二阶多智能体系统采样控制的一致性

研究在固定拓扑和切换拓扑下,二阶多智能体系统通过采样控制的一致性问题。首先,对于固定拓扑,给出了二阶多智能体系统通过采样控制达到一致性的充要条件;其次,对于切换拓扑,在所有联合切换拓扑有生成树的前提下,建立基于控制参数和采样周期使二阶系统实现一致性的充分条件。最后,用数值仿真验证所给结论的有效性。     

二阶多智能体系统参数自适应的有限时间一致性算法

目前二阶多智能体系统尚未明确给出自适应参数的确定方法,且系统的收敛速度较慢.为在实际应用中预测飞行器多智能体系统下一时刻的状态并提高收敛速度,提出一种参数自适应的一致性算法.将当前智能体间位置和速度的差值作为一致性协议的反馈参数,研究固定拓扑和切换拓扑情形下二阶多智能体系统的有限时间一致性问题,构造Lyapunov函数,同时利用LaSalle不变集原理和齐次理论,得到系统在有限时间内达到稳定的条件,实现对不同飞行器输入状态的自适应调节.仿真结果表明,该算法能够保证多智能体系统在有限时间内实现一致跟踪,且收敛速度较快.     

二阶多智能体系统的线性广义一致性

首次针对二阶多智能体系统提出广义一致性的概念;然后探讨有向网络拓扑结构下的二阶多智能体系统的线性广义一致性问题.通过设计有效的控制协议,使用代数图论和稳定性理论,推导获得二阶的多智能体系统以及带有通信延迟的二阶系统实现线性广义一致性的充分且必要条件.结果表明,在有向网络中,耦合增益参数和拉普拉斯矩阵的特征值对达到广义一致起着关键作用;最后,数值仿真验证了结果的正确性.     

具有随机通信时延的二阶多智能体系统的一致性控制

研究了具有随机通信时延的二阶多智能体系统的一致性控制问题.分别讨论了具有固定拓扑结构和变化拓扑结构两种情形下二阶多智能体系统在具有随机通信时延情况下的一致性问题.通过构造Lyapunov函数的方法得到多智能体系统的时延依赖稳定判据,并以线性矩阵不等式(LMI)的形式给出了系统稳定的条件.最后,仿真和实验结果验证了研究所得结论的正确性和有效性.     

多智能体系统自适应跟踪控制

基于带有非线性动态的二阶多智能体系统,研究了在有动态领导者条件下的跟踪一致性问题。假设跟随者只能获取邻居智能体的相对状态信息,只有一部分跟随者可以获得领导者的位置和速度信息,领导者的控制输入非零且不被任何一个跟随者可知。在通信拓扑为无向连通图的条件下,为了避免全局信息的不确定性,设计了分布式自适应控制协议。将系统的一致性问题转化为误差系统的一致性问题,通过Lyapunov稳定性理论和矩阵理论分析得到了该协议使系统达到一致的充分条件。最后用仿真例子证明了设计方法的有效性。     

通信受限的网络化多智能体系统编队控制

主要研究了具有通信受限及不确定性的无线网络下的二阶多智能体系统的编队控制问题.针对无线网络的介质访问约束,采用二进制序列设计智能体节点调度协议,使得满足约束条件的智能体节点经网络传输其采样信息;另一方面,为建立更符合实际的通信信道模型,区别于传统的固定连接权重拓扑图,考虑到无线网络的不确定性及拓扑连接权重与智能体节点之间距离的关系,利用无线信道的度量指标构建了多智能体通信拓扑的新模型.定义信息更新误差及编队误差,将二阶多智能体系统模型转化为闭环延时系统模型.然后,构造Lyapunov-Krasovskii函数并利用LMI方法设计了编队控制协议.最后,通过仿真验证了所提方法的有效性.     

离散异质多智能体系统的分组一致性控制

针对一类混合异质多智能体系统的分组一致性控制问题进行了研究。具体分析了由一阶智能体和二阶智能体组成的混合异质系统,研究其在离散情况下的分组一致性。基于两个合理的假设提出了线性控制协议,运用代数图论、稳定性理论和矩阵理论,分析协议作用下闭环系统的系统矩阵及动态特性,取得了系统渐近实现分组一致性的充分条件,该条件与系统拓扑结构、采样周期以及控制参数有关。结论同时适用于有向拓扑与无向拓扑,最后通过仿真实例对所得分析结果进行了验证。     

具有通信时延的二阶多智能体系统有限时间一致性跟踪控制

针对具有通信时延的二阶多智能体系统的有限时间一致性控制问题,分别研究了具有固定拓扑和切换拓扑网络结构情形下的二阶多智能体系统的有限时间一致性。为使多智能体系统能在有限时间内可以达到一致,引入一致性控制增益矩阵并设计了相应的基于相对位置和相对速度的时延状态误差有限时间一致性控制算法,利用系统模型转换,泛函微分方程稳定性理论和有限时间Lyapunov稳定性定理得到了使系统在有限时间内达到一致跟踪的最大时延上界值。最后,仿真实验结果验证了所得理论的正确性和有效性。     

具有时变通信延迟的多智能体系统改进蜂拥控制

针对不确定非线性二阶多智能体系统中存在的时变通信时延和未知干扰问题,提出了一种鲁棒自适应蜂拥控制规律。为了使二阶多智能体系统能够具有更好的抗干扰能力,设计了基于智能体位置状态信息和速度状态信息的鲁棒自适应算子,实现了系统在时变通信时延扰动下的分布控制。通过使用Lyapunov-Krasovskii方法构造能量函数,证明了多智能体系统的网络连通性,智能体的速度收敛于虚拟领导者的速度,并给出了具有时变通信时延的多智能体系统收敛条件。仿真实验结果表明,在不同干扰强度和不同通信时延下系统均能实现快速收敛,形成稳定的拓扑结构,证明所提方法正确有效。     

自适应耦合权重下的异质群体一致性研究

研究了由一阶、二阶智能体组成的异质多智能体系统群体一致性问题。针对固定通信拓扑结构设计了一种基于边的自适应耦合权重控制协议,根据智能体在移动过程中的相对位置调节不同子群中智能体之间的耦合权重,使得多智能体系统仅依赖智能体的邻居信息即可实现群体一致性。通过构造合适的Lyapunov函数,结合图论知识和Lasalle不变原理对系统稳定性进行推理验证。数值仿真结果表明了理论分析的正确性和可行性。     

Second-order consensus in multi-agent dynamical systems with sampled position data

This paper studies second-order consensus in multi-agent dynamical systems with sampled position data. A distributed linear consensus protocol with second-order dynamics is designed, where both the current and some sampled past position data are utilized. It is found that second-order consensus in such a multi-agent system cannot be reached without any sampled position data under the given protocol while it can be achieved by appropriately choosing the sampling period. A necessary and sufficient condition for reaching consensus of the system in this setting is established, based on which consensus regions are then characterized. It is shown that if all the eigenvalues of the Laplacian matrix are real, then second-order consensus in the multi-agent system can be reached for any sampling period except at some critical points depending on the spectrum of the Laplacian matrix. However, if there exists at least one eigenvalue of the Laplacian matrix with a nonzero imaginary part, second-order consensus cannot be reached for sufficiently small or sufficiently large sampling periods. In such cases, one nevertheless may be able to find some disconnected stable consensus regions determined by choosing appropriate sampling periods. Finally, simulation examples are given to verify and illustrate the theoretical analysis.     

Some necessary and sufficient conditions for second-order consensus in multi-agent dynamical systems

This paper studies some necessary and sufficient conditions for second-order consensus in multi-agent dynamical systems. First, basic theoretical analysis is carried out for the case where for each agent the second-order dynamics are governed by the position and velocity terms and the asymptotic velocity is constant. A necessary and sufficient condition is given to ensure second-order consensus and it is found that both the real and imaginary parts of the eigenvalues of the Laplacian matrix of the corresponding network play key roles in reaching consensus. Based on this result, a second-order consensus algorithm is derived for the multi-agent system facing communication delays. A necessary and sufficient condition is provided, which shows that consensus can be achieved in a multi-agent system whose network topology contains a directed spanning tree if and only if the time delay is less than a critical value. Finally, simulation examples are given to verify the theoretical analysis.     

On the general consensus protocol in multi‐agent networks with second‐order dynamics and sampled data

This paper considers the problem of the convergence of the consensus for multiple agents in a directed network. A general distributed consensus protocol is designed, the advantage of this protocol is that almost all the existing linear local interaction consensus protocols can be considered as special cases of the present paper. Necessary and sufficient conditions are established for reaching consensus of the system by choosing the appropriate sampling period, the control parameters and the spectra of the Laplacian matrix. It is found that second‐order consensus cannot be reached for a sufficiently large sampling period while it can be reached for a sufficiently small one. Furthermore, the coupling gains can be carefully designed under the given network structure and the sampling period. Finally, a simulation example is given to verify and illustrate the theoretical analysis.     

Stochastic consensus of double-integrator leader-following multi-agent systems with measurement noises and time delays

This paper studies a leader-following consensus problem of continuous-time double-integrator multi-agent systems with measurement noises and time-varying communication delays under directed topology. By utilising the neighbour position and velocity information, which are delayed and disturbed by measurement noises whose intensities are considered a function related to the neighbour position and velocity of agents, a distributed consensus protocol is presented, sufficient conditions of the tracking consensus in the sense of mean square are derived. Finally, the effectiveness of the proposed consensus protocol is proved by some simulations.     

Distributed optimal consensus of multiple double integrators under bounded velocity and acceleration

This paper studies a distributed optimal consensus problem for multiple double integrators under bounded velocity and acceleration. Assigned with an individual and private convex cost which is dependent on the position, each agent needs to achieve consensus at the optimum of the aggregate cost under bounded velocity and acceleration. Based on relative positions and velocities to neighbor agents, we design a distributed control law by including the integration feedback of position and velocity errors. By employing quadratic Lyapunov functions, we solve the optimal consensus problem of double-integrators when the fixed topology is strongly connected and weight-balanced. Furthermore, if an initial estimate of the optimum can be known, then control gains can be properly selected to achieve an exponentially fast convergence under bounded velocity and acceleration. The result still holds when the relative velocity is not available, and we also discuss an extension for heterogeneous Euler-Lagrange systems by inverse dynamics control. A numeric example is provided to illustrate the result.     

Sampled-data discrete-time coordination algorithms for double-integrator dynamics under dynamic directed interaction

In this article, we study two sampled-data-based discrete-time coordination algorithms for multi-vehicle systems with double-integrator dynamics under dynamic directed interaction. For both algorithms, we derive sufficient conditions on the interaction graph, the damping gain and the sampling period to guarantee coordination by using the property of infinity products of stochastic matrices. When the conditions on the damping gain and the sampling period are satisfied, the first algorithm guarantees coordination on positions with a zero final velocity if the interaction graph has a directed spanning tree jointly while the second algorithm guarantees coordination on positions with a constant final velocity if the interaction graph has a directed spanning tree at each time interval. Simulation results are presented to show the effectiveness of the theoretical results.     

Observer-based consensus in networks of discrete-time switched linear dynamics under a fixed topology

This paper considers the consensus problem of discrete-time switched linear multi-agent systems under a fixed communication topology. An observer-based protocol with sampled data is proposed for solving such a problem. Assume that the digraph has a directed spanning tree and that all switched subsystem of each agent are stabilisable and detectable. It is shown that the proposed protocol solves the consensus problem when the sampling period is sufficiently small and the average dwell time of the switching signal is sufficiently large. Moreover, to reduce the conservatism, a sufficient condition for consensus is obtained to design the feedback gain matrices and the observer gain matrices by linear matrix inequalities, which guarantee that consensus can be achieved when the sampling period and the average dwell time are in the general case. Finally, the effectiveness of the theoretical results is demonstrated through an example.     

Leader-following consensus of double-integrator multi-agent systems with noisy measurements

This paper proposes a leader-following consensus control for continuous-time double-integrator multi-agent systems in noisy communication environment with a constant velocity reference state. Each follower in the team inaccurately measures its neighbors’ positions and the leader’s position if this follower has access to the leader, that the measured positions are corrupted by noises. The constant velocity of the leader is a priori well known. The consensus protocol is constructed based on algebraic graph theory and some stochastic tools. Conditions to ensure the tracking consensus in mean square are derived for both fixed and switching directed topologies. Finally, to illustrate the approach presented, some numerical simulations are carried out.     

Second‐order consensus for directed multi‐agent systems with sampled data

This paper deals with the consensus problem of second‐order multi‐agent systems with sampled data. Because of the unavailable velocity information, consensus problem is studied only by using the sampled position information. The final consensus states of multi‐agent system are given. And a necessary and sufficient consensus condition is provided, which depends on the parameters of sampling interval, eigenvalues of Laplacian matrix, and coupling strengths. Then, the case that both the sampled position and velocity information can be obtained is discussed. On the basis of introducing a time‐varying piecewise‐continuous delay and proposing a novel time‐dependent Lyapunov functional, the sufficient consensus condition is presented, and the upper bound of sampling interval can be estimated. Simulation examples are provided finally to demonstrate the effectiveness of the proposed design methods. Copyright © 2013 John Wiley & Sons, Ltd.     

基于非光滑采样控制算法的二阶有向多智能体系统的一致性

针对二阶有向多智能体系统的一致性问题,在连续时间域和离散时间域分别提出一种非光滑控制协议.首先,提出一种连续时间非光滑一致性协议,通过李雅普诺夫理论和齐次系统理论,证明在无扰动情况下可以实现智能体状态的有限时间一致,而在有扰动情况下智能体状态之间的误差将收敛到一个与控制参数和外部扰动相关的范围内;然后,基于采样控制,提出离散非光滑一致性协议,进一步分析采样周期对智能体状态之间误差的影响,并给出误差收敛区间与控制参数、外部扰动和采样周期关系的显性表达式;最后,通过仿真实例验证理论的正确性和有效性.