General Linear Multi-agent Systems Research Articles

Distributed Event-Triggered Consensus of General Linear Multiagent Systems Under Directed Graphs.

This article investigates the consensus problem of general linear multiagent systems under directed communication graphs with event-triggered mechanisms. First, a novel distributed static event-triggered mechanism with a state-dependent threshold is proposed to solve the consensus problem, both with a positive lower bound on the average time interval of the communication among agents and updates of controllers. Thus, the Zeno behavior is excluded for communication among agents and controller updates. Next, to further reduce the frequencies of communication among agents and updates of controllers, a distributed dynamic event-triggered mechanism is introduced. By applying the static and dynamic mechanisms, the problem can be addressed with the reduced use of system resources compared with that in most existing control algorithms. Finally, numerical simulations are presented to verify the effectiveness of the results.

Event-Based Consensus for General Linear Multiagent Systems under Switching Topologies

In this paper, event-triggered leader-following consensus of general linear multiagent systems under both fixed topology and switching topologies is studied. First, centralised and decentralised event-triggered control strategies based on neighbors’ state estimation are proposed under fixed topology, in which the controller is only updated at the time of triggering. Obviously, compared with the continuous time control algorithms, the event-triggered control strategies can reduce the communication frequency among agents effectively. Meanwhile, event-triggering conditions are derived for systems to achieve consensus by using the Lyapunov stability theory and model transformation method. Then, the theoretical results obtained under the fixed topology are extended to the switching topologies, and the sufficient conditions for the system to achieve leader-following consensus under the switching topologies are given. However, different from fixed topology, the control input of each agent is updated both at event-triggering and topology switching time. Finally, Zeno behaviors can be excluded by proving that the minimum triggering interval of each agent is strictly positive, and the effectiveness of the event-triggered protocol is verified by simulation experiments.

A New Perspective to Algebraic Characterization on Controllability of Multiagent Systems

Recently, algebraic characterization of multiagent controllability through its topology has been widely concerned by the systems and control community. The controllability of leader-follower networked multiagent systems under the framework of generic linear dynamics is firstly discussed via λ-matrix. Some new algebra-theoretic necessary and/or sufficient conditions of the controllability for generic linear multiagent systems are established. Moreover, the controllable conditions for multiagent networks with special topological graphs through λ-matrix are presented.

Output-based event-triggered consensus of general linear multi-agent systems with communication delay under directed graphs

This paper studies the output-based event-triggered consensus problem of general linear multi-agent systems with communication delay under directed communication graphs. The influence of time delay on performance of multi-agent systems is investigated : the stability margin of time delay is explicitly calculated to measure the capability of proposed control algorithm to tolerate the time delay. By the designed output-based event-triggered mechanism, both communication among agents and update of controller are intermittent without Zeno behavior. Consequently, this control mechanism prolongs the lifespan of multi-agent systems in the sense that it saves intensive resource for communication and update of controller. Finally, numerical simulations are given to demonstrate the correctness of results in this paper.

Sliding Mode Control for Robust Consensus of General Linear Uncertain Multi-agent Systems

This paper investigates the robust consensus problem for general high-order linear multi-agent systems with external disturbances and internal uncertainties in coefficient matrices. Distributed protocols based on sliding mode control are proposed to realize the robust consensus under matched uncertainties.

Distributed Consensus of Linear Multiagent Systems: Laplacian Spectra-Based Method

The consensusability problems of general linear multiagent systems considering directed topologies are explored from a frequency domain perspective in this paper. By investigating the properties of Laplacian spectra, a consensus criterion is established based on the stability of several complex weighted closed-loop systems. Furthermore, for single-input multiagent systems, frequency domain consensusability criteria are proposed on the basis of the stability margins, which depend on the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> norm of the complementary sensitivity function determined by the agents' unstable poles. The corresponding design procedure is also developed. A numerical example is also presented to validate the proposed consensusability results.

Predefined containment control for general linear multiagent systems with time‐varying delays and switching topologies

AbstractContainment control problems for general linear multiagent systems with switching interaction topologies and time‐varying delays are studied. Firstly, state observers are constructed to estimate the multiple leaders under the influence of switching graphs and time‐varying delays. Secondly, a predefined containment protocol is presented based on the distributed state observer, where the expected convex combination of multiple leaders is predefined by several given weights. Moreover, an algorithm with two steps to confirm the gain matrices of the containment protocol and state observer is given. Based on linear matrix inequality technique and common Lyapunov‐Krasovskii stability theory, the convergence of this control strategy for multiagent systems with switching topologies and time‐varying delays to achieve state containment is proved. Finally, a numerical simulation is given to verify the validity of the theoretical results.

Dynamic Adaptive Event-Triggered Scheme for General Linear Multi-Agent Systems

Abstract This paper proposes a novel dynamic adaptive event-triggered scheme to deal with consensus problems in a class of general linear multi-agent systems. Firstly, a fully distributed event-triggered consensus protocol is proposed by assigning a time-varying coupling weight for each edge. Then by introducing an additional internal dynamic variable, a dynamic adaptive event condition is skillfully constructed and Zeno behavior is also successfully excluded. Based on this, the asymptotic consensus is eventually achieved and the frequency of communication among agents is significantly reduced. Finally, one simulation example is provided to verify the effectiveness of the proposed scheme.

Dynamic Quantized Consensus of General Linear Multi-agent Systems under Denial-of-Service Attacks

In this paper, we study a multi-agent consensus problem under Denial-of-Service (DoS) attacks with data rate constraints. We consider leaderless consensus under an undirected communication graph and assume that the graph is connected in the absence of DoS. The dynamics of the agents take general forms modeled as homogeneous linear time-invariant systems. In our analysis, we derive specific bounds on the data rate for the multi-agent system to achieve consensus even in the presence of DoS attacks. The main contribution of the paper is the characterization of the trade-off between the tolerable DoS attack level and the required data rates for the communication among the agents. To avoid quantizer saturation under DoS attacks, we employ dynamic quantization with zoom-in and zoom-out capabilities.

Stabilizability and Bipartite Containment Control of Multi-Agent Systems Over Signed Directed Graphs

This paper investigates the stabilizability and bipartite containment control problem of general linear multi-agent systems over signed directed graphs, where the negative edges indicate the antagonistic interactions between agents. By employing the proposed bipartite containment control protocols over signed directed graphs, and combining the linear system stabilization theory and the signed Laplacian matrix, the necessary condition for the stabilization of multi-agent systems with multiple leaders is discussed. According to this necessary condition, a leader-follower matching method is presented to establish leader-follower multi-agent system networks. Based on the leader-follower topology established above and the designed state feedback gain, the stability of multi-agent systems is proved by using the system error and the algebraic Riccati equation. It is shown that the followers can gradually converge into the convex hull spanned by the states and the sign-inverted states of leaders, and the bipartite containment control of multi-agent systems can be realized. The simulation results verify the feasibility of the theoretical analysis.

Distributed PI Formation Control Design for Autonomous Vehicles Using Edge Dynamics

A novel fully distributed proportional-integral (PI) formation controller design approach is proposed in this paper for general linear multi-agent systems (MASs) with model uncertainties and disturbances. First, an edge dynamics is developed for uncertain and perturbed linear MASs, based on which the formation control problem for the initial MAS is shown to be equivalent to a decentralized stabilizing problem for the obtained edge dynamics. Afterward, a necessary and sufficient condition for the PI controller gains is derived. A corollary of this condition shows that for integrator agents, PI controller gains can be any positive scalars. This result is then applied to the formation control of autonomous four-wheel vehicles described by nonlinear models, of which the efficiency of the proposed method is demonstrated in presence of both uncertainties and disturbances.

Quantized Consensus of Linear Multi-Agent Systems Under An Event-triggered Strategy

Abstract This paper addresses a quantized consensus problem of general linear multi-agent systems in a symmetric network under an event-triggered scheme. Firstly, a distributed event-triggered strategy is developed with a dynamic threshold to reduce the unnecessary control update. Then, based on absolute quantized state measurements, a distributed controller is proposed and then a consensus criterion is derived, which ensures bounded consensus of linear multi-agent systems. The Zeno behavior is also successfully excluded. Finally, a numerical simulation is presented to validate theoretical results.

Distributed Consensus Control for General Linear Multi-agent Systems via a Dynamic Event-triggered Strategy

This paper puts forward a distributed dynamic event-triggered strategy to solve the distributed event-triggered consensus problem of linear multi-agent systems under directed graphs. Based on dynamic triggering function, each agent can reach consensus asymptotically. Different from existing static triggering schemes, the proposed dynamic triggering scheme, where an internal dynamic variable is involved, results in larger inter-event times and also leads to less communication overheads among agents, which is conducive to guaranteeing that Zeno behavior is excluded for each agent. In addition, under the proposed strategy, neither controller updates nor triggering threshold detections require continuous communication. Finally, the effectiveness of the theoretical analysis is demonstrated by numerical simulations.

Distributed Adaptive Time-Varying Formation Tracking Control for General Linear Multi-Agent Systems Based on Event-Triggered Strategy

This paper is concerned with the time-varying formation tracking issue for high-order multi-agent systems based on event-triggered mechanism and adaptive control strategy. The time-varying formation configuration involved in our work is expressed as a bounded piecewise continuously differentiable vector function. The follower agents are required to achieve a pre-specified time-varying formation while tracking the state trajectory of the leader. First of all, in the light of event-triggered schema, we constructed an adaptive control protocol with adjustable time-variant parameters for achieving time-varying formation tracking. Meanwhile, the corresponding triggering conditions were designed to avoid continuous communication. Then, a four-step algorithm and feasible conditions have been provided to determine protocol parameters. Additionally, theoretically proof reveals that the specified formation tracking could be realized while excluding Zeno behavior. Two simulation examples were finally provided to illustrate the effectiveness of the obtained results.

Leader-Following Consensus for Linear Multiagent Systems via Asynchronous Sampled-Data Control

In this article, we consider the sampled-data leader-following consensus problem for a class of general linear multiagent systems over both static directed networks and switching directed networks. A distributed asynchronous sampled-data state feedback control law is proposed. We show by Lyapunov analysis that the problem can be solved by the proposed control law as long as the sampling periods of all agents are smaller than a given threshold, which can be explicitly calculated. An example is given to illustrate the effectiveness of our approach.

Fully distributed consensus for general linear multi‐agent systems with unknown external disturbances

This study investigates the consensus problem for general linear multi-agent systems with unknown external disturbances. Both the leaderless and the leader-follower consensus problems are considered. By using the absolute output information of each agent, the local states and external disturbances of each agent can be estimated by an extended state observer. Then, by using the relative estimated states and disturbance estimation, the continuous controller can be designed in a fully distributed fashion, which ensures that the consensus error of general linear multi-agent systems converges to zero eventually with the complete disturbance rejection. Moreover, when the absolute output information of each agent is not available, it is shown that the consensus problem can be solved by using only relative output information of neighbouring agents but only the part of the disturbances that affect the common trajectories will be rejected. Finally, simulation examples are given to demonstrate the effectiveness of the proposed protocols. Compared with the previous related works, fully distributed consensus disturbance rejection protocols are developed based on node-based adaptive design and edge-based adaptive design, which require neither global information of the communication graph nor the prior knowledge of the disturbance model.

Coordinated Tracking Control With Asynchronous Edge-Based Event-Triggered Communications

This paper studies the distributed event-triggered tracking control problem of general linear multiagent systems with a dynamic leader, whose control input might be nonzero and unknown. The existence of the leader's unknown input renders the network heterogeneous and largely increases the difficulty of designing distributed event-based protocols. To solve this problem, we establish a novel asynchronous edge-based event-triggered mechanism, under which communication is not required from the leader to its out-neighbors (informed followers) or by the edge, unless the embedded triggering functions are triggered. Using this mechanism, we design a static asynchronous edge-based event-triggered protocol and an adaptive one, both of which guarantee the achievement of the leader–follower consensus and the exclusion of the Zeno behavior. Note that the adaptive event-based protocol is fully distributed, requiring no global information of the network topology, such as the network's scale, the smallest nonzero eigenvalue of the Laplacian matrix, and the upper bound of the leader's control input.

Distributed event-triggered output-feedback control for sampled-data consensus of multi-agent systems

This paper addresses the consensus problem for general linear multi-agent systems with switching directed network topologies. A novel distributed event-triggered communication mechanism is developed to reduce some unnecessary data exchange among agents and the update frequency of the actuator. Different from the previous related works, the threshold parameters in the developed event-triggered conditions can be adaptively adjusted according to the sampled-data errors. Moreover, a distributed output-feedback consensus control protocol is presented. By applying an input delay approach, the considered consensus problem is transformed into the stability problem of linear time-delay system. Then, a sufficient condition for designing both the desired consensus controllers and the parameters of event-triggering conditions is derived. Finally, the effectiveness of the proposed method is demonstrated through numerical examples.

Multi-Agent Bipartite Tracking Control Over General Cooperative-Hostile Networks

This brief investigates the problem of bipartite tracking control for general linear multi-agent systems with cooperation and hostility. Compared with the existing studies over structurally balanced networks where hostile relations can only exist between two agent subgroups, the main highlight of this brief is to extend the bipartite tracking behavior to a more general cooperative-hostile network, in which hostile relations can exist within and between agent subgroups at the same time. Based on products of super-stochastic matrices, a sufficient criterion related to the network structure, such as network connectivity and positive and negative edge weights, is established. Meanwhile, it is also shown theoretically that each subsystem can be allowed to be strictly unstable, and the upper bound of unstable eigenvalue modules of the system matrix is given. Finally, a simulation example is provided to demonstrate the effectiveness of the theoretical result.

Distributed event-triggered protocols with [formula omitted]-functional observer for leader-following multi-agent systems

This paper is concerned with the leader-following consensus problem of general linear multi-agent systems under directed topology graph. Compared with the most of the prior works, we assume that the state information is unknown for each following agent and only the relative output information between neighboring agents can be measured. Then, two new types of functional observer-based output feedback event-triggered protocols are designed, where the Kx-functional observer designed in this paper may have lower dimension than the full-order and reduced-order observer, which can ensure that leader-following consensus is achieved. Furthermore, the Zeno behavior is excluded by showing that the inter-event time between any two triggering events is lower bounded by a strictly positive value. Finally, a numerical simulation example is presented to demonstrate the effectiveness of the proposed control protocols.