Consensus problems of first-order dynamic multi-agent systems with multiple time delays

Consensus problems of first-order multi-agent systems with multiple time delays are investigated in this paper. We discuss three cases： 1） continuous, 2） discrete, and 3） a continuous system with a proportional plus derivative controller. In each case, the system contains simultaneous communication and input time delays. Supposing a dynamic multi-agent system with directed topology that contains a globally reachable node, the sufficient convergence condition of the system is discussed with respect to each of the three cases based on the generalized Nyquist criterion and the frequency-domain analysis approach, yielding conclusions that are either less conservative than or agree with previously published results. We know that the convergence condition of the system depends mainly on each agent’s input time delay and the adjacent weights but is independent of the communication delay between agents, whether the system is continuous or discrete. Finally, simulation examples are given to verify the theoretical analysis.

Guaranteed Cost Consensus for High-dimensional Multi-agent Systems With Time-varying Delays

Guaranteed cost consensus analysis and design problems for high-dimensional multi-agent systems with time varying delays are investigated. The idea of guaranteed cost con trol is introduced into consensus problems for high-dimensiona multi-agent systems with time-varying delays, where a cos function is defined based on state errors among neighboring agents and control inputs of all the agents. By the state space decomposition approach and the linear matrix inequality(LMI)sufficient conditions for guaranteed cost consensus and consensu alization are given. Moreover, a guaranteed cost upper bound o the cost function is determined. It should be mentioned that these LMI criteria are dependent on the change rate of time delays and the maximum time delay, the guaranteed cost upper bound is only dependent on the maximum time delay but independen of the Laplacian matrix. Finally, numerical simulations are given to demonstrate theoretical results.

Consensus problem of second-order multi-agent systems with time-varying communication delay and switching topology

Leader-following stationary consensus problem is investigated for the second-order multi-agent systems with timevarying communication delay and switching topology. Based on Lyapunov-Krasovskii functional and Lyapunov-Razumikhin functions respectively, consensus criterions in the form of linear matrix inequality （LMI） are obtained for the system with time-varying communication delays under static interconnection topology con- verging to the leader＇s states. Moreover, the delay-dependent consensus criterion in the form of LMI is also obtained for the system with time-invariant communication delay and switching topologies by constructing Lyapunov-Krasovskii functional. Numerical simulations present the correctness of the results.

Leader-following consensus criteria for multi-agent systems with time-varying delays and switching interconnection topologies

We consider multi-agent systems with time-varying delays and switching interconnection topologies. By con- structing a suitable Lyapunov-Krasovskii functional and using the reciprocally convex approach, new delay-dependent consensus criteria for the systems are established in terms of linear matrix inequalities （LMIs）, which can be easily solved by using various effective optimization algorithms. Two numerical examples are given to illustrate the effectiveness of the proposed methods.

Multi-agent consensus with time-varying delays and switching topologies

The consensus problems of multi-agents with time-varying delays and switching topologies are studied. First, assume that an agent receives state information from its neighbors with fixed communication delays and processes its own state information with time-varying self-delay respectively. The state time-delay feedback is introduced into the existing consensus protocol to begenerate an improved protocol. Then a sufficient condition is derived which can make the system with time-varying self-delays achieve the consensus. On this basis, a specific form of consensus equilibrium influenced by the initial states of agents, time-delays and state feedback intensity is figured out. In addition, the multi-agent consensus is considered with time-varying topologies. Finally, simulations are presented to il ustrate the validity of theoretical results.

Average consensus of multi-agent systems with communication time delays and noisy links

In this paper,we consider the average-consensus problem with communication time delays and noisy links.We analyze two different cases of coupling topologies：fixed and switching topologies.By utilizing the stability theory of the stochastic differential equations,we analytically show that the average consensus could be achieved almost surely with the perturbation of noise and the communication time delays even if the time delay is time-varying.The theoretical results show that multi-agent systems can tolerate relatively large time delays if the noise is weak,and they can tolerate relatively strong noise if the time delays are low.The simulation results show that systems with strong noise intensities yield slow convergence.

Hybrid-triggered consensus for multi-agent systems with time-delays,uncertain switching topologies, and stochastic cyber-attacks

We propose a new approach to discuss the consensus problem of multi-agent systems with time-varying delayed control inputs, switching topologies, and stochastic cyber-attacks under hybrid-triggered mechanism.A Bernoulli variable is used to describe the hybrid-triggered scheme, which is introduced to alleviate the burden of the network.The mathematical model of the closed-loop control system is established by taking the influences of time-varying delayed control inputs,switching topologies, and stochastic cyber-attacks into account under the hybrid-triggered scheme.A theorem as the main result is given to make the system consistent based on the theory of Lyapunov stability and linear matrix inequality.Markov jumps with uncertain rates of transitions are applied to describe the switch of topologies.Finally, a simulation example demonstrates the feasibility of the theory in this paper.

Finite-time consensus of heterogeneous multi-agent systems

We investigate the finite-time consensus problem for heterogeneous multi-agent systems composed of first-order and second-order agents.A novel continuous nonlinear distributed consensus protocol is constructed,and finite-time consensus criteria are obtained for the heterogeneous multi-agent systems.Compared with the existing results,the stationary and kinetic consensuses of the heterogeneous multi-agent systems can be achieved in a finite time respectively.Moreover,the leader can be a first-order or a second-order integrator agent.Finally,some simulation examples are employed to verify the efficiency of the theoretical results.

Consensus of high-order dynamic multi-agent systems with switching topology and time-varying delays

This paper studies the consensus problems for a group of agents with switching topology and time-varying communication delays, where the dynamics of agents is modeled as a high-order integrator. A linear distributed consensus protocol is proposed, which only depends on the agent＇s own information and its neighbors＇ partial information. By introducing a decomposition of the state vector and performing a state space transformation, the closed-loop dynamics of the multi-agent system is converted into two decoupled subsystems. Based on the decoupled subsystems, some sufficient conditions for the convergence to consensus are established, which provide the upper bounds on the admissible communication delays. Also, the explicit expression of the consensus state is derived. Moreover, the results on the consensus seeking of the group of high-order agents have been extended to a network of agents with dynamics modeled as a completely controllable linear time-invariant system. It is proved that the convergence to consensus of this network is equivalent to that of the group of high-order agents. Finally, some numerical examples are given to demonstrate the effectiveness of the main results.

Consensus of second-order multi-agent systems with nonuniform time delays

In this study, the consensus problem for a class of second-order multi-agent systems with nonuniform time delays is investigated. A linear consensus protocol is used to make all agents reach consensus and move with a constant velocity. By a frequency-domain analysis, a simplified sufficient condition is given to guarantee the consensus stability of the dynamic system. Finally, the effectiveness of the obtained theoretical results is illustrated through numerical simulations.

Distributed Fault Detection for Consensus in Second-Order Discrete-Time Multiagent Systems with Adversary

This paper is concerned with distributed fault detection of second-order discrete-time multi-agent systems with adversary,where the adversary is regarded as a slowly time-varying signal.Firstly,a novel intrusion detection scheme based on the theory of unknown input observability( UIO) is proposed. By constructing a bank of UIO,the states of the malicious agents can be directly estimated. Secondly,the faulty-node-removal algorithm is provided.Simulations are also provided to demonstrate the effectiveness of the theoretical results.

基于概率时间自动机的异构多agent自适应运行时验证

多agent自适应系统在运行过程中需要根据环境进行自适应调整。异构agent能够提高agent的使用效率和降低系统的构建成本,但存在复杂的协作问题,因此提出一种基于概率时间自动机的异构多agent自适应系统运行时验证方法。该方法通过形式化描述异构agent的功能特征并融合环境中的随机因素构建概率时间自动机模型模拟自适应系统的运行过程,针对异构agent之间的协作逻辑制定安全约束条件以确保系统运行中状态迁移流程的安全性。通过模型检查结合运行时定量验证方法进行实验验证,在智能泊车系统案例中应用该方法。实验结果表明,agent之间协作逻辑的正确性可以有效保证系统运行时的稳定性,且相较于不使用运行时定量验证的初始系统在相同时间内正常运行的时间提升了21%左右。

Sufficient Condition for Average Consensus of Directed Networked Multi-agent Systems with Time Delays

The average consensus problem in a directed network of multi-agent systems with communication time delays was investigated. The directed networks were balanced and weakly connected with fixed or switching topology digraph. Based on frequency domain analysis method, a sufficient condition of asymptotic stability of multi-agent systems with time delays was obtained,where the analytic formula between the maximum time delay and the directed network structure was provided. The maximum time delay can be derived directly and easily by the eigenvalue of Laplacian L. Numerical examples confirm the effectiveness of the proposed technique.

Finite-time consensus for leader-following multi-agent systems over switching network topologies

Finite-time consensus problem of the leader-following multi-agent system under switching network topologies is studied in this paper. Based on the graph theory, matrix theory, homogeneity with dilation, and LaSalle＇s invariance principle, the control protocol of each agent using local information is designed, and the detailed analysis of the leader- following finite-time consensus is provided. Some examples and simulation results are given to illustrate the effectiveness of the obtained theoretical results.

Effect of Nucleating Agent on the Crystallization of Tailings Glass Ceramics Prepared by One-time Sintering

Glass ceramics was made by the one-time sintering method using the main raw material of iron tailings. On the basis of quaternary system of CaO-MgO-Al2O3-SiO2, using DTA, XRD and SEM, the effects of different nucleating agents and mixing amounts as well as heat treatment on the crystallization of railings glass ceramics were studied. The experimental results show that, nucleating agent and heat treatment are two necessary conditions for one-time sintering preparation of tailings glass ceramics namely, only adding nucleating agent or experiencing heat treatment, the quaternary system can not crystallize. The composite nucleating agent consisting of Cr2O3 and TiO2 can further lead to the crystallization of the CaO-MgO-A1203-SiO2 quaternary system at the lower temperature, with the major phase of diopside. In the range of mass content, 0%-4%, crystal intensity and crystal content grow. But when mass content is more than 4%, the crystal size will become coarser and the crystal distribution will be less regular. Different heat treatment regimes do not change the composition of the crystalline major phase in the glass ceramics crystallization of CaO-MgO-Al2O3-SiO2 system. In the range of 30-60 minutes, with the extension of nucleation and crystallization, crystallization degree enhanced, but if the holding time surpasses 60 minutes, the crystallization is worse.

Fixed-time Consensus for Leader-follower Second-order Multi-agent Systems

We analyse the fixed-time consensus problem for multi-agent systems with leaderfollower mode. Based on a follower’s observation structure for the leader’s information, it is proved that the estimation errors can be converged to zero at a fixed time. From this stability and a sliding mode structure, we derive a control input of followers, which provides a critical support for fixed-time consensus. The simulation results demonstrate that this control approach does conduce to the implementation of the fixed-time synchronization.

Weighted average consensus problem in networks of agents with diverse time-delays

This paper studies the weighted average consensus problem for networks of agents with fixed directed asymmetric unbalance information exchange topology. We suppose that the classical distributed consensus protocol is destroyed by diverse time-delays which include communication time-delay and self time-delay. Based on the generalized Nyquist stability criterion and the Gerschgorin disk theorem, some sufficient conditions for the consensus of multi-agent systems are obtained. And we give the expression of the weighted average consensus value for our consensus protocol. Finally, numerical examples are presented to illustrate the theoretical results.