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.     

Decentralized event‐triggered circle formation control for multiagent systems via synchronous periodic event detection

This paper investigates circle formation problem of multiagent systems over a kind of strongly connected and weight‐unbalanced directed graphs. To solve the concerned problem, decentralized periodic event‐triggered algorithms subject to or not to time delays are proposed, which have the advantages of decreasing the overall burden of the network in terms of finite communication and control input updates. In such algorithms, each agent independently evaluates whether the locally sampled information of itself should be broadcasted to or not to its neighbors. Furthermore, another advantage of our proposed algorithms is to automatically exclude Zeno behavior, which should be seriously considered in a variety of event‐based network systems. Sufficient conditions on circle formation control are derived under which the states of all agents can be ensured to converge to some desired equilibrium point. Simulation results are given to validate the effectiveness of the proposed methods.     

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.     

Adaptive architectures for resilient control of networked multiagent systems in the presence of misbehaving agents

Control algorithms of networked multiagent systems are generally computed distributively without having a centralised entity monitoring the activity of agents; and therefore, unforeseen adverse conditions such as uncertainties or attacks to the communication network and/or failure of agent-wise components can easily result in system instability and prohibit the accomplishment of system-level objectives. In this paper, we study resilient coordination of networked multiagent systems in the presence of misbehaving agents, i.e. agents that are subject to exogenous disturbances that represent a class of adverse conditions. In particular, a distributed adaptive control architecture is presented for directed and time-varying graph topologies to retrieve a desired networked multiagent system behaviour. Apart from the existing relevant literature that make specific assumptions on the graph topology and/or the fraction of misbehaving agents, we show that the considered class of adverse conditions can be mitigated by the proposed adaptive control approach that utilises a local state emulator – even if all agents are misbehaving. Illustrative numerical examples are provided to demonstrate the theoretical findings.     

基于观测器的多智能体系统的有限时间包含控制

在固定有向拓扑结构下,研究了具有多个静态或动态领导者的多智能体有限时间包含控制问题;假设领导者之间不存在信息的交互,提出基于快速终端滑模的控制算法,该算法驱使跟随者的运动轨迹在有限时间收敛到由领导者组成的凸包中;进一步,考虑实际应用中跟随者状态不能在线获得的情况,提出基于有限时间观测器的包含控制协议;利用图论和Lyapunov有限时间稳定性理论,给出了有限时间包含控制的充分条件;最后通过仿真示例,验证了算法的有效性。     

广义系统的有限时间滑模变结构控制

研究了一类广义系统的有限时间滑模变结构控制问题。通过非奇异线性变换把广义系统变换成受限等价形式,利用Lyapunov函数的方法,提出了一种新型的有限时间滑模变结构控制策略,给出了特殊的开关型滑模面,设计了相应的滑模变结构控制器,使得闭环系统渐进稳定,实现了滑模运动,保证了在滑模面上系统状态变量在有限时间内到达平衡点。给出了可行性算例,说明了设计的有效性。     

Robust formation control of multiagent systems on the Lie group SE(3)

This paper addresses the robust formation control problem of multiple rigid bodies whose kinematics and dynamics evolve on the Lie group SE(3). First, it is assumed that all followers have access to the state information of a virtual leader. Then, a novel adaptive super‐twisting sliding mode control with an intrinsic proportional‐integral‐derivative sliding surface is proposed for the formation control problem of multiagent system using a virtual structure (VS) approach. The advantages of this control scheme are twofold: elimination of the chattering phenomenon without affecting the control performance and no requirement of prior knowledge about the upper bound of uncertainty/disturbance due to adaptive‐tuning law. Since the VS method is suffering from the disadvantages of centralized control, in the second step, considering a network as an undirected connected graph, we assume that only a few agents have access to the state information of the leader. Afterward, using the gradient of modified error function, a distributed adaptive velocity‐free consensus‐based formation control law is proposed where reduced‐order observers are introduced to remove the requirements of velocity measurements. Furthermore, to relax the requirement that all agents have access to the states of the leader, a distributed finite‐time super‐twisting sliding mode estimator is proposed to obtain an accurate estimation of the leader's states in a finite time for each agent. In both steps, the proposed control schemes are directly developed on the Lie group SE(3) to avoid singularity and ambiguities associated with the attitude representations. Numerical simulation results illustrated the effectiveness of the proposed control schemes.     

Fixed‐time output‐feedback consensus tracking control for second‐order multiagent systems

This paper is concerned with the problem of fixed‐time consensus tracking control for a class of second‐order multiagent systems under an undirected communication graph. A distributed output‐feedback fixed‐time consensus tracking control scheme is proposed to make the states of all individual agents simultaneously track a time‐varying reference state even when the reference state is available only to a subset of the group members and only output measurements are available for feedback. Homogeneous Lyapunov function and homogeneity property are employed to show that the control scheme can guarantee the consensus tracking errors converging the origin in finite time which is bounded by a fixed constant independent of initial conditions. Numerical simulations are carried out to demonstrate the effectiveness of the proposed control law.     

基于事件驱动的多智能体有限时间分群一致控制

针对二阶线性多智能体系统的分群一致控制问题,考虑智能体通信拓扑同时包含协作和对抗关系,提出一种基于事件驱动控制的有限时间分布式领航跟随分群一致性算法,该算法可使多智能体系统在有限时间内实现分群一致,即各子组内的智能体实现状态一致,不同子组收敛至不同一致状态.采用事件驱动控制机制,设计事件驱动函数及事件触发条件,降低智能体控制器更新频率,减少系统能耗.基于代数图论和李雅普诺夫稳定性理论推导出系统的有限时间稳定性条件,通过巧妙构造Lyapunov函数,给出系统有限收敛时间的显式估计,同时证明在所提出的事件驱动机制下,每个智能体相邻触发时间间隔有严格的正下界,即避免了芝诺行为.仿真实验验证了所提出的有限时间事件驱动分群一致控制算法的有效性.     

Connectivity preservation of second-order nonlinear multiagent systems with hybrid event-driven and time-driven control

In practice, the capability of communication between each pair of agents is within a finite range. This paper investigates how to preserve connectivity for nonlinear multiagent systems while reaching consensus under event-driven control technique. By introducing an appropriate potential function based on the distance of two agents, we can demonstrate that all the agents will not lose connectivity if the initial undirected graph is connected. Furthermore, due to the existence of friction and time delay, we utilise the Young's inequality and a Lyapunov–Krasovskii functional to eliminate the negative effects of time delay. The use of impulse functions is considered which can avoid the singularity in the control input. Moreover, the hybrid event-driven and time-driven control technique is utilised to reduce the requirements of communication resources. Finally, numerical simulations are conducted to demonstrate the effectiveness of our methodology.     

多航天器系统分布式有限时间姿态协同跟踪控制

基于一致性算法, 在有向通讯拓扑下, 研究存在状态约束的多航天器系统分布式有限时间姿态协同跟踪控制问题. 在仅有部分跟随航天器可以获取领航航天器状态, 并且跟随航天器之间存在不完全信息交互的情形下, 设计了分布式快速终端滑模面, 提出了不依赖于模型的分布式有限时间姿态协同跟踪控制律. 根据有限时间Lyapunov 稳定性定理, 证明了系统的状态在有限时间内收敛于领航航天器状态的小邻域内. 最后通过仿真算例验证了所提出算法的有效性.

     

Leader–follower fixed-time consensus of multi-agent systems with high-order integrator dynamics

The leader–follower fixed-time consensus of high-order multi-agent systems with external disturbances is investigated in this paper. A novel sliding manifold is designed to ensure that the tracking errors converge to zero in a fixed-time during the sliding motion. Then, a distributed control law is designed based on Lyapunov technique to drive the system states to the sliding manifold in finite-time independent of initial conditions. Finally, the efficiency of the proposed method is illustrated by numerical simulations.     

新型有限时间收敛滑模扩张状态观测器研究

针对一类具有量测噪声的非线性不确定系统,设计了基于新型滑模扩张状态观测器的Terminal滑模控制方案．首先对系统进行两次状态扩张,然后设计一种新型滑模扩张状态观测器,通过采用特殊的滑模面保证观测误差在有限时间内收敛到零．在此基础上,设计Terminal滑模控制器,使系统状态也能在有限时间内收敛到零．严格的理论证明和仿真结果均证明了所设计新型滑模观测器及闭环控制方案的有效性和快速性．     

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.     

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.     

Optimal control of distributed multiagent systems with finite-time group flocking

The flocking of multiple intelligent agents, inspired by the swarm behavior of natural phenomena, has been widely used in the engineering fields such as in unmanned aerial vehicle (UAV) and robots system. However, the performance of the system (such as response time, network throughput, and resource utilization) may be greatly affected while the intelligent agents are engaged in cooperative work. Therefore, it is concerned to accomplish the distributed cooperation while ensuring the optimal performance of the intelligent system. In this paper, we investigated the optimal control problem of distributed multiagent systems (MASs) with finite-time group flocking movement. Specifically, we propose two optimal group flocking algorithms of MASs with single-integrator model and double-integrator model. Then, we study the group consensus of distributed MASs by using modern control theory and finite-time convergence theory, where the proposed optimal control algorithms can drive MASs to achieve the group convergence in finite-time while minimizing the performance index of the intelligence system. Finally, experimental simulation shows that MASs can keep the minimum energy function under the effect of optimal control algorithm, while the intelligent agents can follow the optimal trajectory to achieve group flocking in finite time.     

Decentralized tube‐based model predictive control of uncertain nonlinear multiagent systems

This paper addresses the problem of decentralized tube‐based nonlinear model predictive control (NMPC) for a general class of uncertain nonlinear continuous‐time multiagent systems with additive and bounded disturbance. In particular, the problem of robust navigation of a multiagent system to predefined states of the workspace while using only local information is addressed under certain distance and control input constraints. We propose a decentralized feedback control protocol that consists of two terms: a nominal control input, which is computed online and is the outcome of a decentralized finite horizon optimal control problem that each agent solves at every sampling time, for its nominal system dynamics; and an additive state‐feedback law which is computed offline and guarantees that the real trajectories of each agent will belong to a hypertube centered along the nominal trajectory, for all times. The volume of the hypertube depends on the upper bound of the disturbances as well as the bounds of the derivatives of the dynamics. In addition, by introducing certain distance constraints, the proposed scheme guarantees that the initially connected agents remain connected for all times. Under standard assumptions that arise in nominal NMPC schemes, controllability assumptions, communication capabilities between the agents, it is guaranteed that the multiagent system is input‐to‐state stable with respect to the disturbances, for all initial conditions satisfying the state constraints. Simulation results verify the correctness of the proposed framework.     

一类二阶非线性系统的有限时间状态反馈镇定方法

针对一类二阶非线性系统的有限时间状态反馈镇定问题进行了讨论. 给出了三种基于连续状态反馈的全局有限时间状态反馈镇定方法. 首先，利用非线性齐次系统性质，设计出一种状态反馈控制器，使得闭环系统渐近稳定并且具有负的齐次度；其次，基于有限时间Lyapunov函数的反步构造法，给出了一种有限时间控制器；最后，利用非奇异终端滑模控制技术，得到了一种使闭环系统有限时间收敛到平衡点的反馈镇定控制器. 仿真结果表明了这些方法的有效性.     

A sliding mode observer design for uncertain fractional Ito stochastic systems with state delay

This paper addresses the robust observer design problem for uncertain time-delay fractional Ito stochastic systems. A sliding surface is proposed and it is shown that state estimates converge towards it and remain there for the subsequent time. Additionally, by constructing a novel Lyapunov functional, a sufficient condition for the stability of the sliding motion of the estimated states is given in the form of Linear Matrix Inequalities (LMIs). It is demonstrated that the state estimates are stabilizable in probability provided that the LMI is feasible. Moreover, a finite-time sliding mode control law based on the estimated states is proposed. Simulation examples are given to show the validity and effectiveness of the results.     

Distributed consensus control for multi‐agent systems using terminal sliding mode and Chebyshev neural networks

This paper investigates the problem of consensus tracking control for second‐order multi‐agent systems in the presence of uncertain dynamics and bounded external disturbances. The communication ?ow among neighbor agents is described by an undirected connected graph. A fast terminal sliding manifold based on lumped state errors that include absolute and relative state errors is proposed, and then a distributed finite‐time consensus tracking controller is developed by using terminal sliding mode and Chebyshev neural networks. In the proposed control scheme, Chebyshev neural networks are used as universal approximators to learn unknown nonlinear functions in the agent dynamics online, and a robust control term using the hyperbolic tangent function is applied to counteract neural‐network approximation errors and external disturbances, which makes the proposed controller be continuous and hence chattering‐free. Meanwhile, a smooth projection algorithm is employed to guarantee that estimated parameters remain within some known bounded sets. Furthermore, the proposed control scheme for each agent only employs the information of its neighbor agents and guarantees a group of agents to track a time‐varying reference trajectory even when the reference signals are available to only a subset of the group members. Most importantly, finite‐time stability in both the reaching phase and the sliding phase is guaranteed by a Lyapunov‐based approach. Finally, numerical simulations are presented to demonstrate the performance of the proposed controller and show that the proposed controller exceeds to a linear hyperplane‐based sliding mode controller. Copyright © 2011 John Wiley & Sons, Ltd.