Finite-time consensus protocols for networks of dynamic agents by terminal iterative learning

This paper aims to address finite-time consensus problems for multi-agent systems under the iterative learning control framework. Distributed iterative learning protocols are presented, which adopt the terminal laws to update the control input and are offline feedforward design approaches. It is shown that iterative learning protocols can guarantee all agents in a directed graph to reach the finite-time consensus. Furthermore, the multi-agent systems can be enabled to achieve a finite-time consensus at any desired terminal state/output if iterative learning protocols can be improved by introducing the desired terminal state/output to a portion of agents. Simulation results show that iterative learning protocols can effectively accomplish finite-time consensus objectives for both first-order and higher order multi-agent systems.     

Robust iterative learning protocols for finite-time consensus of multi-agent systems with interval uncertain topologies

This paper is devoted to the robust finite-time output consensus problems of multi-agent systems under directed graphs, where all agents and their communication topologies are subject to interval uncertainties. Distributed protocols are constructed by using iterative learning control (ILC) algorithms, where information is exchanged only at the end of one iteration and learning is used to update the control inputs after each iteration. It is proved that under ILC-based protocols, the finite-time consensus can be achieved with an increasing number of iterations if the communication network of agents is guaranteed to have a spanning tree. Moreover, if the information of any desired terminal output is available to a portion (not necessarily all) of the agents, then the consensus output that all agents finally reach can be enabled to be the desired terminal output. It is also proved that for all ILC-based protocols, gain selections can be provided in terms of bound values, and consensus conditions can be developed associated with bound matrices. Simulation results are given to demonstrate the effectiveness of our theoretical results.     

基于迭代学习的多智能体系统分布式跟踪控制

文章考虑了具适多智能体系统的分布式跟踪控制问题。通过设计带有初始学习机制的$P$型和$PD^{\alpha}$ 型迭代学习控制策略求解跟踪问题。具适导数具有良好的性质且可以刻画不同步长的实际数据采样情况。初始学习机制放松了初始值条件且提高了算法实现趋同跟踪的性能。在可重复操作环境和有向通信拓扑的假设下,提出了一种分布式迭代学习方案,通过重复同一轨迹的控制尝试和用跟踪误差修正不满意的控制信号来实现有限时间趋同。严格证明了随着迭代次数增加,提出的$P$型和$PD^{\alpha}$ 型迭代学习控制策略使得所有智能体能渐近跟踪上参考轨迹。两个代表性数值仿真验证了算法的有效性。     

Consensus seeking of multi-agent systems from an iterative learning perspective

The consensus seeking problems for both discrete and continuous multi-agent networks are discussed from an iterative learning perspective. It is shown that the consensus seeking process can be viewed as an iterative learning process for agents under directed networks to improve their performances from time to time in order to achieve consensus. If a desired consensus state is specified, then the multi-agent system can be guaranteed to reach consensus through reducing the tracking error between each agent’s state and the desired consensus state monotonically to zero with respect to the increasing of time. If there is no desired consensus state, then the agents can achieve consensus through reducing their states monotonically to the minimum quantity with increasing time. Simulations illustrate the observed results.     

Finite-time median-related group consensus over directed networks

ABSTRACT

In this paper, we investigate a novel finite-time median-related group consensus problem, where the finial consensus value can be identified as a desired function of the median of initial states instead of the much studied average value. The underlying communication topology is modelled by a weighted dynamical directed network. A distributed control protocol is firstly introduced to ensure that the agents can reach a median-related consensus in finite time in a collaboration network, meaning that all edge-weights of the communication network are non-negative. We then generalise the results to cooperation–competition networks, where the communication network is divided into predetermined collaboration subnetworks allowing possibly negative weights. Effective group control protocols are designed to guarantee the median-related group consensus in finite time. Finally, numerical simulations are presented to illustrate the availability of our theoretical results.     

Nonlinear finite-time bipartite consensus protocol for multi-agent systems associated with signed graphs

In this paper, finite-time multi-agent consensus problems are considered under networks associated with signed graphs whose edge weights can be not only positive but also negative. A nonlinear consensus protocol is proposed to guarantee the states of all agents to converge in a finite time. If the signed graph is structurally balanced, then the final consensus states of all agents are the same in modulus but not in sign. Otherwise, if the signed graph is structurally unbalanced, then the states of all agents converge to zero. Moreover, the final consensus states of agents can be provided uniformly regarding a signed-average quantity that depends on both the initial states of agents and the topology structure of the whole multi-agent network. Numerical simulations illustrate that the protocol is effective in achieving the finite-time consensus of agents under signed graphs and can particularly solve the finite-time average consensus problem of agents when their associated graph has all positive edge weights.     

A distributed finite-time optimization algorithm for directed networks of continuous-time agents

This article proposes a new distributed finite-time optimization algorithm for agents under directed graphs. By employing the nonsmooth technique and graph theory, a distributed discontinuous algorithm for continuous-time agents subject to strongly convex local cost functions is first designed with a finite-time distributed estimator, where the gradients of the local cost functions are estimated in finite time. It is shown that for a strongly connected graph and arbitrary initial conditions, the proposed algorithms can achieve consensus, and the systems can converge to the optimal point in finite time. Then, a two-step approach is proposed to achieve finite-time optimization of high-order agents with disturbances under directed graphs. Finally, the validity of the proposed finite-time optimization algorithm is verified by two numerical examples.     

Finite-time consensus for multi-agent networks with unknown inherent nonlinear dynamics

The objective of this paper is to analyze the finite-time convergence of a nonlinear but continuous consensus algorithm for multi-agent networks with unknown inherent nonlinear dynamics. Due to the existence of the unknown inherent nonlinear dynamics, the stability analysis and the finite-time convergence analysis are more challenging than those under the well-studied consensus algorithms for known linear systems. For this purpose, we propose a novel comparison based tool. By using this tool, it is shown that the proposed nonlinear consensus algorithm can guarantee finite-time convergence if the directed switching interaction graph has a directed spanning tree at each time interval. Specifically, the finite-time convergence is shown by comparing the closed-loop system under the proposed consensus algorithm with some well-designed closed-loop system whose stability properties are easier to obtain. Moreover, the stability and the finite-time convergence of the closed-loop system using the proposed consensus algorithm under a (general) directed switching interaction graph can even be guaranteed by the stability and the finite-time convergence of some well-designed nonlinear closed-loop system under some special directed switching interaction graph. This provides a stimulating example for the potential applications of the proposed comparison based tool in the stability analysis of linear/nonlinear closed-loop systems by making use of known results in linear/nonlinear systems.     

Finite-time consensus tracking for multi-agent systems with inherent uncertainties and disturbances

In this paper, finite-time consensus tracking is investigated via time-varying feedback for uncertain nonlinear multi-agent systems (NMASs). The presence of inherent uncertainties and disturbances in the NMASs highlights the main novelty : (1) The inherent uncertainties imply that more serious unknowns and time-variations are allowed in the nonlineartities and the control coefficients of the NMASs. (2) The inherent disturbances mean that the upper bound of the disturbances is unknown. To compensate the inherent uncertainties and disturbances, time-varying protocols are proposed by integrating time-varying technique and sliding mode method. Based on the proposed protocols, the finite-time leader-following consensus and finite-time containment are achieved under directed graph. Finally, the validation of the proposed protocols is verified by two examples.     

Distributed adaptive output consensus control of second-order systems containing unknown non-linear control gains

In this paper, we address the output consensus problem of tracking a desired trajectory for a group of second-order agents on a directed graph with a fixed topology. Each agent is modelled by a second-order non-linear system with unknown non-linear dynamics and unknown non-linear control gains. Only a subset of the agents is given access to the desired trajectory information directly. A distributed adaptive consensus protocol driving all agents to track the desired trajectory is presented using the backstepping technique and approximation technique of Fourier series (FSs). The FS structure is taken not only for tracking the non-linear dynamics but also the unknown portion in the controller design procedure, which can avoid virtual controllers containing the uncertain terms. Stability analysis and parameter convergence of the proposed algorithm are conducted based on the Lyapunov theory and the algebraic graph theory. It is also demonstrated that arbitrary small tracking errors can be achieved by appropriately choosing design parameters. Though the proposed work is applicable for second-order non-linear systems containing unknown non-linear control gains, the proposed controller design can be easily extended to higher-order non-linear systems containing unknown non-linear control gains. Simulation results show the effectiveness of the proposed schemes.     

端口受控哈密顿多智能体系统的输出一致性协议设计

研究了端口受控哈密顿（PCH）多智能体系统分别在固定和切换拓扑下的输出一致性问题. 首先根据哈密顿系统特有的优势,运用能量整形思路设计了一个全局稳定的群组输出一致性协议,该协议通过构造虚拟邻居的方式将有向图转化成无向图. 其次通过利用推广的LaSalle's不变原理将切换拓扑的问题转化成切换系统来研究. 例子证明,本文很好的解决端口受控哈密顿（PCH）多智能体系统的输出一致性问题.     

端口受控哈密顿多智能体系统的输出一致性协议设计（英文）

This paper investigates the output consensus problem of port-controlled Hamiltonian(PCH) multi-agent systems with both fixed and switching topologies. Firstly, a distributed group output consensus protocol is designed via the energy shaping method to reach globally stability and group output consensus. Secondly, a new distributed control protocol is proposed by using the structural properties of the PCH systems. The advantage of this protocol is that it can transform the directed graph to the undirected graph by constructing a kind of virtual neighbors. Thirdly, a control protocol is designed with the extended LaSalle s invariance principle developed for switched systems under the jointly connected topology condition to make all the agents reach output consensus when the topology is switching. Finally, some illustrative examples with simulations are provided to demonstrate the effectiveness of the protocols designed in this paper.     

Finite-time consensus for multi-agent systems via nonlinear control protocols

This paper investigates the fnite-time consensus problem of multi-agent systems with single and double integrator dynamics,respectively.Some novel nonlinear protocols are constructed for frst-order and second-order leader-follower multi-agent systems,respectively.Based on the fnite-time control technique,the graph theory and Lyapunov direct method,some theoretical results are proposed to ensure that the states of all the follower agents can converge to its leader agent s state in fnite time.Finally,some simulation results are presented to illustrate the efectiveness of our theoretical results.     

Adaptive iterative learning control for coordination of second‐order multi‐agent systems

In this paper, an efficient framework is proposed to the consensus and formation control of distributed multi‐agent systems with second‐order dynamics and unknown time‐varying parameters, by means of an adaptive iterative learning control approach. Under the assumption that the acceleration of the leader is unknown to any follower agents, a new adaptive auxiliary control and the distributed adaptive iterative learning protocols are designed. Then, all follower agents track the leader uniformly on [0,T] for consensus problem and keep the desired distance from the leader and achieve velocity consensus uniformly on [0,T] for the formation problem, respectively. The distributed multi‐agent coordinations performance is analyzed based on the Lyapunov stability theory. Finally, simulation examples are given to illustrate the effectiveness of the proposed protocols in this paper.Copyright © 2013 John Wiley & Sons, Ltd.     

Active fault‐tolerant consensus control of Lipschitz nonlinear multiagent systems

This article investigates the active fault‐tolerant consensus problem for Lipschitz nonlinear multiagent systems under detailed balanced directed graph and actuator faults. First, a fault detection filter for each agent is designed, and all agents can be divided into two categories: healthy agents and possibly faulty agents. Second, fully distributed adaptive fault‐tolerant consensus protocols for healthy and possibly faulty agents are proposed to achieve state consensus. Third, based on the fault detection method and fault‐tolerant consensus protocols, active fault‐tolerant consensus algorithms are given. Simulation examples are presented to verify the effectiveness of the proposed active fault‐tolerant algorithms.     

线性和非线性动态异构多自主体系统的有限时间一致性（英文）

In this paper, the finite-time consensus problems of heterogeneous multi-agent systems composed of both linear and nonlinear dynamics agents are investigated. Nonlinear consensus protocols are proposed for the heterogeneous multi-agent systems.Some sufficient conditions for the finite-time consensus are established in the leaderless and leader-following cases. The results are also extended to the case where the communication topology is directed and satisfies a detailed balance condition on coupling weights.At last, some simulation results are given to illustrate the effectiveness of the obtained theoretical results.     

线性和非线性动态异构多自主体系统的有限时间一致性

研究了由线性和非线性动态自主体组成的异构多自主体系统的有限时间一致性问题.针对该异构系统提出了非线性的一致性协议,并分别给出了无领航者和有领航者情形下异构系统在有限时间内实现一致性的充分条件.所得结果还推广到具有有向通信拓扑且满足细致平衡条件的多自主体系统情形.最后,给出一些仿真结果来验证所得结论的正确性和有效性.     

Finite-time consensus algorithm for multi-agent systems with double-integrator dynamics

In this paper, we discuss the finite-time consensus problem for leaderless and leader–follower multi-agent systems with external disturbances. Based on the finite-time control technique, continuous distributed control algorithms are designed for these agents described by double integrators. Firstly, for the leaderless multi-agent systems, it is shown that the states of all agents can reach a consensus in finite time in the absence of disturbances. In the presence of disturbances, the steady-state errors of any two agents can reach a region in finite time. Secondly, for the leader–follower multi-agent systems, finite-time consensus algorithms are also designed based on distributed finite-time observers. Rigorous proof is given by using Lyapunov theory and graph theory. Finally, one example is employed to verify the efficiency of the proposed method.     

输出饱和多智能体系统的迭代学习趋同跟踪控制

针对带有输出饱和的多智能体系统有限时间趋同跟踪控制问题,提出了一种分布式迭代学习控制算法.首先假设多智能体系统具有固定拓扑结构,且仅有部分智能体可获取到期望轨迹信息.基于输出约束条件构造一致性跟踪误差,在此基础上设计了P型迭代学习控制率.然后采用压缩映射方法给出了一个算法收敛的充分条件,并在理论上证明了跟踪误差的收敛性.最后,将理论结果推广至具有随机切换拓扑结构的多智能体系统中.仿真结果验证了所提出算法的有效性.     

Iterative Learning Control Design for Multiagent Systems Based on 2D Models

This paper considers a group of systems (agents) described by linear continuous or discrete models. All systems operate in the repetitive mode with a constant pass length, with resetting to the initial state after each pass is complete. Information exchange among the systems is described by a directed graph. The problem of reaching a consensus is formulated as designing an iterative learning control law (protocol) under which the output variable of each agent converges to a reference trajectory (pass profile) as the number of passes grows infinitely. This problem is solved using an original approach based on 2D models and a 2D modification of the vector Lyapunov function method. The ultimate results are written in form of linear matrix inequalities. 2D counterparts of the Fax–Murray theorem are established. An illustrative example is given.