader-following consensus of fractional-order multi-agent systems (FMASs), where the inherent dynamics is modeled to be discontinuous, and subject to nonlinear growth. Firstly, based on convex functions, three formulas on fractional derivative are established respectively. By applying the proposed formulas, a principle of convergence in finite-time for absolutely continuous functions is developed. Secondly, a new nonlinear control protocol, which includes discontinuous factors, is designed. Under fractional differential inclusion framework, by means of Lyapunov functional approach and Clarke’s non-smooth analysis technique, the sufficient conditions with respect to the global consensus are achieved. In addition, the setting time is explicitly evaluated for the global leader-following consensus in finite time. Finally, two illustrative examples are provided to check the correction of the obtained results in this paper.

Semi-Global Cooperative Output Regulation Problem for Heterogeneous Swarm Systems With Input Saturation Under Switching Network

In this paper, the semi-global cooperative output regulation problem of heterogeneous swarm systems subject to saturation under switching network is investigated. Like the common consensus problems, the swarm systems consist of some followers cannot access the state of the leader directly. But the difference is that some even cannot measure the state of the leader all the time. By utilizing the distributed output feedback control method, the low-gain feedback technique and the output regulation theories, we establish two sets of consensus control laws, respectively, based on the state feedback method and the output feedback method, to solve the output consensus problems in this kind. Besides, the global leader-following output consensus problem under switching network is proved to be a special case of semi-global cooperative output regulation problem under switching network, and as a consequence, it can also be solved by our method. A simulation example is proposed to illustrate the results very well.

Global leader-following consensus of nonlinear multi-agent systems with unknown control directions and unknown external disturbances

This paper is concerned with the distributed leader-following consensus problem for a class of first-order and second-order Lipschitz nonlinear multi-agent systems with unknown control directions and unknown bounded external disturbances. Moreover, the Lipschitz constant is unknown for controller design and the disturbances are only required to have unknown upper bounds and not necessarily have explicit expression. Some distributed protocols are proposed by using the Nussbaum gain function combing with adaptive control technique. By virtue of algebraic graph theory, Barbalat’s lemma and Lyapunov theory and under the assumption that the interconnection topology is undirected and connected, it is proved that the multi-agent systems can achieve global asymptotic consensus even in the presence of external disturbances. Simulation examples are provided to illustrate the effectiveness of the proposed methods.

Global leader-following consensus of a group of discrete-time neutrally stable linear systems by event-triggered bounded controls

This paper studies the global leader-following consensus problem for a group of discrete-time neutrally stable linear systems subject to actuator saturation. An event-triggered linear feedback law, either of the state feedback type or the output feedback type, is constructed for each follower agent and an event-triggering strategy is designed for updating these control laws. These event-triggered control laws are shown to achieve global leader-following consensus when the communication topology among the follower agents is strongly connected and detailed balanced and the leader is a neighbor of at least one follower agent. Simulation results illustrate the theoretical validity.

Global leader-following consensus of a group of general linear systems using bounded controls

This paper studies the global leader-following consensus problem for a multi-agent system with bounded controls. The follower agents and the leader agent are all described by a general linear system. Both a bounded state feedback control law and a bounded output feedback control law are constructed for each follower agent in the group. The feedback law for each input of an agent uses a multi-hop relay protocol, in which the agent obtains the information of other agents through multi-hop paths in the communication network. The number of hops each agent uses to obtain its information about other agents for an input is less than or equal to the sum of the number of eigenvalues at the origin and the number of pairs of non-zero imaginary eigenvalues of the sub-system corresponding to the input, and the feedback gains are constructed from the adjacency matrix of the communication network. It is shown that global leader-following consensus is achieved under these feedback control laws when the communication topology among follower agents is a strongly connected and detailed balanced directed graph and the leader is a neighbor of at least one follower.

Global consensus of single‐integrator agents subject to saturation constraints

This paper investigates the problem of leader-following consensus of single-integrator agents subject to saturation constraints. Global leader-following consensus protocol is developed with proper choice of the relative coupling gain. Both the case of input saturation and the case of actuator saturation are considered. It is shown that global consensus of the multiagent system can be reached under the general undirected graph provided that its augmented graph contains a directed spanning tree. Numerical examples are provided to demonstrate the theoretical results.

Global Leader Following Consensus of a Group of Discrete-Time Linear Systems Using Bounded Controls

This paper studies the global leader-following consensus problem for a group of discrete-time linear systems with bounded controls. For each follower agent, we construct a bounded nonlinear feedback control law which uses the information of other agents obtained through multi-hop paths in the communication network. The number of hops each agent uses to obtain its information about other agents is no bigger than the largest algebraic multiplicity of the eigenvalues on the unit circle of the system matrix. We show that these control laws achieve global leader-following consensus when the communication topology is a strongly connected and detailed balanced directed graph and the leader is a neighbor of at least one follower agent.

Cooperative global output regulation of heterogeneous second-order nonlinear uncertain multi-agent systems

In this paper, we study the cooperative global output regulation problem for a class of heterogeneous second order nonlinear uncertain multi-agent systems. We first introduce a type of distributed internal model that converts the cooperative global output regulation problem into the global robust stabilization problem of the so-called augmented multi-agent system. Then we further globally stabilize this augmented multi-agent system via a distributed state feedback control law, thus leading to the solution of the original problem. A special case of our result leads to the solution of the global leader-following consensus problem for the second order nonlinear multi-agent systems without satisfying the global Lipschitz condition.

Global consensus of multiple integrator agents via saturated controls

This paper investigates the problem of global leader-following consensus of multiple integrator agents subject to control input saturation. A weighted and saturated consensus algorithm is proposed to solve this problem. Both the case of an undirected communication topology and the case of a directed communication topology are considered. It is shown that global consensus of the multiple integrator agents can be reached under a general undirected graph or a detailed balanced directed graph provided that its generated graph contains a directed spanning tree. Numerical examples are provided to demonstrate the theoretical results.

On global leader-following consensus of identical linear dynamic systems subject to actuator saturation

This paper studies the leader-following consensus problem for a group of agents with identical linear systems subject to control input saturation. We focus on two classes of linear systems, neutrally stable systems and double integrator systems. For neurally stable systems, we establish that global consensus can be achieved by linear local feedback laws over a fixed communication topology, and with proper choices of relative potential functions, global consensus can also be achieved over a switching communication topology. For double integrator systems, we establish that global consensus can be achieved by linear local feedback laws over a fixed communication topology, and with the help of a simple saturation function in the local feedback laws, global consensus can also be achieved over a switching communication topology. Simulation results illustrate the theoretical results.