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This study is concerned with the problem of dynamical distributed consensus for multi-agent systems with nonlinear dynamics. Following the nearest neighbour rule, an adaptive consensus protocol is designed for such systems without using any global information, where the coupling weight of an agent from its neighbours adaptively updates according to the differences from the mean activity of the agent and its neighbours. The analysis shows that, under some mild assumptions, the adaptive law can achieve local and global consensus for any network with connected communication graph. Numerical simulations, illustrated by a common second-order consensus example, are performed to demonstrate the effectiveness of the presented results.

This paper provides a review of the consensus problem as one of the most challenging issues in the distributed control of the multi-agent systems (MASs). In this survey, firstly, the consensus algorithms for the agents with the single-integrator, double-integrator and high-order dynamic models were collected from various research works, and the convergence condition for each of these algorithms was explained. Secondly, all the consensus-related problems such as those in the sampled-data consensus, quantized consensus, random-network consensus, leader–follower consensus, finite-time consensus, bipartite consensus, group consensus/cluster consensus, and the scaled consensus were analyzed and compared with each other. Thirdly, we focused on the common control techniques used for the consensus problems in the presence of disturbance and divided all these control methods into two categories: robust control and adaptive control. Finally, we reviewed the most prevalent consensus applications in the MASs, including the subjects of rendezvous, formation control, axial alignment and the wireless sensor networks.

A novel distributed prescribed-time leader–follower tracking consensus control strategy is proposed for high-order nonlinear multi-agent systems with lower triangular time-varying dynamics in directed communication topology. Firstly, a distributed prescribed-time state observer (DPTSO) is presented for each follower to estimate the states of the leader. Based on the DPTSO, the consensus problem is transformed into a tracking control problem; that is, the follower tracks the estimations of the DPTSO. Then, a distributed prescribed-time controller is developed by using the cascade control framework and dynamic control, which avoids the problem of differential explosion in traditional back-stepping control. The convergence time of the DPTSO and distributed prescribed-time controller is not only explicitly pre-specified but also determined regardless of the initial states of the system and control parameters. Finally, it is demonstrated that the closed-loop systems realize prescribed-time full-state leader–follower tracking consensus. Simulation results show that the method is effective and feasible.

This study addresses leader-following consensus problems for multi-agent systems with second-order non-linear dynamics, under the assumption that each agent can only communicate with its neighbouring agents intermittently and the communication topology does not keep strongly connected or contain a spanning tree all along. Firstly, a class of distributed consensus algorithms are designed only based on the relative local intermittent information. Notions of completely and partly intermittent communication are proposed. Some sufficient conditions are derived for achieving consensus tracking under a general fixed topology with completely and partly intermittent communication. Then, as an extension, leader-following consensus tracking is studied under time-varying intermittent communication topologies. Finally, the effectiveness of the main results is illustrated by numerical simulations.

In this paper, a consensus tracking protocol for nonlinear agents is presented, which is based on the Nonlinear Dynamic Inversion (NDI) technique. Implementation of such a technique is new in the context of the consensus tracking problem. The tracking capability of nonlinear dynamic inversion (NDI) is exploited for a leader-follower multi-agent scenario. We have provided all the mathematical details to establish its theoretical foundation. Additionally, a convergence study is provided to show the efficiency of the proposed controller. The performance of the proposed controller is evaluated in the presence of both (a) random switching topology among the agents and (b) random switching of leader–follower connections, which is realistic and not reported in the literature. The follower agents track various trajectories generated by a dynamic leader, which describes the tracking capability of the proposed controller. The results obtained from the simulation study show how efficiently this controller can handle the switching topology and switching leader-follower connections.

The article investigates the consensus of nonlinear stochastic multi-agent systems with input and output delay using a distributed predictive controller. First, an error is defined for the design of dynamic reference information, which can be used to estimate the leader-following consensus error. Second, a prediction scheme is employed to eliminate the effect of time delays, and a distributed predictive controller is established by utilizing dynamic reference and prediction information. Then, the consensus error is considered through a new closed-loop system, and it is proved that the distributed predictive control method can achieve leader-following consensus on a nonlinear stochastic multi-agent system with input and output delays. Finally, the single-link robotic arms model is utilized to validate the effectiveness of the distributed predictive control.

Networked systems are often subject to environmental uncertainties and communication delays, which make timely and accurate information exchange among neighbours difficult or impossible. This study investigates the distributed consensus problem of dynamical networks of multi-agents in which each agent can only obtain noisy and delayed measurements of the states of its neighbours. The authors consider consensus protocols that take into account both the noisy measurements and the communication time delays, and introduce the notions of almost sure average-consensus and pth moment average-consensus. Using a convergence theorem for continuous-time semimartingales and moment inequality techniques for stochastic delay differential equations, the authors establish sufficient conditions for both almost sure and moment average-consensus. These results naturally generalise to networks with arbitrary and Markovian switching topologies. The consensus protocol considered here can be applied to networks with arbitrary bounded communication delays, which appears to the first consensus algorithm that is both average preserving and robust to arbitrarily sized delays. Numerical simulations are also provided to demonstrate the theoretical results.

In this paper, the asymmetric bipartite consensus problem of a nonlinear multi-agent system is solved using Distributed Nonlinear Dynamic Inversion (DNDI) based controller. The application of DNDI is new in the context of asymmetric bipartite consensus, and it inherits all the advantages of NDI and works efficiently to solve the asymmetric bipartite problem. The mathematical details presented provide theoretical proof of its efficiency. A realistic simulation study is performed to establish the claims. The controller’s performance has been tested in the presence of communication noise, and the results are promising.

The deepening integration of distributed energy resources in smart grids catalyzes the development of distributed energy management methods owing to their superiorities in flexibility, scalability, and robustness against single-point failures. Nevertheless, the reliance on localized implementation of distributed methods increases the susceptibility to malicious attacks. This paper focuses on the economic dispatch of smart grids under deception attacks which can artificially tamper with the information among the communication network. We investigate and reveal how such attacks deteriorate the results of optimal power generation schedule. Then, an easy-to-implement defense strategy based on the extreme values discarding technique is developed to realize resilient energy management. It is shown that under a 2 R + 1 -robustness assumption on communication networks, the proposed method is resilient to R -local deception attacks. Compared with existing works, the benefits of the defense strategy include no restricted form of deception attacks and no isolation of attacked nodes. Finally, simulation examples verify the effectiveness of the proposed method.

This paper investigates the problem of global consensus between a complex dynamical network (CDN) and a known goal signal by designing an impulsive consensus control scheme. The dynamical network is complex with respect to the uncertainties, nonidentical nodes, and coupling time-delays. The goal signal can be a measurable vector function or a solution of a dynamical system. By utilizing the Lyapunov function and Lyapunov-Krasovskii functional methods, robust global exponential stability criteria are derived for the error system, under which global exponential impulsive consensus is achieved for the CDN. These criteria are expressed in terms of linear matrix inequalities (LMIs) and algebraic inequalities. Thus, the impulsive controller can be easily designed by solving the derived inequalities. Meanwhile, the estimations of the consensus rate for global exponential consensus are also obtained. Two examples with numerical simulations are worked out for illustration. [PUBLICATION ABSTRACT]