Discrete-time Multi-agent Consensus Research Articles

Consensus of multiagent with interaction distortions via echo control

This paper studies the discrete-time multiagent consensus problem with kinds of diverse interaction distortions which are related to the states of agents, and a novel dual switching control strategy is proposed, named echo control, to make the system achieve state consensus. The main feature of the echo control strategy is that agents resend the information flows (received from neighbors) to the corresponding neighbor, just like the reflecting of sound waves. In other words, every individual under the echo control strategy is not only the sender and receiver of the information flows, but also the reflector of its neighbors’ messages. In this way, a negative feedback loop is constructed between every two agents, which is designed to ensure the stability of the multiagent system (MAS), and then the agents’ states will converge to a common value. The effectiveness of the echo control protocol is theoretically analyzed, and numerical simulations validate the correctness of the relevant results.

Dynamic Event-triggered Control in Discrete-time Multi-agent Consensus over Directed Topologies

In this paper, we study the problem of multi-agent consensus in networks of discrete-time integrator agents with directed topologies. With the aim to reduce the frequency of interaction among agents for saving energy expenses, we develop three triggering-based protocols for strongly connected agent networks. Our common strategy is to use triggering protocols that take account of the state values received from neighbors in determining the event times. The first two protocols are event-triggering type, where the thresholds are state dependent so that when the agents are far from consensus, the events take place less frequently. The two protocols are called static and dynamic depending on the use of auxiliary variables in determining the thresholds. The third protocol is self-triggering type, where at each triggering time, an agent computes the time for its next transmission, which is communicated to its neighbors together with its state data. For these protocols, we present Lyapunov-based design methods, and demonstrate their efficacy through numerical examples.

Event-based discrete-time multi-agent consensus over signed digraphs with communication delays

The ability to ensure the desired performance of the cooperative-antagonistic multi-agent networks (MANs) in the presence of communication constraints is an important task in many applications of real systems. In this paper, under the proposed event-triggered condition (ETC), different types of consensus are obtained under different network topology. We concentrates on the event-based bipartite consensus. It is shown that under the proposed ETC (i) the addressed cooperative-antagonistic network with arbitrary communication delays reaches bipartite consensus provided that the network is balanced; (ii) the network model reaches zero if the network is unbalanced. Further, to avoid the continuously verifying the triggering condition, a self-triggered algorithm is proposed for realizing the bipartite consensus of the network model. A numerical example is given to illustrate the effectiveness of the theoretical results.

Resilient Consensus Through Event-Based Communication

We consider resilient versions of discrete-time multi-agent consensus in the presence of faulty or even malicious agents in the network. In particular, we develop event-triggered update rules which can mitigate the influence of the malicious agents and at the same time reduce the necessary communication. Each regular agent updates its state based on a given rule using its neighbors' information. Only when the triggering condition is satisfied, the regular agents send their current states to their neighbors. Otherwise, the neighbors will continue to use the state received the last time. Assuming that a bound on the number of malicious nodes is known, we propose two update rules with event-triggered communication. They follow the so-called mean subsequence reduced (MSR) type algorithms and ignore values received from potentially malicious neighbors. We provide full characterizations for the necessary connectivity in the network for the algorithms to perform correctly, which are stated in terms of the notion of graph robustness. A numerical example is provided to demonstrate the effectiveness of the proposed approach.

Convergence Rate of Discrete-Time Stochastic Approximation Type Consensus Algorithms

In this paper, we study the convergence rate of the distributed stochastic approximation (SA) type algorithm for the discrete-time multi-agent consensus with communication noises. Basic results of algebraic graph theory and probability limit theory are used to study the closed-form solution of the consensus error. Under mild conditions on the decreasing step size and the network topology, we give upper bounds for the mean square and almost sure convergence rates of the consensus errors. Furthermore, for the case with balanced graphs, the exact convergence rate is provided for the mean square of the consensus error.

A distributed event‐triggered scheme for discrete‐time multi‐agent consensus with communication delays

This study mainly investigates the event-triggered data transmission in discrete-time multi-agent consensus problem with communication delays. A new distributed event-triggered scheme is proposed for the considered multi-agent network model. An action of the agent is triggered by an `event' which is a well-defined condition on the system state. For the proposed event-triggered protocol, the authors prove that the multi-agent network will achieve consensus asymptotically. Numerical examples are provided to demonstrate the effectiveness of the obtained theoretical results.

Discrete-time multi-agent consensus with quantization and communication delays

In this paper, discrete-time multi-agent consensus problem with quantization and communication delays is investigated. A new discrete-time multi-agent consensus model is considered in which each agent can only receive the delayed quantized information from its neighbors. In the presence of quantization and communication delays, it is shown that the multi-agent network can achieve consensus under the connectivity network topology. Simulation examples are also provided to demonstrate the correctness of the theoretical results.