Leader-following Cluster Consensus in Multi-agent Systems with Intermittence

In this paper, the cluster consensus problem of first-order nonlinear multi-agent systems with aperiodic intermittent communication is studied through pinning leader-following approach. The pinning consensus algorithm based on the relative local intermittent information is designed according to the varies linking ways of clustered network structure. New notions of leading intermittence and inter-cluster intermittence which related to the intermittent linking ways of leader-following clustered structure are developed, and several new systems with intermittence are established due to the new notions. Besides, dynamics with inherent delay are also considered to extend our results to a more general framework. The original communication graph without intermittent pattern is supposed to be directed and weakly connected. Some consensus criteria are derived to guarantee that the cluster consensus problem for the systems with intermittent communication can be solved. Finally, numerical simulations are given to illustrate the effectiveness of the theoretical results.     

Distributed consensus of delayed multi‐agent systems with nonlinear dynamics via intermittent control

In this paper, a distributed consensus of delayed multi‐agent systems with a leader is investigated, and a nonlinear protocol is proposed based on intermittent control. A notable feature of this protocol is to address second‐order consensus problems for delayed nonlinear multi‐agent systems, where agents can only communicate with each other over some disconnected time intervals. Some sufficient conditions to guarantee the consensus over fixed and switching topologies are derived. It is shown that second‐order consensus for delayed multi‐agent system with intermittent control can be achieved if the time delay is less than a critical value and the communication time duration is larger than a threshold value. In addition, some numerical examples are given to illustrate the effectiveness and feasibility of the theoretical results.     

Synchronization of complex networks with coupling delays via adaptive pinning intermittent control

The problem of exponential synchronization for a class of general complex dynamical networks with nonlinear coupling delays by adaptive pinning periodically intermittent control is considered in this paper. We use the methods of the adaptive control, pinning control and periodically intermittent control. Based on the piecewise Lyapunov stability theory, some less conservative criteria are derived for the global exponential synchronization of the complex dynamical networks with coupling delays. And several corresponding adaptive pinning feedback synchronization controllers are designed. These controllers have strong robustness against the coupling strength and topological structure of the network. Using the delayed nonlinear system as the nodes of the networks, a numerical example of the complex dynamical networks with nonlinear coupling delays is given to demonstrate the effectiveness of the control strategy.     

Asynchronous Consensus in Continuous-Time Multi-Agent Systems With Switching Topology and Time-Varying Delays

The paper studies asynchronous consensus problems of continuous-time multi-agent systems with discontinuous information transmission. The proposed consensus control strategy is implemented based on the state information of each agent's neighbors at some discrete times. The asynchrony means that each agent's update times, at which the agent adjusts its dynamics, are independent of others'. Furthermore, it is assumed that the communication topology among agents is time-dependent and the information transmission is with bounded time-varying delays. If the union of the communication topology across any time interval with some given length contains a spanning tree, the consensus problem is shown to be solvable. The analysis tool developed in this paper is based on nonnegative matrix theory and graph theory. The main contribution of this paper is to provide a valid distributed consensus algorithm that overcomes the difficulties caused by unreliable communication channels, such as intermittent information transmission, switching communication topology, and time-varying communication delays, and therefore has its obvious practical applications. Simulation examples are provided to demonstrate the effectiveness of the theoretical results.     

Consensus of multiagent systems based on disturbance observer

The objectives of this work are the development and design of disturbance observers (DO’s) for a team of agents that accomplish consensus on agents’ states in the presence of exogenous disturbances. A pinning control strategy is designed for a part of agents of the multiagent systems without disturbances, and this pinning control can bring multiple agents’ states to reaching an expected consensus value. Under the effect of the disturbances, nonlinear disturbance observers are developed for disturbances generated by an exogenous system to estimate the disturbances. Asymptotical consensus of the multiagent systems with disturbances under the composite controller can be achieved. Finally, by applying an example of multiagent systems with switching topologies and exogenous disturbances, the design of the parameters of DO’s are illuminated.     

Scaled cluster consensus of discrete-time multi-agent systems with general directed topologies

This note proposes a notion of scaled cluster consensus, wherein the final consensus states within different clusters converge to prescribed ratios. Unlike most results in existing literature on cluster consensus, no constraints are imposed on the system topologies under the designed protocol, i.e. the agents are not required to possess any cluster affiliation information of others. For the delay-free case, an explicit scaled cluster consensus function is provided by exploring the characteristics of stochastic matrices. Diverse input delays and asymmetric communication delays are both considered, and sufficient condition for scaled cluster consensus is derived based on frequency domain analysis. Finally, numerical examples are given to illustrate the effectiveness of the presented results.     

Consensus of Multi-Agent Systems in Directed Networks With Nonuniform Time-Varying Delays

In this note, we study consensus problems for continuous-time multi-agent systems in directed networks with dynamically changing topologies and nonuniform time-varying delays. We have analyzed consensus problems in the following three cases: 1) directed networks with dynamically changing topologies and nonuniform time-varying delays; 2) directed networks with intermittent communication and data packet dropout; and 3) finite-time consensus in directed networks with dynamically changing topologies and nonuniform time-varying delays. We propose a new approach based on a tree-type transformation to investigate consensus problems in all three cases. Some necessary and/ or sufficient conditions are established. Simulation results are also given to demonstrate the theoretical results.      

Pinning Exponential Synchronization of Nonlinearly Coupled Neural Networks with Mixed Delays via Intermittent Control

This paper is concerned with the exponential synchronization problem of nonlinearly coupled neural networks with mixed delays. By employing the intermittent control strategy, several appropriate linear and adaptive pinning controllers are designed in each control period. With the help of a new differential inequality, some conditions are proposed to guarantee that the coupled networks can realize pinning synchronization exponentially. The minimum number of pinned nodes is determined by using high-degree pinning scheme. Two numerical examples are provided finally to demonstrate the effectiveness of the theoretical results.     

Consensus of Delayed Multi‐agent Systems via Intermittent Impulsive Control

A novel intermittent impulsive scheme is presented to realize consensus of multi‐agent systems with time‐varying delay in this paper because intermittent impulsive control may break through the limitation of upper bound of impulsive intervals in general impulsive control in our consensus scheme. Instead of activating all the time, we introduce the intermittent impulsive control approach into the delayed multi‐agent systems where the impulsive controller is only functioned in the control windows. Based on the algebraic graph theory, the Lyapunov stability theory, and Halanay inequality matrix theory, some adequate conditions are proposed to guarantee the consensus of delayed multi‐agent systems via pinning intermittent impulsive control. Simulation results are provided ultimately to verify the validity of the proposed control mechanism.     

Intermittent observer-based consensus control for multi-agent systems with switching topologies

In this paper, we focus on the consensus problem for leaderless and leader–followers multi-agent systems with periodically intermittent control. The dynamics of each agent in the system is a linear system, and the interconnection topology among the agents is assumed to be switching. We assume that each agent can only share the outputs with its neighbours. Therefore, a class of distributed intermittent observer-based consensus protocols are proposed for each agent. First, in order to solve this problem, a parameter-dependent common Lyapunov function is constructed. Using this function, we prove that all agents can access a prescribed value, under the designed intermittent controller and observer, if there are suitable conditions on communication. Second, based on the investigation of the leader-following consensus problem, we design a new distributed intermittent observer-based protocol for each following agent. Finally, we provide an illustrative example to verify the effectiveness of the proposed approach.     

Robust consensus of multi-agent systems with time-delays and exogenous disturbances

In this paper, the robust consensus of multi-agent dynamical systems with time-delays and exogenous disturbances is studied. A pinning control strategy is designed for a parts of agents of the multi-agent systems without disturbances, and this pinning control can bring multiple agents?? states to an expected consensus track. Under the effects of the disturbances, disturbance observers based control (DOBC) are developed for disturbances generated by an exogenous system to estimate the disturbances. Asymptotical consensus of the multi-agent systems with disturbances under the composite controller can be achieved for fixed and switching topologies. Finally, by applying an example of multi-agent systems with switching topologies and exogenous disturbances, the design of the parameters of DOBC are illuminated.     

Modified leader-following consensus of time-delay multi-agent systems via sampled control and smart leader

In this paper, the consensus problems of multiple agents with continuous-time single-integrator dynamics are studied, where each agent can obtain the position data of its neighboring agents at discrete-time points by using the periodic sampling technology and zero-order hold circuit. The smart leader is introduced, which can adjust the interaction strength between itself and the target point according to the state errors between itself and its neighboring followers. The modified leader-following consensus problem is defined as the leader-following consensus problem when the smart leader is adopted. Different leader-following consensus protocols are obtained for the multi-agent systems with or without sampling delays. The theoretical results, which are analysed with Lyapunov stability theory, can decrease the tracking error of the system, especially for the multi-agent systems with disturbance generated by actuator faults. Some simulation examples and real experiments are presented for illustration.     

Clustering in diffusively coupled networks

This paper shows how different mechanisms may lead to clustering behavior in connected networks consisting of diffusively coupled agents. In contrast to the widely studied synchronization processes, in which the states of all the coupled agents converge to the same value asymptotically, in the cluster synchronization problem studied in this paper, we require all the interconnected agents to evolve into several clusters and each agent only to synchronize within its cluster. The first mechanism is that agents have different self-dynamics, and those agents having the same self-dynamics may evolve into the same cluster. When the agents’ self-dynamics are identical, we present two other mechanisms under which cluster synchronization might be achieved. One is the presence of delays and the other is the existence of both positive and negative couplings between the agents. Some sufficient and/or necessary conditions are constructed to guarantee n-cluster synchronization. Simulation results are presented to illustrate the effectiveness of the theoretical analysis.     

基于牵制控制的异质多智能体系统的群一致性研究

为了研究由线性的一阶智能体、二阶智能体和非线性的EL （Euler-Lagrange）结构智能体组成的异质多智能体系统的群一致性,并实现同一个子群中智能体状态趋于期望的状态,针对无向的固定拓扑情况,提出了基于牵制控制的分布式控制协议。并通过代数图论、李雅普诺夫函数和拉塞尔不变集原理证明了控制协议的可行性。数值仿真结果表明:在所提控制协议作用下能够实现包含非线性EL结构的异质多智能体系统的群一致性,与未引入牵制控制的群一致性算法相比各个子群能够趋于期望的状态。     

Consensus with guaranteed convergence rate of high-order integrator agents in the presence of time-varying delays

This paper aims to study the consensus problem in directed networks of agents with high-order integrator dynamics and fixed topology. It is considered the existence of non-uniform time-varying delays in the agents control laws for each interaction between agents and their neighbours. Based on Lyapunov–Krasovskii stability theory and algebraic graph theory, sufficient conditions, in terms of linear matrix inequalities, are given to verify if consensus is achieved with guaranteed exponential convergence rate. The efficiency of the proposed method is verified by numerical simulations. The simulations reveal that the conditions established in this work outperformed the similar existing ones in all numerical tests accomplished in this paper.     

Group consensus of multi-agent systems in directed networks with noises and time delays

In this paper, group consensus problems in fixed directed networks of dynamic agents are investigated. Group consensus means that the agents in each group share a consistent value while there is no agreement between any two groups. Based on algebraic graph theory, sufficient conditions guaranteeing group consensus under the proposed control protocol in the presence of random noises and communication delays are derived. The analysis uses a stability result of Mao for stochastic differential delay equations, which ensures the consensus can be achieved almost surely and exponentially fast. Numerical examples are provided to demonstrate the availability of the obtained results as well as the effect of time delay/noise intensity.     

Exponential finite-time couple-group consensus for agents in cooperative-competitive networks via pinning method

This paper investigates the exponential finite-time couple-group consensus problem for multi-agent systems via pinning control method. Considering the hybrid cooperative and competitive interactions among the agents, a new nonlinear distributed control protocol is proposed. Under the pinning control scheme, the criteria for guaranteeing the system with weakly connected communication topology achieve exponential couple-group consensus in finite time are obtained, and the pinning control strategies are presented as well. Furthermore, the results show that the settling time for the system to reach consensus is independent of the initial states of the agents. Finally, the correctness of our results is verified by some simulations.     

Consensus problems in networks of agents with double-integrator dynamics and time-varying delays

In this article, we consider consensus problems in networks of agents with double-integrator dynamics and non-uniform time-varying delays. The agent dynamics is adopted as a typical point mass model based on Newton's law. Without assuming that the weighting factors in the information update schemes are non-negative, we propose two protocols such that both the state and the velocity of agents achieve consensus. An equivalent reduced-order system is introduced to analyse the convergence of the protocols. Some necessary and (or) sufficient conditions for consensus are established in terms of linear matrix inequalities. Simulation results are provided that demonstrate the effectiveness of our theoretical results.     

Exhaustive stability analysis in a consensus system with time delay and irregular topologies

A consensus problem and its stability are studied for a group of agents with second-order dynamics and communication delays. The communication topologies are taken as irregular but always connected and undirected. The delays are assumed to be quasi-static and the same for all the interagent channels. A decentralised, PD-like control structure is proposed to create a consensus in the position and velocity of the agents. We present an interesting factorisation feature for the characteristic equation of the system which simplifies the stability analysis considerably from a prohibitively large dimensional problem to a manageable small scale. It facilitates a rare stability picture in the space of the control parameters and the delay, utilising a paradigm named cluster treatment of characteristic roots (CTCR). The influence of the individual factors on the absolute and relative stability of the system is studied. This leads to the introduction of two novel concepts: the most exigent eigenvalue, which refers to the one that defines the delay stability margin of the system, and the most critical eigenvalue, which is the one that dictates the consensus speed of the system. It is observed that the most exigent eigenvalue is not always the most critical, and this feature may be used as a design tool for the control logic. Case studies and simulations results are presented to verify these concepts.     

Stability of formation control using a consensus protocol under directed communications with two time delays and delay scheduling

We consider a linear algorithm to achieve formation control in a group of agents which are driven by second-order dynamics and affected by two rationally independent delays. One of the delays is in the position and the other in the velocity information channels. These delays are taken as constant and uniform throughout the system. The communication topology is assumed to be directed and fixed. The formation is attained by adding a supplementary control term to the stabilising consensus protocol. In preparation for the formation control logic, we first study the stability of the consensus, using the recent cluster treatment of characteristic roots (CTCR) paradigm. This effort results in a unique depiction of the non-conservative stability boundaries in the domain of the delays. However, CTCR requires the knowledge of the potential stability switching loci exhaustively within this domain. The creation of these loci is done in a new surrogate coordinate system, called the ‘spectral delay space (SDS)’. The relative stability is also investigated, which has to do with the speed of reaching consensus. This step leads to a paradoxical control design concept, called the ‘delay scheduling’, which highlights the fact that the group behaviour may be enhanced by increasing the delays. These steps lead to a control strategy to establish a desired group formation that guarantees spacing among the agents. Example case studies are presented to validate the underlying analytical derivations.