多智能体系统可控性的图论刻画

研究领航者-跟随者结构多智能体系统的可控性问题.利用松弛的等价分化刻画了系统可控性与信息拓扑结构之间的关系,为系统可控性提供了基于图论的判别方法.基于置换群理论将对称的概念推广到多领航者系统,并证明了3种图论工具（对称性、等价分化和松弛的等价分化）之间的包含关系.仿真结果验证了所提出方法的有效性.     

二阶邻居协议下多智能体系统能控能观性保持

为了研究多智能体系统的一致性特点及能控、能观性保持策略,分析了具有时变拓扑结构的多智能体系统在一阶邻居协议和二阶邻居协议下的一致性速度,针对拓扑结构的特殊性,利用结构能控性性质和拉普拉斯矩阵第二小特征值与一致性速度之间存在的关系设计出一种使能控性和能观测性保持的控制策略。此外,得出多智能体系统在二阶邻居协议下,具有更快的一致性速度的结论。文中2个主要定理分别通过算例和仿真进行验证,算例和仿真结果与定理结论一致。     

Controllability of multi-agent systems with time-delay in state and switching topology

In this article, the controllability issue is addressed for an interconnected system of multiple agents. The network associated with the system is of the leader–follower structure with some agents taking leader role and others being followers interconnected via the neighbour-based rule. Sufficient conditions are derived for the controllability of multi-agent systems with time-delay in state, as well as a graph-based uncontrollability topology structure is revealed. Both single and double integrator dynamics are considered. For switching topology, two algebraic necessary and sufficient conditions are derived for the controllability of multi-agent systems. Several examples are also presented to illustrate how to control the system to shape into the desired configurations.     

多智能体网络系统的能控性代数条件

能控性是多智能体系统研究的核心问题,主要包括结构可控性和精准可控性。对多智能体系统的模型和能控性代数条件进行了总结。在相对协议和绝对协议条件下,运用图论和矩阵论的知识系统分析了多智能体系统能控性的代数条件。按照同质多智能体到异质多智能体的顺序,对现有的多智能体系统模型和代数条件进行了梳理,并在已有结论的基础上对多智能体系统能控性的代数条件进行了改善,进一步提出了新的代数条件。多智能体能控性代数条件的改进大大简化了能控性的计算量。     

Graph-theoretic characterisations of the steady states for containment control

Containment control is a consensus-like protocol whose objective is to drive all the followers into the convex hull formed by the leaders. The steady states of the followers have great effect on system performance. Two kinds of cell partitions from graph theory are employed to investigate the reflections of the information topology on the steady states of the followers. It is proved that agents that belong to the same cell have the same steady states.     

多智能体系统能控性研究进展

能控性问题是多智能体协调控制领域中一个基本又十分重要的研究课题.本文对多智能体系统能控性问题的研究现状进行综述.介绍了多智能体能控性领域的基本问题和特点,并结合智能体自身动力学与邻居交互协议,从拓扑结构角度对该领域当前的研究热点和前沿进行分析阐述.进一步,对结构能控性的研究成果进行归纳总结,并对能观测性、可镇定性和复杂网络能控性等相关问题进行阐述.最后给出了仍需解决的问题和可能的研究方向.     

Further developments in output structural controllability and an assessment of structural techniques

Modifications have been made to the technique of output structural controllability to overcome some limitations of this useful technique. A critical assessment of the usefulness of various structural controllability techniques for control system synthesis is given through the analysis of key examples.     

具有引导者的多智能体网络系统的脉冲一致性

多智能体网络系统的协调与控制在工程领域中有着重要的作用. 本文给出了具有引导者的一阶多智能体网络系统的动力学模型. 模型中, 假设网络系统中仅有一个智能体在一系列离散时刻基于自身及引导者的信息, 以脉冲跳跃方式改变自身的状态.应用矩阵理论、数值分析理论、脉冲微分方程等理论给出了网络系统达到一致的一个充分条件. 计算机仿真实验验证了算法的正确性和有效性,展示了系统的一致收敛速度与脉冲间隔、脉冲强度之间的关系.     

多智能体聚集问题研究综述

多智能体聚集在分布式协调控制领域具有广阔的应用前景,近年来受到持续关注并且研究成果颇丰。首先梳理了多智能体聚集问题中涉及的理论基础与框架;接着综述了近几年多智能体聚集问题主要研究成果,重点从保持拓扑连通性和提升抗干扰性以及受资源限制两个方面介绍多智能体聚集问题研究进展,并对其中主流控制方法深入阐述;归纳总结了多智能体聚集协议优化在降低系统功耗和提升收敛速度方面的研究成果;最后,提出多智能体聚集问题若干未来的研究方向。     

切换拓扑下测量受限多智能体系统一致性迭代学习控制

针对通信拓扑至少含有一个沿迭代轴的联合生成树且同时沿有限时间轴和无限迭代轴切换的情况,文本研究了存在测量受限的连续线性多智能体系统输出一致性迭代学习控制问题.首先,文章采用迭代学习控制方法设计了一种基于跟随者局部信息的分布式输出一致性协议.然后,给出了系统可解输出一致性问题的两个充分性条件,其中之一可使跟随者实时获取迭代学习增益,避免了全局信息对学习增益设计的影响,且保证了算法的分布式实现.接着,利用λ范数理论和圆盘定理严格证明了所设计算法的收敛性.最后,通过实例仿真验证了所得结论的有效性.     

Minimal structural perturbations for controllability of a networked system: Complexities and approximations

Link additions/deletions and actuator/sensor failures are common structural perturbations for real networked systems. In this paper, we consider three related problems on determining the minimal cost structural perturbations, including link additions, link deletions, and input deletions to make a networked system structurally controllable/uncontrollable, mainly focusing on their computational complexities and approximations. Formally, given a structured system, it is proven that (i) it is NP‐hard to add the minimal cost of links, including links among state variables (ie, state links) and links from the existing inputs to state variables (ie, input links), from a given set of links to make the system structurally controllable; (ii) it is NP‐hard to determine the minimal cost of links whose deletions deteriorate structural controllability of the system, even when the removable links are restricted in either the input links or the state links. It is also proven that determining the minimal cost of inputs whose deletions cause structural uncontrollability is strongly NP‐hard even with dedicated input structure. Furthermore, some fundamental approximation results for these problems are established. These results may serve an answer to the general hardness and approximability of optimally designing (modifying) a structurally controllable network topology and of measuring controllability robustness against link/input failures. Additionally, several polynomial‐time tractable cases of the aforementioned problems are also identified.     

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.     

基于切换拓扑的多智能体协作控制研究综述

多智能体系统一直是众多学科领域研究的主要研究对象,基于切换拓扑的多智能体协作控制理论研究作为多智能体系统研究的重要部分,一直是近年来的热点。为了推进基于切换拓扑的多智能体协作控制理论研究,在广泛调研现有文献和最新成果的基础上,从一致性问题、分布式优化问题和分布式估计问题三个方面对该领域的发展现状进行了总结;探讨了诸如一致性协议的设计、一致性协议的性能分析方法及其优缺点、分布式优化的实现方式和分布式估计的实际应用。最后指出当前该领域尚未解决的问题和未来的研究方向。     

随机拓扑结构下多智能体系统的平均一致性*

利用马尔可夫收敛准则、图的Laplace矩阵谱特性和欧氏度量的极值,对一类具有随机拓扑结构的离散时间多智能体系统平均一致性问题进行了深入讨论。引入完好概率矩阵的概念,建立随机拓扑结构下离散时间系统的一致性算法,应用马尔可夫过程收敛相关结论及伴随算子,从欧氏度量极值的角度证明了系统可达到渐近平均一致,并得出了所需满足的条件,该条件放宽了对系统连通性的要求。最后,采用六个智能体组成的多智能体系统进行计算机仿真,对理论的正确性进行了验证。     

Controllability of discrete-time multi-agent systems with directed topology and input delay

This paper investigates the controllability of first-order and second-order discrete-time multi-agent systems with directed topology and input delay. The problem is studied in the leader–follower framework where a number of agents are selected to be leaders and serve as control inputs to all other agents. Sufficient and necessary conditions are derived for the controllability of first-order discrete-time multi-agent systems. With sampling period and feedback gain satisfying certain conditions, it is proved under three different protocols that the controllability of second-order discrete-time multi-agent systems is equivalent to that of a pair of submatrices of Laplacian matrix. In addition, the controllability of both first-order and second-order discrete-time multi-agent systems with input delay is shown, through some transformations, to be equivalent to that of the transformed non-delayed systems. Finally, some simulation examples are given to illustrate the theoretical results.     

Fixed-time consensus for multi-agent systems with discontinuous inherent dynamics over switching topology

This paper is concerned with the fixed-time consensus problem of multi-agent systems. Unlike conventional consensus-based investigations, where nonlinear inherent dynamics satisfying the Lipschitz continuous condition is assumed or simply no inherent dynamics is involved for each agent, we are dealing with a more general case: agents with discontinuous nonlinear inherent dynamics. By using non-smooth analysis and fixed-time stability techniques, distributed protocols are proposed to achieve the fixed-time consensus over fixed and switching topology. Then, for a class of linear multi-agent systems, a new distributed controller is proposed to further reduce the calculation cost while achieving the agreement. A distinctive feature of the work is that the estimation of settling time for consensus is independent of initial states of agents, which provides flexibility for applications implemented in unknown environment. Finally, numerical simulations are given to demonstrate the effectiveness of the theoretical results.     

Minimum-energy time-varying formation of distributed multi-agent systems with interaction constraints

In the current paper, minimum-energy time-varying formation design and analysis problems of distributed multi-agent systems (DMASs) subjected to randomly switching topologies and aperiodic interaction pauses are investigated, which can ensure the time-varying formation achievement with the minimum-energy consumption in the sense of the linear matrix inequality. Firstly, a formation control protocol is designed with local information of neighboring agents, where the total energy consumption during the formation process is constructed and the impacts of interaction constraints are imposed. Then, minimum-energy formation design and analysis criteria of DMASs are presented in terms of the linear matrix inequality tool, which can be checked by the generalized eigenvalue method. Finally, a numerical simulation is shown to verify the effectiveness of the main results.     

Distributed cooperative reinforcement learning for multi-agent system with collision avoidance

In this work, we present an optimal cooperative control scheme for a multi-agent system in an unknown dynamic obstacle environment, based on an improved distributed cooperative reinforcement learning (RL) strategy with a three-layer collaborative mechanism. The three collaborative layers are collaborative perception layer, collaborative control layer, and collaborative evaluation layer. The incorporation of collaborative perception expands the perception range of a single agent, and improves the early warning ability of the agents for the obstacles. Neural networks (NNs) are employed to approximate the cost function and the optimal controller of each agent, where the NN weight matrices are collaboratively optimized to achieve global optimal performance. The distinction of the proposed control strategy is that cooperation of the agents is embodied not only in the input of NNs (in a collaborative perception layer) but also in their weight updating procedure (in the collaborative evaluation and collaborative control layers). Comparative simulations are carried out to demonstrate the effectiveness and performance of the proposed RL-based cooperative control scheme.     

Second-order tracking control for leader-follower multi-agent flocking in directed graphs with switching topology

This paper investigates the flocking problem for leader-follower multi-agent systems in directed graphs with switching topology. A decentralized state control rule, namely, a second-order protocol, is designed for each agent to track the leader. And it is proved that the proposed control scheme can effectively estimate the tracking error of each agent when the leader is active. Particularly, to ensure the tracking error can be estimated, the following two questions are solved: (1) How many agents are needed to connect to the leader? (2) How should these connections be distributed? Finally, a simple example is also given to verify the effectiveness of the proposed theorems.     

Connectability and structural controllability of composite systems

The notion of connectability for multivariable composite systems consisting of a number of subsystems interconnected in an arbitrary way is introduced in this paper. It is shown that connectability plays a fundamental role in composite systems; in particular, it is shown that under certain mild conditions, almost all composite interconnected systems are controllable and observable from any nontrivial input and output if and only if the resultant composite system is connectable. A class of composite systems called general input-output hierarchical systems, which has the property of always being connectable is then defined. Since such systems are almost always controllable, this observation perhaps gives some insight in explaining why so many real world systems have as their basis a hierarchical structure. An application of the previous results is then made to show that a system (C, A, B) is structurally controllable and observable if and only if it is connectable and a certain non-pathological rank condition holds.