Robust and nonfragile consensus of positive multiagent systems via observer‐based output‐feedback protocols

This article investigates the consensus problem for positive multiagent systems via an observer‐based dynamic output‐feedback protocol. The dynamics of the agents are modeled by linear positive systems and the communication topology of the agents is expressed by an undirected connected graph. For the consensus problem, the nominal case is studied under the semidefinite programming framework while the robust and nonfragile cases are investigated under the linear programming framework. It is required that the distributed state‐feedback controller and observer gains should be structured to preserve the positivity of multiagent systems. Necessary and/or sufficient conditions for the analysis of consensus are obtained by using positive systems theory and graph theory. For the nominal case, necessary and sufficient conditions for the codesign of state‐feedback controller and observer of consensus are derived in terms of matrix inequalities. Sufficient conditions for the robust and nonfragile consensus designs are derived and the codesign of state‐feedback controller and observer can be obtained in terms of solving a set of linear programs. Numerical simulations are provided to show the effectiveness and applicability of the theoretical results and algorithms.     

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.     

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.     

Controller design for consensus of non-uniform rank systems with switching topology and relative output measurements

This paper studies the design problem of a controller to achieve an asymptotic consensus for a class of non-uniform rank linear systems. The interconnection topology for the N non-uniform rank systems is assumed to be modeled by a time-varying graph that switches in a finite set of connected and undirected graphs and has a non-vanishing dwell time. Under these conditions, we propose a controller for the asymptotic consensus of the N systems and provide a closed formula for an agreed trajectory that in fact indicates the attainment of average consensus. The controller is implemented through the backstepping and high-gain observer techniques, and uses only relative output measurements from the neighboring systems for the purpose of feedback. The idea behind this implementation is that the output feedback controller implemented in this way can make the norm of the state of the closed-loop system arbitrary small within any given dwell time, even for non-uniform rank systems.     

Output consensus for heterogeneous multiagent systems with Markovian switching network topologies

This paper investigates the output consensus problem of heterogeneous continuous‐time multiagent systems under randomly switching communication topologies. The switching mechanism is governed by a time‐homogeneous Markov process, whose states correspond to all possible communication topologies among agents. A novel dynamic consensus controller is proposed. The controller gains are designed based on the information of the expectation graph and the solutions to regulator equations. Furthermore, a necessary and sufficient condition is presented for output consensus of the controlled multiagent system in mean square sense. Finally, a simulation example is provided to corroborate the effectiveness of the proposed controller.     

多智能体系统一致性问题的控制器与拓扑协同优化设计

本文考虑多智能体系统一致性问题的控制与拓扑协同优化设计.首先在给定的二次性能指标下,对多智能体系统的分布式一致性控制协议寻优,得到依赖于网络拓扑图拉普拉斯矩阵的最优控制器.其次,为进一步最大限度地减少拓扑之间的连边,又不降低多智能体系统的收敛速度,通过权衡系统的通信能量和控制能量,寻求网络拓扑的优化设计,给出了拓扑优化算法和多智能体系统特征值的优化方法.最后,仿真研究验证了在控制器优化的基础上进一步寻求拓扑优化,可大大提升系统的一致性性能.     

Cooperative adaptive consensus tracking for multiple nonholonomic mobile robots

This paper addresses the cooperative adaptive consensus tracking for a group of multiple nonholonomic mobile robots, where the nonholonomic robot model is assumed to be a canonical vehicle having two actuated wheels and one passive wheel. By integrating a kinematic controller and a torque controller for the nonholonomic robotic system, a cooperative adaptive consensus tracking strategy is developed for the uncertain dynamic models using Lyapunov-like analysis in combination with backstepping approach and sliding mode technique. A key feature of the developed adaptive consensus tracking algorithm is the introduction of a directed network topology into the control constraints based on algebraic graph theory to characterise the communication interaction among robots, which plays an important role in realising the cooperative consensus tracking with respect to a specific common reference trajectory. Furthermore, a novel framework is proposed for developing a unified methodology for the convergence analysis of the closed-loop control systems, which can fully ensure the desired adaptive consensus tracking for multiple nonholonomic mobile robots. Subsequently, illustrative examples and numerical simulations are provided to demonstrate and visualise the theoretical results.     

牵制控制下的多智能体系统群一致性

本文研究了一类多智能体系统在牵制控制下的群一致性问题,提出了融合群内信息交互、群间信息交互和牵制控制器的一致性协议.对固定拓扑下的二群组智能体系统和切换拓扑下的多群组智能体系统,利用稳定性理论和图论分别给出了适用于任意拓扑结构的充要条件,使得智能体系统在所提协议和牵制控制器的联合作用下实现预期的群一致.针对拓扑图中含有生成树这一特例,分析了被施加牵制控制的智能体在结构中的具体位置.此外,对切换拓扑下进行非线性交互的多群组智能体系统,利用Lyapunov方法推导出一充分条件,得出只要对多智能体系统的一部分主体进行牵制控制,则所有智能体即可在所提协议和牵制控制器的作用下渐近收敛于各自的期望一致平衡点.最后,仿真例子验证了所提方法的有效性.     

Finite-time output feedback stabilisation of chained-form systems with inputs saturation

This paper investigates the problem of finite-time stabilisation by output feedback for a class of non-holonomic systems in chained form with input saturation. Rigorous design procedure for saturated output feedback control is presented by using the homogeneous domination approach and the nested saturation technique. Together with a novel switching control strategy, the designed controller renders that the states of closed-loop system are regulated to zero in a finite time. A simulation example is provided to illustrate the effectiveness of the proposed approach.     

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.     

Cooperative control design for non-holonomic chained-form systems

Consensus and formation control problems for multiple non-holonomic chained-form systems are solved in this paper. For consensus problem, based on cascaded structure of the chained-form systems, it amounts to solving two consensus subproblems of two linear subsystems transformed from the original system. With the obtained consensus protocols and the method of virtual structure, decentralised formation controllers can then be designed. According to different desired motion patterns of the entire group, both the formation tracking and formation stabilisation problems can be considered. The significance of this paper lies in adapting theories from non-autonomous cascaded systems for cooperative control design for non-holonomic chained-form systems. A unique feature of our proposed solution is that all states can be cooperatively controlled to achieve the desired references for non-holonomic chained-form system. Simulation results are included to illustrate the effectiveness of the proposed methods in solving cooperative control problems of non-holonomic chained-form systems.     

Cooperative tracking control for general linear multiagent systems with directed intermittent communications: An artificial delay approach

This paper investigates the consensus tracking problem for general linear multiagent systems on directed graph containing a spanning tree. For the considered linear systems, the consensus tracking aim cannot be achieved by using only memoryless static relative output feedbacks. Of particular interest is that both current and delayed relative output information of agents are required to achieve consensus. For the case of continuous communication among agents, an artificial delay output feedback control method is proposed. By utilizing the Taylor representation for the delayed signal with the remainder in the integral form, a delay‐dependent sufficient condition is presented to guarantee the exponential convergence of the global tracking error systems. For the intermittent case, the consensus tracking performance can still be guaranteed based on a multiple graph‐dependent Lyapunov functionals method. It is theoretically revealed that the time delay plays a key role in the exponential convergence of the closed‐loop systems, and the definite relationships among the time delay, network structure, communication rate, and consensus convergence rate are also provided. The effectiveness of the proposed control scheme is confirmed by numerical simulations.     

Distributed consensus of heterogeneous multi-agent systems with fixed and switching topologies

In this article, we study distributed consensus of heterogeneous multi-agent systems with fixed and switching topologies. The analysis is based on graph theory and nonnegative matrix theory. We propose two kinds of consensus protocols based on the consensus protocol of first-order and second-order multi-agent systems. Some necessary and sufficient conditions that the heterogeneous multi-agent system solves the consensus problems under different consensus protocols are presented with fixed topology. We also give some sufficient conditions for consensus of the heterogeneous multi-agent system with switching topology. Simulation examples are provided to demonstrate the effectiveness of the theoretical results.     

受干预多智能体系统平衡状态及目标追踪设计

针对拓扑结构无向连通的多智能体系统受到干预的问题,运用图论,矩阵论及极限理论,分析了系统状态保持一致性的条件,并得到了系统的平衡状态.设计了干预控制器,引导系统向任意指定地点聚集.给出了多智能体系统一致追踪移动目标的一致追踪算法.最后仿真研究实验说明了本文结论的正确性.     

Graph topology and gap topology for unstable systems

A reformation is provided of the graph topology and the gap topology for a general setting (including lumped linear time-invariant systems and distributed linear time-invariant systems) in the frequency domain. Some essential properties and their comparisons are clearly presented in the reformulation. It is shown that the gap topology is suitable for general systems rather than square systems with unity feedback. It is shown that whenever an unstable plant can be stabilized by feedback, it is a closed operator, mapping a subspace of the input space to the output space. Hence, the gap topology can always be applied whenever the unstable plant can be stabilized. The graph topology and the gap topology are suitable for different subsets of systems and have many similar characteristics. If one confines them to the same subset, they will be identical. The definitions of the graph metric and the gap metric are discussed     

Lyapunov design of global state and output feedback trackers for non-holonomic control systems

In this paper, new results are obtained for the global tracking of a class of non-holonomic dynamic systems via state and output feedback. The tracking controllers are systematically constructed on the basis of a recursive technique and a full exploitation of the system structure. When disturbances occur in a non-holonomic chained system, it is shown how to modify the controller design procedure to yield robust tracking control laws. The proposed method is demonstrated and discussed by means of a benchmark non-holonomic knife-edge mechanical system.     

Consensus of single integrator multi-agent systems with directed topology and communication delays

In this paper, a distributed control scheme has been developed for consensus of single integrator multi-agent systems with directed fixed communication topology for arbitrarily large constant, time-varying or distributed communication delays. It is proved that the closed loop control system can reach consensus with an exponential convergence rate if and only if the topology is quasi-strongly connected. Simulation results are also provided to demonstrate the effectiveness of the proposed controller.     

部分拓扑切换概率未知的移动传感网保性能一致性控制研究

本文研究了基于马尔科夫切换拓扑的移动传感网保性能一致性问题.网络拓扑切换由一般的马尔科夫链驱动,其初始和转移概率部分未知.切换拓扑集中的每个拓扑皆是带有树的有向拓扑图.借助定义包括接收、发送信息和控制输入的新的全局能耗函数,可以得到切换分布式一致性控制器集合.然后经过状态变换,一致性控制问题转化为减阶的马尔科夫跳跃系统的保性能问题.通过分析马尔科夫跳跃系统的稳定性,提出了可以同时计算次优的一致性控制器增益和次小能耗上界的算法.最后,通过数值仿真检验了控制器设计方法的性能.     

基于事件触发非线性多智能体系统的固定时间一致性

本文研究了在有向拓扑下,带有非线性动力学多智能体系统的固定时间一致性问题.提出了一种新的基于事件触发机制的非线性控制策略,对于每个智能体给出了基于状态信息的事件触发条件,当状态误差满足所给条件时才触发事件,能有效的减小系统的能量耗散和控制器的更新频次.利用Lyapunov稳定性理论和代数图论,证明在该控制策略下,多智能体系统在固定时间能实现领导跟随一致性,且不存在Zeno行为.相较于有限时间一致性策略,采用固定时间一致性策略系统的收敛时间不再依赖于系统的初始状态.最后,仿真实例验证了理论结果的有效性.     

Leader‐following control for multiple inertial agents

This paper investigates distributed controller design problem for a leader‐follower network in the presence of communication delays. Two main contributions are made in this work. First, the second‐order controlled consensus scheme for the weakly connected communication graph topology is proposed. A necessary and sufficient condition is given under which the exponential consensus is achieved. Meanwhile, the relationship among the agents' inertias, the allowable delay bound, the communication topology, the consensus convergence rate, and the control gains is unveiled. Second, the robustness performances of the distributed control scheme with respect to the communication failures and delays are provided. It is shown that if the communication failure rate and the topology switching frequency, respectively, satisfy the given bounds, the exponential second‐order controlled consensus can be achieved under a bounded delay. Numerical examples are given to illustrate the theoretical results. Copyright © 2010 John Wiley & Sons, Ltd.