Practically finite-time H ∞ deployment of large-scale multi-agent systems with sequence-dependent switching topology: a fuzzy PDE-based approach

ABSTRACTThis article investigates the containment control problem for a class of second-order multi-agent systems with inherent nonlinear dynamics, under the common assumption that each agent can only obtain the relative information of its neighbours intermittently. A kind of distributed protocol based only on the relative local intermittent measurements of neighbouring agents is designed for containment control under fixed directed topology. In the absence of delays, based on the Lyapunov function technology and the intermittent control method, some sufficient conditions are presented to guarantee the intermittent containment control of second-order nonlinear multi-agent systems. In the presence of delays, some containment conditions are also obtained for a second-order multi-agent systems with inherent delayed nonlinear dynamics and intermittent communications. Moreover, the similar results are obtained for second-order nonlinear multi-agent systems under switching directed topology. Finally, simulation examples are given to illustrate the correctness and effectiveness of the theoretical analysis.

<abstract><p>The deployment of multi-agent systems (MASs) is widely used in the fields of unmanned agricultural machineries, unmanned aerial vehicles, intelligent transportation, etc. To make up for the defect that the existing PDE-based results are overly idealistic in terms of system models and control strategies, we study the PDE-based deployment of clustered nonlinear first-order and second-order MASs over a finite-time interval (FTI). By designing special communication protocols, the collective dynamics of numerous agents are modeled by simple fist-order and second-order PDEs. Two practical factors, external disturbance and Markov switching topology, are considered in this paper to better match actual situations. Besides, T–S fuzzy technology is used to approximate the unknown nonlinearity of MASs. Then, by using boundary control scheme with collocated measurements, two theorems are obtained to ensure the finite-time $ H_\infty $ deployment of first-order and second-order agents, respectively. Finally, numerical examples are provided to illustrate the effectiveness of the proposed approaches.</p></abstract>

In this paper, the leader-following consensus of second-order nonlinear multiagent systems (SONMASs) with external disturbances is studied. Firstly, based on terminal sliding model control method, a distributed control protocol is proposed over undirected networks, which can not only suppress the external disturbances, but also make the SONMASs achieve consensus in finite time. Secondly, to make the settling time independent of the initial values of systems, we improve the protocol and ensure that the SONMASs can reach the sliding surface and achieve consensus in fixed time if the control parameters satisfy some conditions. Moreover, for general directed networks, we design a new fixed-time control protocol and prove that both the sliding mode surface and consensus for SONMASs can be reached in fixed time. Finally, several numerical simulations are given to show the effectiveness of the proposed protocols.

A distributed consensus control method is developed in this paper for second-order nonlinear multiagent systems with external stochastic disturbances. By utilizing the graph theory, the stochastic theory, the control technique, and the linear matrix inequality method, sufficient conditions are derived to guarantee the convergence to mean-square exponential consensus for strongly connected proximity networks and proximity networks with directed spanning trees, respectively. Particularly, using such a methodology, a detailed distributed consensus controller design procedure is provided for networked Euler–Lagrange systems, which are often used in mechanical engineering processes. Finally, the effectiveness of the proposed consensus control method is illustrated by numerical simulations on networked Euler–Lagrange systems.

This article attempts to design the prescribed-time time-varying deployment schemes for first-order and second-order nonlinear multiagent systems (MASs). We assume that all agents can obtain the information of their current and final relative positions with their neighbors, and the final absolute velocities (as well as their current and final relative velocities, the final absolute accelerations for the second-order MASs) through a communication network, whereas two boundary agents are able to obtain their current and final absolute positions (as well as their current and final absolute velocities for the second-order MASs). The neighbor relationship of all agents is described by a spatial variable and two static-feedback controllers are introduced, which can be expressed as a second-order space difference of the spatial variable. Then, the deployment of MASs can be transformed into the stabilization of discrete-space partial differential equation (PDE) systems. Three virtual agents are introduced to constitute the Dirchlet and Neumann boundary conditions. Several algebraic inequality criteria are derived to guarantee that the prescribed-time time-varying deployment can be achieved within a prescribed time under the Dirchlet and mixed boundary conditions. Unlike the published results, our results are derived based on the discrete-space PDE systems instead of continuous-space PDE systems, which is consistent with the discrete spatial distribution of agents. Finally, two numerical examples are given to illustrate the effectiveness of our results.

This brief investigates the problem of finite-time robust consensus (FTRC) for second-order nonlinear multiagent systems with external disturbances. Based on the global finite-time stability theory of discontinuous homogeneous systems, a novel finite-time convergent discontinuous disturbed observer (DDO) is proposed for the leader-following multiagent systems. The states of the designed DDO are then used to design the control inputs to achieve the FTRC of nonlinear multiagent systems in the presence of bounded disturbances. The simulation results are provided to validate the effectiveness of these theoretical results.This brief investigates the problem of finite-time robust consensus (FTRC) for second-order nonlinear multiagent systems with external disturbances. Based on the global finite-time stability theory of discontinuous homogeneous systems, a novel finite-time convergent discontinuous disturbed observer (DDO) is proposed for the leader-following multiagent systems. The states of the designed DDO are then used to design the control inputs to achieve the FTRC of nonlinear multiagent systems in the presence of bounded disturbances. The simulation results are provided to validate the effectiveness of these theoretical results.

Bipartite formation problem of second-order nonlinear multi-agent systems with hybrid impulses

In this paper, the delay consensus of second-order nonlinear leader-following multi-agent systems is discussed. The considered multi-agent system has an active leader and the information exchange between two different agents possesses directional. A simple input control law is proposed. Based on the matrix theory and Lyapunov stability theory, the effectiveness of this control law is proved and a sufficient condition is obtained to realize delay consensus of the second-order multi-agent system.

This article introduces a safe consensus protocol of second-order unknown nonlinear multi-agent systems (MASs) subjected to hybrid false data injection cyberattacks (FDICAs), external disturbance, and directed network. All followers can be prone to FDICA and external disturbance. In an MAS, agents measure their state variables by sensors and then send them to neighbor agents through wireless systems. Therefore, both sensors and wireless systems can be prone to FDICAs. These attacks can deteriorate the closed-loop performance, reliability, and safety or even cause instability since they can easily propagate errors among the agents. So that, it is vital to design control policies enhancing resilience against FDICA. It is assumed that different bounded attacks are applied to position and speed channels. Our purpose is to plan a global safe adaptive resilient consensus protocol to guarantee the asymptotic stability. To this aim, by employing artificial neural networks (ANNs), the nonlinear dynamics of each agent is estimated. Afterward, a safe adaptive control law is planned to compensate for the effects of nonlinearity, disturbance, and FDICA to achieve the consensus. By means of the Lyapunov’s second theory, the global asymptotic stability (GAS) of the system is proved. Different numerical results confirm the theoretical investigations and illustrate the efficiency of the presented approach on controlling agents in the proposed second-order nonlinear MAS.

Containment control for second-order nonlinear multi-agent systems with aperiodically intermittent position measurements

<p>This paper investigates fixed-time consensus (FXTC) for second-order nonlinear multi-agent systems under denial of service (DoS) attacks using event-triggered control. First, consensus in second-order nonlinear multi-agent systems with directed topologies is studied under a static event-triggered mechanism. Building upon this, dynamic auxiliary variables are introduced, and a dynamic event-triggered mechanism is designed. Consensus control protocols are proposed for both leader-follower and leaderless scenarios. Using Lyapunov stability theory and algebraic graph theory, the fixed-time consensus of multi-agent systems with directed topologies under DoS attacks is analyzed. Furthermore, Zeno behavior is excluded. Finally, numerical examples are presented to validate the theoretical results.</p>

This paper investigates the second-order nonlinear multi-agent systems subject to the cluster-delay consensus. The multi-agent systems consist of leader and agents, whose dynamics are second-order nonlinear. The objective is that the agents track the leader asymptotically with different time delays, i.e., the agents in different groups reach delay consensus, while the agents in the same group reach identical consensus. To guarantee the cluster-delay consensus for the second-order multi-agent systems, a new control protocol is proposed. Then some corresponding conditions for cluster-delay consensus are derived by using Lyapunov directed method and matrix theory. Finally, the effectiveness of the theoretical analysis results are verified by some numerical simulations.

Integral sliding-mode fixed-time consensus tracking for second-order non-linear and time delay multi-agent systems

This article deals with the event-triggered leader-following guaranteed cost consensus control problem for second-order nonlinear multiagent systems, in which the guaranteed cost function is proposed to facilitate to enhance the consensus tracking regulation performance. To reduce the frequency of information transmission, a distributed event-triggered mechanism, which broadcasts the triggered states to its neighbours for each agent, is designed, and the triggering condition is then constructed for leader-following second-order nonlinear multiagent systems. By employing Lyapunov–Krasovskii method and Barbalat’s lemma, some sufficient conditions are derived to ensure the leader-following consensus and guaranteed cost performance for second-order nonlinear multiagent systems. It is also exhibited that the constructed triggering condition can efficaciously exclude the Zeno behavior. To testify the efficacy of the proposed theoretical methodology, a simulation example is offered.

Adaptive leader-following formation control with collision avoidance for a class of second-order nonlinear multi-agent systems