Consensus Of Multi-agent Networks Research Articles

Novel Stability Conditions for Nonlinear Monotone Systems and Consensus in Multiagent Networks

We introduce a novel definition of monotonicity, termed “type-K” in honor of Kamke, and study nonlinear type-K monotone dynamical systems possessing the plus-subhomogeneity property, which we call “K-subtopical” systems after Gunawardena and Keane. We show that type-K monotonicity, which is weaker than strong monotonicity, is also equivalent to monotonicity for smooth systems evolving in continuous-time, but not in discrete-time. K-subtopical systems are proved to converge toward equilibrium points, if any exists, generalizing the result of Angeli and Sontag about convergence of topical systems' trajectories toward the unique equilibrium point when strong monotonicity is considered. The theory provides an new methodology to study the consensus problem in nonlinear multi-agent systems (MASs). Necessary and sufficient conditions on the local interaction rule of the agents ensuring the K-subtopicality of MASs are provided, and consensus is proven to be achieved asymptotically by the agents under given connectivity assumptions on directed graphs. Examples in continuous-time and discrete-time corroborate the relevance of our results in different applications

Scaled group consensus in multi-agent networks with high-order continuous dynamics

We investigate scaled group consensus problems of high-order multi-agent systems with directed information exchanges. As one of multiple consensus, the scaled group consensus focuses on both cooperations and competitions among multi-agent sub-networks and cooperations among agents belonging to a sub-network. Two distributed protocols are designed to solve the scaled group consensus problems. The (generalised) Routh–Hurwitz stability criterion and matrix theory are utilised to establish necessary and sufficient conditions guaranteeing the agents reaching the scaled group consensus. Finally, several simulations are presented to demonstrate the effectiveness of the theoretical results.

Resilient group consensus in the presence of Byzantine agents

In this paper, we address the resilient group consensus of multi-agent networks in the presence of structured and unstructured Byzantine faults. In the case of structured Byzantine faults that feed different but structured values to the network, it is shown that non-faulty nodes can achieve group consensus without using any fault tolerant algorithm. Necessary and sufficient conditions on the network are derived so that the conventional consensus algorithm leads to group consensus values in the range determined by the initial values of the non-faulty nodes. In the presence of unstructured Byzantine faults, two fault tolerant algorithms are proposed to overcome the highly disruptive behaviour. Subsequently, convergence analysis of these algorithms is carried out by exploiting the robustness properties of the network. Finally, theoretical results are illustrated with several simulation examples.

Cluster consensus in multi-agent networks with mutual information exchange

The emergence of new technologies such as the Internet of things and the Cloud transforms the way we interact. Whether it be human to human interaction or human to machine interaction, the size of the networks keeps growing. As the networks get more complex nowadays with many interconnected components, it is necessary to develop distributed scalable algorithms so as to minimize the computation required in decision making in such large-scale systems. In this paper, we consider a setup where each agent in the network updates its opinion by relying on its neighbors’ opinions. The information exchange between the agents is assumed to be mutual. The cluster consensus problem is investigated for networks represented by static or time-varying graphs. Joint and integral connectivity conditions are utilized to determine the number of clusters that are formed, as the interactions among the agents evolve over time. Finally, some numerical examples are given to illustrate the theoretical results.

Guaranteed‐cost consensus for multiagent networks with Lipschitz nonlinear dynamics and switching topologies

SummaryGuaranteed‐cost consensus for high‐order nonlinear multiagent networks with switching topologies is investigated. By constructing a time‐varying nonsingular matrix with a specific structure, the whole dynamics of multiagent networks is decomposed into the consensus and disagreement parts with nonlinear terms, which is the key challenge to be dealt with. An explicit expression of the consensus dynamics, which contains the nonlinear term, is given and its initial state is determined. Furthermore, by the structure property of the time‐varying nonsingular transformation matrix and the Lipschitz condition, the impacts of the nonlinear term on the disagreement dynamics are linearized, and the gain matrix of the consensus protocol is determined on the basis of the Riccati equation. Moreover, an approach to minimize the guaranteed cost is given in terms of linear matrix inequalities. Finally, the numerical simulation is shown to demonstrate the effectiveness of theoretical results.

Consensus in Networks of Multiagents with Stochastically Switching Topologies and Time-Varying Delays

In this paper, we investigated a very general model of discrete-time consensus algorithm in networks of multiagents with stochastically switching topologies and bounded time-varying delays. Here no...

Constrained Consensus Algorithms With Fixed Step Size for Distributed Convex Optimization Over Multiagent Networks

In this technical note, we are concerned with constrained consensus algorithms for distributed convex optimization with a sum of convex objective functions subject to local bound and equality constraints. In multiagent networks, each agent has its own data on objective function and constraints. All the agents cooperatively find the minimizer, while each agent can only communicate with its neighbors. The consensus of multiagent networks with time-invariant and undirected graphs is proven by the Lyapunov method. Compared with existing consensus algorithms for distributed optimization with diminishing step sizes, the proposed algorithms with fixed step size have better convergence rate. Simulation results on a numerical example are presented to substantiate the performance and characteristics of the proposed algorithms.

Maximizing Algebraic Connectivity in the Space of Graphs With a Fixed Number of Vertices and Edges

The second smallest eigenvalue of the Laplacian matrix, also known as the algebraic connectivity, characterizes the performance of some dynamic processes on networks, such as consensus in multiagent networks, synchronization of coupled oscillators, random walks on graphs, and so on. In a multiagent network, for example, the larger the algebraic connectivity of the graph representing interactions between agents is, the faster the convergence speed of a representative consensus algorithm is. This paper tackles the problem of finding graphs that maximize or locally maximize the algebraic connectivity in the space of graphs with a fixed number of vertices and edges. It is shown that some well-known classes of graphs such as star graphs, cycle graphs, complete bipartite graphs, and circulant graphs are algebraic connectivity maximizers or local maximizers under certain conditions.

Finite-time consensus of a leader-following multi-agent network with non-identical nonlinear dynamics and time-varying topologies

In this paper, the finite-time consensus of a leader-following multi-agent network with non-identical nonlinear dynamics and time-varying topologies is investigated. All the agents, especially the leaders, have non-identical and nonlinear dynamics. According to the algebraic graph theory, Lyapunov stability theory and Kronecker product, a control strategy strategy is established to guarantee the finite-time consensus of multi-agent network with multiple leaders. Furthermore, several numerical simulations illustrate the effectiveness and feasibility of the proposed method.

Adaptive Group Consensus of Multi-Agent Networks via Pinning Control

This paper studies the group consensus problem in networks of multi-agent systems, in which the nonlinear dynamics of all agents are unknown and nonidentical. We assume that the unknown dynamics are linearly parameterized. Adaptive control method is adopted in the algorithm design. A novel algorithm is proposed for the multi-agent systems to reach group consensus via pinning control strategies, which only rely on the relative position information between neighboring agents. The stability and parameter convergence analysis are done based on Lyapunov theory, Barbalat's lemma, adaptive control theory and algebraic graph theory. Finally, a simulation example is given to validate our theoretical results.

On Couple-Group Consensus of Multiagent Networks with Communication and Input Time Delays

This paper investigated the couple-group consensus problems of the multiagent networks with the influence of communication and input time delays. Based on the frequency-domain theory, some algebraic criteria are addressed analytically. From the results, it is found that the input time delays and the coupling strengths between agents of the systems play a crucial role in reaching group consensus. The convergence of the system is independent of the communication delays, but it will affect the convergence rate of the system. Finally, several simulated examples are provided to verify the validity and correctness of our theoretical results.

Collision-free consensus in multi-agent networks: A monotone systems perspective

This paper addresses the collision-free consensus problem in a network of agents with single-integrator dynamics. Distributed algorithms with local interactions are proposed to achieve consensus while guaranteeing collision-free among agents during the evolution of the multi-agent networks. The novelty of the proposed algorithms lies in the definition of neighbors for each agent, which is different from the usual sense that neighbors are selected by the distance between agents in the state space. In the proposed strategies, the neighbor set for each agent is determined by the distance or difference between agents in the index space after ordering and labeling all agents according to certain ordering rules including weighted order and lexicographic order. The consensus analysis of the proposed algorithms is presented with some existing results on algebraic graph theory and matrix analysis. Meanwhile, by realizing the relations between order preservation and collision-free, a systematic analysis framework on order preservation and hence collision-free for agents in arbitrary dimension is provided based on tools from monotone systems theory. Illustrated numerical examples are presented to validate the effectiveness of the proposed strategies.

Synchronous Hybrid Event- and Time-Driven Consensus in Multiagent Networks With Time Delays.

This paper studies the delay robustness of a class of synchronous hybrid event- and time-driven consensus protocols in undirected networks. These protocols can ensure the system performance at reduced data-sampling rates. We consider three types of time delays in feedbacks, including one common time delay, multiple time-invariant delays, and multiple time-varying delays; and by sampled-data control techniques, we characterize the maximum allowable time delay and the event-detecting period for solving the average consensus problem in terms of the algebraic structure of interaction topologies. Simulations are given to show the effectiveness of theoretical results.

Second-order global consensus in multiagent networks with random directional link failure.

In this paper, we consider the second-order globally nonlinear consensus in a multiagent network with general directed topology and random interconnection failure by characterizing the behavior of stochastic dynamical system with the corresponding time-averaged system. A criterion for the second-order consensus is derived by constructing a Lyapunov function for the time-averaged network. By associating the solution of random switching nonlinear system with the constructed Lyapunov function, a sufficient condition for second-order globally nonlinear consensus in a multiagent network with random directed interconnections is also established. It is required that the second-order consensus can be achieved in the time-averaged network and the Lyapunov function decreases along the solution of the random switching nonlinear system at an infinite subsequence of the switching moments. A numerical example is presented to justify the correctness of the theoretical results.

Distributed average consensus in multi-agent networks with limited bandwidth and time-delays

This paper studies the distributed average consensus problem of multi-agent digital networks with time-delays. For the network, each agent can only exchange symbolic data with its neighbours. We provide a distributed average consensus protocol which uses the quantized and time-delay information. We consider two types of dynamic encoders/decoders in our protocol. One uses inverse proportion function as scaling function, while the other uses exponential function as scaling function. All agents can reach average consensus asymptotically with our protocol. Furthermore, we show that the average consensus protocol is robust to finite symmetric time-delays, but is sensitive to asymmetric time-delays that will destroy the average consensus of the networks. Finally, simulations are presented to illustrate validity of our theoretical results.

Consensus of Multiagent Networks with Intermittent Interaction and Directed Topology

Intermittent interaction control is introduced to solve the consensus problem for second-order multiagent networks due to the limited sensing abilities and environmental changes periodically. And, we get some sufficient conditions for the agents to reach consensus with linear protocol from the theoretical findings by using the Lyapunov control approach. Finally, the validity of the theoretical results is validated through the numerical example.

Algebraic criteria for second-order global consensus in multi-agent networks with intrinsic nonlinear dynamics and directed topologies

This paper discusses the second-order globally nonlinear consensus in general multi-agent directed networks with both non-time-delay and time-delay couplings. Some easily manageable delay-independent algebraic criteria are presented to unravel the underlying mechanics for reaching the second-order consensus. The obtained results are associated with the underlying network interactive topologies, inner coupling matrices and coupling gains between agents. Theoretical derivation is complemented by its validation on a simulation example.

Adaptive finite-time consensus in multi-agent networks

This paper is concerned with the finite-time consensus problem of distributed agents having non-identical unknown nonlinear dynamics, to a leader agent that also has unknown nonlinear control input signal. By parameterization of unknown nonlinear dynamics, a Lyapunov technique in conjunction with homogeneity technique is presented for designing a decentralized adaptive finite-time consensus control protocol in undirected networks. Homogeneous Lyapunov functions and homogeneous vector fields are introduced in the stability analysis although the whole system is not homogeneous. Theoretical analysis shows that leader-following consensus can be achieved in finite-time, meanwhile, finite-time parameter convergence can be also guaranteed under the proposed control scheme. An example is given to validate the theoretical results.

Pinning consensus in networks of multiagents via a single impulsive controller.

In this paper, we discuss pinning consensus in networks of multiagents via impulsive controllers. In particular, we consider the case of using only one impulsive controller. We provide a sufficient condition to pin the network to a prescribed value. It is rigorously proven that in case the underlying graph of the network has spanning trees, the network can reach consensus on the prescribed value when the impulsive controller is imposed on the root with appropriate impulsive strength and impulse intervals. Interestingly, we find that the permissible range of the impulsive strength completely depends on the left eigenvector of the graph Laplacian corresponding to the zero eigenvalue and the pinning node we choose. The impulses can be very sparse, with the impulsive intervals being lower bounded. Examples with numerical simulations are also provided to illustrate the theoretical results.

Stability Switches of Arbitrary High-Order Consensus in Multiagent Networks with Time Delays

High-order consensus seeking, in which individual high-order dynamic agents share a consistent view of the objectives and the world in a distributed manner, finds its potential broad applications in the field of cooperative control. This paper presents stability switches analysis of arbitrary high-order consensus in multiagent networks with time delays. By employing a frequency domain method, we explicitly derive analytical equations that clarify a rigorous connection between the stability of general high-order consensus and the system parameters such as the network topology, communication time-delays, and feedback gains. Particularly, our results provide a general and a fairly precise notion of how increasing communication time-delay causes the stability switches of consensus. Furthermore, under communication constraints, the stability and robustness problems of consensus algorithms up to third order are discussed in details to illustrate our central results. Numerical examples and simulation results for fourth-order consensus are provided to demonstrate the effectiveness of our theoretical results.