二阶非线性多智能体系统领导跟随一致性研究

为减少通信时延对系统一致性的影响,针对有领导者的二阶非线性多智能体系统的领导跟随一致性进行了研究,新颖的提出近似随机脉冲时延的概念并应用于新协议。相比于传统协议,新协议在脉冲时刻通信时延较小时,各智能体基于时延态对自身当前时刻状态进行预测,并以自身未来预测状态取代时延态发送给各邻接智能体同时补偿自身反馈通道时延,从而使系统更快实现一致性。基于Lyapunov稳定性理论,利用一类再推广的Halanay不等式的性质给出两个保证系统实现一致性的充分条件。最后,实例仿真证明了新协议的优越性。     

Leader-following consensus for uncertain second-order nonlinear multi-agent systems

This paper studies the leader-following consensus problem for a class of second-order nonlinear multi-agent systems subject to linearly parameterized uncertainty and disturbance. The problem is solved by integrating the adaptive control technique and the adaptive distributed observer method. The design procedure is illustrated by an example with a group of Van der Pol oscillators as the followers and a harmonic system as the leader.     

Leader-following consensus for a class of second-order nonlinear multi-agent systems

This paper deals with the leader-following consensus problem for a class of multi-agent systems with nonlinear dynamics and directed communication topology. The control input of the leader agent is assumed to be unknown to all follower agents. A distributed adaptive nonlinear control law is constructed using the relative state information between neighboring agents, which achieves leader-following consensus for any directed communication graph that contains a spanning tree with the root node being the leader agent. Compared with previous results, the nonlinear functions are not required to satisfy the globally Lipschitz or Lipschitz-like condition and the adaptive consensus protocol is in a distributed fashion. A numerical example is given to verify our proposed protocol.     

Adaptive finite-time consensus in multi-agent networks

This paper is concerned with the finite-time consensus problem of distributed agents having non-identical unknown nonlinear dynamics, to a leader agent that also has unknown nonlinear control input signal. By parameterization of unknown nonlinear dynamics, a Lyapunov technique in conjunction with homogeneity technique is presented for designing a decentralized adaptive finite-time consensus control protocol in undirected networks. Homogeneous Lyapunov functions and homogeneous vector fields are introduced in the stability analysis although the whole system is not homogeneous. Theoretical analysis shows that leader-following consensus can be achieved in finite-time, meanwhile, finite-time parameter convergence can be also guaranteed under the proposed control scheme. An example is given to validate the theoretical results.     

Leader-following consensus control of second-order nonlinear multi-agent systems with applications to slew rate control

This paper addresses the distributed leader-following consensus control of second-order strict-feedback nonlinear multi-agent systems. By employing mean value theorem, variable separation technique, and backstepping methodology, a fully distributed adaptive control law is designed using only local relative state information. The proposed control law solves the leader-following consensus problem for any directed communication graph that contains a spanning tree with the root node being the leader agent. The application to hovercraft slew rate control system is given to verify the effectiveness of the theoretical results.     

基于事件触发的二阶多智能体领导跟随一致性

研究二阶多智能体系统在固定有向拓扑下的领导跟随一致性问题.为了节省网络和计算资源,给出一种基于事件触发控制的一致性算法.针对每个跟随者智能体,设计基于状态误差形式的触发函数,只有当状态误差满足一定条件,即触发函数取值为零时智能体才触发事件,同时更新并传递自身的采样信息,在两个相邻事件触发时刻之间,控制输入只受领导者控制信号的影响.利用模型变换、矩阵理论和Lyapunov稳定性理论给出多智能体系统达到领导跟随一致性的充分条件.仿真结果验证了理论方案的可行性和有效性.     

Distributed leader-following consensus for second-order multi-agent systems with nonlinear inherent dynamics

In this paper, the leader-following consensus problem for second-order multi-agent systems with nonlinear inherent dynamics is investigated. Two distributed control protocols are proposed under fixed undirected communication topology and fixed directed communication topology. Some sufficient conditions are obtained for the states of followers converging to the state of virtual leader globally exponentially. Rigorous proofs are given by using graph theory, matrix theory and Lyapunov theory. Simulations are also given to verify the effectiveness of the theoretical results.     

Leader-following scaled consensus of second-order multi-agent systems under directed topologies

ABSTRACT

This paper investigates the leader-following scaled consensus problem of second-order multi-agent systems under directed topologies. Three novel leader-following scaled consensus protocols are designed. First, a novel scaled consensus protocol is proposed. It can guarantee the velocity of each agent in one sub-group exactly follow that of a leader, and the follower agents achieve scaled consensus. Second, another proposed protocol enables the agents' positions and velocities of one sub-group accurately track those of a leader, and the follower agents achieve scaled consensus. Third, consider the case where the leader's states available to one or multiple followers and the leader travels with a varying velocity, a novel scaled consensus tracking protocol is proposed. Sufficient and necessary conditions are obtained to guarantee scaled consensus tracking for the three cases,respectively. Finally, simulation examples are made to verify the effectiveness of the theoretical results.     

Leader-following fixed-time output feedback consensus for second-order multi-agent systems with input saturation

This paper investigates the leader-following fixed-time output feedback consensus problem for second-order multi-agent systems with input saturation. By combing fixed-time control technique and bi-limit homogeneous systems theory, a class of bounded fixed-time consensus protocols are developed for leader-following multi-agent systems. The protocol design is divided into two parts. First, when all the state information of the followers are measurable, a state feedback consensus protocol is designed to achieve fixed-time consensus. Then, when the velocity information is unmeasurable, an observer-based fixed-time consensus protocol is proposed. With the help of Lyapunov stability theorem and the property of a homogeneous function, it is theoretically shown that the states of all followers can track that of the leader in fixed-time in the presence of input saturation. Finally, numerical simulation is carried out to illustrate the effectiveness of theoretical results.     

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.     

符号网络下多智能体系统二分一致性的牵制控制问题

一致性是多智能体系统分布式协同控制的核心.以往关于一致性问题的研究大多集中在个体间只有正权重相互作用的网络中.现研究符号网络(网络中个体间既存在正权重相互作用又存在负权重相互作用)下二分一致性的牵制控制问题.针对外界输入仅作用于网络节点二元划分的同一簇个体和外界输入分别作用于网络节点二元划分的两簇中个体两种情形,给出其二分一致性稳态值的定量化描述,即如果外界输入只控制其中一簇的个体,则当外界输入作用为正(负)权重时,受到外界输入直接影响的 一簇个体的状态收敛到外界输入(外界输入的相反数),另一簇个体状态收敛到外界输入的相反数(外界输入);如果外界输入以相反的权重符号分别控制两簇中的个体,则由正(负)权重外界输入控制的一簇个体状态收敛到外界输入(外界输入的相反数),另一簇个体状态收敛到外界输入的相反数(外界输入).仿真研究验证了所提出理论的有效性.     

Periodic intermittent consensus of second-order agents networks with nonlinear dynamics

The consensus problem for a class of second-order agents networks via periodically intermittent control is investigated in this paper. A novel protocol is designed by periodic intermittent measurements and directed topology. Based on algebraic graph theory, matrix theory and Lyapunov control approach, some sententious conditions are obtained for reaching consensus in agents networks with fixed topology. Finally, one example is given to illustrate the effectiveness of the theoretical results.     

Leader-following consensus of nonlinear fractional-order multi-agent systems via event-triggered control

This paper investigates the consensus problem of leader-following multi-agent systems with fractional-order nonlinear dynamics. A typical event is defined as some error signals exceeding a given threshold. By applying Lyapunov functional approach and skills of computing function limit, consensus of the controlled multi-agent systems can be reached asymptotically. Meanwhile, the event-triggered algorithm can exclude Zeno behaviours. Finally, a numerical simulation is exploited to verify the effectiveness of the theoretical result.     

Distributed robust finite-time nonlinear consensus protocols for multi-agent systems

This paper investigates the robust finite-time consensus problem of multi-agent systems in networks with undirected topology. Global nonlinear consensus protocols augmented with a variable structure are constructed with the aid of Lyapunov functions for each single-integrator agent dynamics in the presence of external disturbances. In particular, it is shown that the finite settling time of the proposed general framework for robust consensus design is upper bounded for any initial condition. This makes it possible for network consensus problems to design and estimate the convergence time offline for a multi-agent team with a given undirected information flow. Finally, simulation results are presented to demonstrate the performance and effectiveness of our finite-time protocols.     

Leader-following consensus of nonlinear multi-agent systems with switching topologies and unreliable communications

In this paper, distributed leader-following consensus for a class of nonlinear multi-agent systems with switching topologies and unreliable communications is studied. Each possible topology contains a directed spanning tree rooted at the leader. Agents share the information only with their neighbors on some disconnected time intervals due to the unreliable communications. By designing suitable distributed controllers, all follower nodes asymptotically synchronize to the leader node if the communication rate is larger than a threshold value for each time interval. By using multiple Lyapunov functions theory and linear matrix inequalities technique, some sufficient conditions are given to guarantee the consensus. Moreover, based on the theoretical results, the admissible communication rate and convergence rate of the whole systems are adjusted by the feedback gain matrix, which provides helpful design guidelines in practical applications. Finally, a simulation example is given to verify the effectiveness of the proposed method.     

Quantised consensus of multi-agent systems with nonlinear dynamics

This paper studies the consensus problem of first-order and second-order multi-agent systems with nonlinear dynamics and quantised interactions. Continuous-time and impulsive control inputs are designed for the multi-agent systems on the logarithmic quantised relative state measurements of agents, respectively. By using nonsmooth analysis tools, we get some sufficient conditions for the consensus of multi-agent systems under the continuous-time inputs. Compared with continuous-time control inputs, impulsive distributed control inputs just use the state variables of the systems at discrete-time instances. Based on impulsive control theory, we prove that the multi-agent systems can reach consensus by choosing proper control gains and impulsive intervals. The simulation results are given to verify the effectiveness of the theoretical results.     

Impulsive consensus algorithms for second-order multi-agent networks with sampled information

In this paper, the distributed consensus problem for second-order continuous-time multi-agent networks with sampled-data communication is investigated. Motivated by impulsive control strategy, two kinds of impulsive distributed consensus algorithm are proposed. These algorithms only utilize the sampled information and are implemented at sampled times. By using the stability theory of impulsive systems and properties of the Laplacian matrix, necessary and sufficient conditions are obtained to ensure the consensus of the controlled networks. It is shown that the control gains, the sampling period and the eigenvalues of the Laplacian matrix of the communication graph play key roles in achieving the consensus. A numerical example is given to illustrate the results.     

多智能体系统离散时间一致性问题中的参数设计

研究二阶多智能体系统在固定、有向通信拓扑条件下的离散时间一致性问题.针对每个智能体,采用基于速度、位置的分布式控制协议,分析速度、位置增益系数以及采样周期等参数对系统一致性的影响.结果表明,要实现二阶多智能体系统的一致性控制,在保持个体之间通信拓扑有生成树的同时,控制协议中的各个参数还必须满足一定的约束条件.系统拉普拉斯矩阵的特征值和采样周期对系统能否实现渐近一致起到了关键的作用.最后,给出一致性控制中参数设计的一种可行方法,并通过仿真对理论分析的正确性进行验证.     

Leader-following consensus of double-integrator multi-agent systems with noisy measurements

This paper proposes a leader-following consensus control for continuous-time double-integrator multi-agent systems in noisy communication environment with a constant velocity reference state. Each follower in the team inaccurately measures its neighbors’ positions and the leader’s position if this follower has access to the leader, that the measured positions are corrupted by noises. The constant velocity of the leader is a priori well known. The consensus protocol is constructed based on algebraic graph theory and some stochastic tools. Conditions to ensure the tracking consensus in mean square are derived for both fixed and switching directed topologies. Finally, to illustrate the approach presented, some numerical simulations are carried out.     

Distributed finite-time consensus tracking for nonlinear multi-agent systems with a time-varying reference state

This paper investigates the consensus tracking problem for nonlinear multi-agent systems with a time-varying reference state. The consensus reference is taken as a virtual leader, whose output is only its position information that is available to only a subset of a group of followers. The dynamics of each follower consists of two terms: nonlinear inherent dynamics and a simple communication protocol relying only on the position of its neighbours. In this paper, the consensus tracking problem is respectively considered under fixed and switching communication topologies. Some corresponding sufficient conditions are obtained to guarantee the states of followers can converge to the state of the virtual leader in finite time. Rigorous proofs are given by using graph theory, matrix theory, and Lyapunov theory. Simulations are presented to illustrate the theoretical analysis.