Tracking control for multi-agent consensus with an active leader and variable topology

In this paper, we consider a multi-agent consensus problem with an active leader and variable interconnection topology. The state of the considered leader not only keeps changing but also may not be measured. To track such a leader, a neighbor-based local controller together with a neighbor-based state-estimation rule is given for each autonomous agent. Then we prove that, with the proposed control scheme, each agent can follow the leader if the (acceleration) input of the active leader is known, and the tracking error is estimated if the input of the leader is unknown.     

Distributed observers design for leader-following control of multi-agent networks

This paper is concerned with a leader-follower problem for a multi-agent system with a switching interconnection topology. Distributed observers are designed for the second-order follower-agents, under the common assumption that the velocity of the active leader cannot be measured in real time. Some dynamic neighbor-based rules, consisting of distributed controllers and observers for the autonomous agents, are developed to keep updating the information of the leader. With the help of an explicitly constructed common Lyapunov function (CLF), it is proved that each agent can follow the active leader. Moreover, the tracking error is estimated even in a noisy environment. Finally, a numerical example is given for illustration.     

有向图中网络Euler-Lagrange系统的自适应协调跟踪

基于一致性理论, 在有向图中研究网络 Euler-Lagrange 系统的协调跟踪控制. 所有跟随智能体的动力学模型均为 Euler-Lagrange 方程. 在仅有部分跟随智能体能获取领航智能体信息的情形下, 同时考虑系统模型的参数不确定性, 设计分布式自适应控制律实现所有跟随智能体对领航智能体的跟踪. 针对领航智能体的运动状态, 考虑以下两种情形: 1) 领航智能体为固定点; 2) 领航智能体为动态点. 对第一种情形, 设计的控制律使得所有跟随智能体渐近交会于固定点; 对第二种情形, 首先对每个跟随智能体设计分布式连续估计器, 然后提出了分布式自适应控制律. 当每个跟随智能体均能获取领航智能体的加速度信息时, 设计的控制律能实现对领航智能体的渐近跟踪, 当跟随智能体不能获取领航智能体的加速度信息时, 跟踪误差是有界的. 最后通过仿真分析验证设计的控制算法是合理有效的.     

Distributed tracking control of leader-follower multi-agent systems under noisy measurement

In this paper, a distributed tracking control scheme with distributed estimators has been developed for a leader-follower multi-agent system with measurement noises and directed interconnection topology. It is supposed that each follower can only measure the relative positions of its neighbors in a noisy environment, including the relative position of the second-order active leader. A neighbor-based tracking protocol together with distributed estimators is designed based on a novel velocity decomposition technique. It is shown that the closed loop tracking control system is stochastically stable in mean square and the estimation errors converge to zero in mean square as well. A simulation example is finally given to illustrate the performance of the proposed control scheme.     

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.     

具有通信时延的跟随者–多领导者聚集控制

本文考虑了一个连续时间多智能体系统跟随者–多领导者聚集控制问题. 假设智能体之间的通信频道是有向的且存在时延. 基于邻居原理, 提出了一个新的跟踪协议. 应用线性矩阵不等式技术和Lyapunov方法得到所有的跟随者都能够群集于由多个领导者组成的凸多边形区域的充分条件. 此外, 并将文中结果推广到通信频道含有时延和噪声情形. 最后, 数值仿真验证了文中理论结果的有效性和正确性.     

Flocking shape analysis of multi-agent systems

In this paper,we consider the shape control in flocking behavior of a multi-agent system with a virtual leader.Besides the traditional flocking control terms,which include a gradient-based term,a velocity consensus term and a navigational feed-back in general,a new piecewise smooth neighbor-based local controller is added to regulate the configuration to the desired flocking shape.All agent velocities approach the desired velocity asymptotically,while collisions among agents can be avoided.Furthermore,based...     

Adaptive cooperative tracking control of higher-order nonlinear systems with unknown dynamics

A practical design method is developed for cooperative tracking control of higher-order nonlinear systems with a dynamic leader. The communication network is a weighted directed graph with a fixed topology. Each follower node is modeled by a higher-order integrator incorporating with unknown nonlinear dynamics and an unknown disturbance. The leader node is modeled as a higher-order nonautonomous nonlinear system. It acts as a command generator giving commands only to a small portion of the networked group. A robust adaptive neural network controller is designed for each follower node such that all follower nodes ultimately synchronize to the leader node with bounded residual errors. Moreover, these controllers are distributed in the sense that the controller design for each follower node only requires relative state information between itself and its neighbors. A simulation example demonstrates the effectiveness of the algorithm.     

Finite-time tracking control for multiple non-holonomic mobile robots based on visual servoing

This paper investigates finite-time tracking control problem of multiple non-holonomic mobile robots via visual servoing. It is assumed that the pinhole camera is fixed to the ceiling, and camera parameters are unknown. The desired reference trajectory is represented by a virtual leader whose states are available to only a subset of the followers, and the followers have only interaction. First, the camera-objective visual kinematic model is introduced by utilising the pinhole camera model for each mobile robot. Second, a unified tracking error system between camera-objective visual servoing model and desired reference trajectory is introduced. Third, based on the neighbour rule and by using finite-time control method, continuous distributed cooperative finite-time tracking control laws are designed for each mobile robot with unknown camera parameters, where the communication topology among the multiple mobile robots is assumed to be a directed graph. Rigorous proof shows that the group of mobile robots converges to the desired reference trajectory in finite time. Simulation example illustrates the effectiveness of our method.     

Attitude synchronization control for a group of flexible spacecraft

To solve the problem of attitude synchronization for a group of flexible spacecraft during formation maneuvers, a distributed attitude cooperative control strategy is investigated in this paper. Based on the backstepping design and the neighbor-based design rule, a distributed attitude control law is constructed step by step. Using cascaded systems’ theory and graph theory, it is shown that the attitude synchronization is achieved asymptotically and the induced vibrations by flexible appendages are simultaneously suppressed under the proposed control law.     

Leader-following control of perturbed second-order integrator systems with binary relative information

In this paper, we study the leader-following control problem for second-order integrator systems with bounded input disturbances using only binary relative position and velocity information. The leader is allowed to be dynamically evolving with a bounded acceleration which is unknown to any of the followers. With the proposed distributed controller, we prove that despite the fact that only very coarse relative information is available, robust finite-time leader-following control can be achieved by properly choosing the control gains. As an extension, robust finite-time formation control can also be achieved with the proposed control strategy using only binary relative information. Two simulation examples are provided to illustrate the results.     

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.     

Adaptive tracking system for a manoeuvring target using images with correlated noises

An effective scheme is proposed for estimating the state parameters of a manoeuvring target from a noisy image sequence, providing the sequence contains correlated noises and the trajectory of the target is disturbed by an unknown acceleration. For the correlated noises, a first-order difference operator is applied to the original image sequence to generate an artificial measurement sequence with only uncorrelated white noises. For the unknown acceleration, a Kalman filter augmented by a semi-Markov process and the bayesian theory is applied to form an adaptive filter. In the proposed tracking system, the filter first generates an artificial measurement at each sampling time from the observation. It then utilizes an artificial measurement sequence up to the current time instance to predict the a posteriori probability of each possible acceleration state. The weighted average of acceleration, where the weight is the a posteriori probability, is applied to derive the optimal estimates of the state parameters. Several computer simulations with external force applied at unknown times are performed to demonstrate the applicability and superiority of the proposed system.     

Interconnection topologies for multi-agent coordination under leader–follower framework

In this paper, the formation control problem of the network of multiple agents is studied in terms of controllability, where the network is of the leader–follower structure with some agents taking leaders role and others being followers interconnected via the neighbor-based rule. It is shown that the controllability of a multi-agent system can be uniquely determined by the topology structure of interconnection graph, for which the investigation comes down to that for a multi-agent system with the interconnection graph being connected. Based on these observations, two kinds of uncontrollable interconnection topologies are characterized, and a necessary and sufficient eigenvector-based condition is presented. Our studies also touch upon the selection of leaders.     

Decision rules for distributed decision networks with uncertainties

The authors study distributed decision networks where uncertainties exist in the statistical environment. Specifically each decision maker (DM) has an unknown probability to be jammed or defective and an unknown probability to provide an incorrect decision when jammed or defective. Each DM in the network has the ability to process its input data consisting of external observations and decisions from preceding DMs, to produce a decision regarding an underlying binary hypothesis testing problem. The local observations are assumed conditionally independent given each hypothesis. The resulting binary hypothesis testing problem is solved using some simple concepts of Dempster-Shafer theory. The performance of the proposed decision rule is compared to that of the minimax decision rule and the decision rule that is optimum when there are no jammed or defective DMs for several distributed decision networks with different topologies. It is shown that the proposed decision rule has a very robust behavior     

Connectivity maintenance and distributed tracking for double‐integrator agents with bounded potential functions

In this paper, we develop a set of decentralized control laws with bounded potential functions. The basic control law is a combination of attractive, repulsive, and alignment forces, which can keep connectivity, avoid collision, synchronize all agents, and further track a constant moving leader. Furthermore, we investigate the distributed tracking problem with a varying‐velocity leader, where the acceleration of the leader can not be measured. Two cases are considered; the acceleration of the leader is bounded, and the acceleration function satisfies Lipschitz condition. In the first case, the relative velocities of neighbors are integrated and transmitted as a new variable to account for the uncertain time‐varying acceleration. In the second case, two distributed estimators are added for the leader's position and velocity. Finally, some simulations are presented to show the effectiveness of the proposed algorithms. Copyright © 2013 John Wiley & Sons, Ltd.     

Human-in-the-Loop Consensus Control for Nonlinear Multi-Agent Systems With Actuator Faults

This paper considers the human-in-the-loop leader-following consensus control problem of multi-agent systems (MASs) with unknown matched nonlinear functions and actuator faults. It is assumed that a human operator controls the MASs via sending the command signal to a non-autonomous leader which generates the desired trajectory. Moreover, the leader’s input is nonzero and not available to all followers. By using neural networks and fault estimators to approximate unknown nonlinear dynamics and identify the actuator faults, respectively, the neighborhood observer-based neural fault-tolerant controller with dynamic coupling gains is designed. It is proved that the state of each follower can synchronize with the leader’s state under a directed graph and all signals in the closed-loop system are guaranteed to be cooperatively uniformly ultimately bounded. Finally, simulation results are presented for verifying the effectiveness of the proposed control method.      

Leader–follower consensus of linear multi-agent systems with unknown external disturbances

This paper addresses the leader–follower consensus tracking problem for multi-agent systems with identical general linear dynamics and unknown external disturbances. First, a distributed extended state observer is proposed, where both the local states and disturbance of each agent are estimated simultaneously by using the relative output information between neighbors. Then a consensus algorithm is proposed for each agent based on the relative estimated states between neighbors and its own disturbance estimate. It is shown that, with the proposed observer-based consensus algorithm, the leader–follower consensus problem can be solved. Finally, we present a simulation example to demonstrate the effectiveness of the proposed algorithm.     

非仿射非线性多智能体系统迭代学习一致跟踪

为了解决非仿射非线性多智能体系统在给定时间区间上一致性完全跟踪问题,基于迭代学习控制方法设计一种分布式一致性跟踪控制算法.首先,由引入的虚拟领导者与所有跟随者组成多智能体系统的通信拓扑,其中虚拟领导者的作用是提供期望轨迹.然后,在只有部分跟随者能够获得领导者信息的条件下,利用每个跟随者及其邻居的跟踪误差构造每个跟随者的迭代学习一致性跟踪控制器.同时采用中值定理将非仿射非线性多智能体系统转化仿射形式,并基于压缩映射方法证明所提算法的收敛性,给出算法的收敛条件.理论分析表明,在智能体的非线性函数未知情况下,利用所提算法可以使非仿射非线性多智能体系统在给定时间区间上随迭代次数增加逐次实现一致性完全跟踪.最后,通过仿真算例进一步验证所提算法的有效性.     

Online tuning of fuzzy PID controllers via rule weighing based on normalized acceleration

In this study, an on-line tuning method is proposed for fuzzy PID controllers via rule weighing. The rule weighing mechanism is a fuzzy rule base with two inputs namely; “error” and “normalized acceleration”. Here, the normalized acceleration provides relative information on the fastness or slowness of the system response. In deriving the fuzzy rules of the weighing mechanism, the transient phase of the unit step response of the closed loop system is to be analyzed. For this purpose, this response is assumed to be divided into certain regions, depending on the number of membership functions defined for the error input of the fuzzy logic controller. Then, the relative importance or influence of the fired fuzzy rules is determined for each region of the transient phase of the unit step response of the closed loop system. The output of the fuzzy rule weighing mechanism is charged as the tuning variable of the rule weights; and, in this manner, an on-line self-tuning rule weight assignment is accomplished. The effectiveness of the proposed on-line weight adjustment method is demonstrated on linear and non-linear systems by simulations. Moreover, a real time application of this new method is accomplished on a pH neutralization process.