Stochastic bounded consensus tracking of second-order multi-agent systems with measurement noises based on sampled-data with small sampling delay

This paper is devoted to the stochastic bounded consensus tracking problems of second-order multi-agent systems, where the control input of each agent can only use the information measured at the sampling instants from its neighbors or the virtual leader with a time-varying reference state, the measurements are corrupted by random noises, and the signal sampling process induces the small sampling delay. The augmented matrix method, the probability limit theory and some other techniques are employed to derive the necessary and sufficient conditions guaranteeing the mean square bounded consensus tracking. We show that the convergence of the proposed protocol simultaneously depends on the constant feedback gains, the network topology, the sampled period and the sampling delay, and that the static consensus tracking error depends on not only the above mentioned factors, but also the noise intensity and the upper bound of the velocity and the acceleration of the virtual leader. The obtained results cover no sampling delay as its one special case. Simulations are provided to demonstrate the effectiveness of the theoretical results.     

Stochastic Bounded Consensus Tracking of Second-Order Multi-Agent Systems with Measurement Noises and Sampled-Data

This paper investigates the stochastic bounded consensus tracking problems of second-order multi-agent systems, where the control input of an agent can only use the information measured at the sampling instants from its neighbors or the virtual leader with a time-varying reference state, and the measurements are corrupted by random noises. The probability limit theory, the algebra graph theory, and some other techniques are employed to derive the necessary and sufficient condition guaranteeing the mean square bounded consensus tracking. It turns out that the maximum allowable sampling period depends on not only the network topology but also the constant feedback gains. Furthermore, the effects of the sampling period on tracking performance, including the tracking speed and the static tracking error, are also analyzed. The results show that reducing the sampling period can accelerate the tracking speed and decrease the static tracking error. Simulations are provided to demonstrate the effectiveness of the theoretical results.     

Consensus of nonlinear multiagent systems with mode-dependent delay via stochastic sampled data under Markovian switching topologies

In this article, we investigate the mean-square consensus problem of multiagent systems with one leader and multiple followers. In consideration of the uncertain disturbance from external environment or internal change of system, the interaction topology and time-varying delay switch randomly which are regulated by a time-homogeneous Markovian chain. The distributed control protocol is designed based on the stochastic sampling information from its neighbors and the leader. Using stochastic Lyapunov theory and linear matrix inequality (LMI) approach, the sufficient condition is concluded to guarantee the mean-square consensus. For the undirected topology case, a low-dimensional LMI-based consensus criterion is further derived based on the matrix diagonalization method. Finally, a numerical simulation is provided to demonstrate the reasonability of the theoretical results.     

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.     

随机多智能体系统一致性增益的设计与分析

在固定和切换拓扑中通信网络含有加性随机噪声的情况下,针对随机多智能体系统一致性跟踪控制问题,本文采用自适应控制方法给出了一种新的一致性增益设计方法.在基于邻居智能体状态设计的分布式自适应控制协议中,每个跟随者的一致性增益自适应律仅仅依赖于跟踪误差,并且与通信网络全局信息无关.结合代数图论,随机理论工具和自适应控制得到两个结论:1)每个跟随者以均方意义下跟踪上领导者; 2)每个跟随者的一致性增益趋于一个理想估计值.通过两个仿真实例验证算法的有效性.     

Distributed node‐to‐node consensus of multi‐agent systems with stochastic sampling

This paper is concerned with the mean square node‐to‐node consensus tracking problem for multi‐agent systems with nonidentical nonlinear dynamics and directed topologies. The randomly occurred uncertainties in the sampling devices may result in stochastically varied sampling periods, which lead to the investigation of node‐to‐node consensus problem under stochastic sampling. By employing the input‐delay method and discontinuous Lyapunov functional approach, it arrives at some sufficient conditions under which the state of each follower can track that of the corresponding leader asymptotically in the mean square sense. Finally, some numerical simulations are provided to verify the effectiveness of the theoretical results. Copyright © 2015 John Wiley & Sons, Ltd.     

Distributed consensus tracking of multi-agent systems with nonlinear dynamics under a reference leader

This paper investigates the distributed consensus tracking problem for multi-agent systems with Lipschitz-type dynamics under a reference leader. It is assumed that the leader state information is only available to a subset of followers, while the bounded reference input of the leader’s is unavailable to any follower. To achieve consensus tracking, a class of discontinuous protocols based on the relative information between the neighbouring agents are proposed. Furthermore, as extensions of the former result, the robust and adaptive consensus tracking problems are studied for the case where there exist parameter uncertainties and external disturbances in the network. Finally, the effectiveness of the theoretical result is demonstrated through a network of single-link manipulators.     

Finite‐time consensus tracking for harmonic oscillators using both state feedback control and output feedback control

This paper investigates the distributed finite‐time consensus‐tracking problem for coupled harmonic oscillators. The objective is to guarantee a team of followers modeled by harmonic oscillators to track a dynamic virtual leader in finite time. Only a subset of followers can access the information of the virtual leader, and the interactions between followers are assumed to be local. We consider two cases: (i) The followers can obtain the relative states between their neighbors and their own; and (ii) Only relative outputs between neighboring agents are available. In the former case, a distributed consensus protocol is adopted to achieve the finite‐time consensus tracking. In the latter case, we propose a novel observer‐based dynamic protocol to guarantee the consensus tracking in finite time. Simulation examples are finally presented to verify the theoretical analysis. Copyright © 2012 John Wiley & Sons, Ltd.     

Pattern preserving path following of unicycle teams with communication delays

This paper examines the problem of pattern-preserving path following control for unicycle teams with time-varying communication delay. A key strategy used here introduces a virtual vehicle formation such that each real vehicle has a corresponding virtual vehicle as its pursuit target. Under an input-driven consensus protocol, the virtual vehicle formation is forced to stay close to the desired vehicle formation; and a novel controller design is proposed to achieve virtual leader tracking for each vehicle with constrained motion. It is shown that, by the proposed strategy, the pattern can be preserved if the formation speed is less than some computable value that decreases with increasing size of delay, and the exact desired formation pattern can be eventually achieved if this speed tends to zero.     

Distributed adaptive output feedback tracking control for a class of uncertain nonlinear multi-agent systems

This paper addresses the distributed output feedback tracking control problem for multi-agent systems with higher order nonlinear non-strict-feedback dynamics and directed communication graphs. The existing works usually design a distributed consensus controller using all the states of each agent, which are often immeasurable, especially in nonlinear systems. In this paper, based only on the relative output between itself and its neighbours, a distributed adaptive consensus control law is proposed for each agent using the backstepping technique and approximation technique of Fourier series (FS) to solve the output feedback tracking control problem of multi-agent systems. The FS structure is taken not only for tracking the unknown nonlinear dynamics but also the unknown derivatives of virtual controllers in the controller design procedure, which can therefore prevent virtual controllers from containing uncertain terms. The projection algorithm is applied to ensure that the estimated parameters remain in some known bounded sets. Lyapunov stability analysis shows that the proposed control law can guarantee that the output of each agent synchronises to the leader with bounded residual errors and that all the signals in the closed-loop system are uniformly ultimately bounded. Simulation results have verified the performance and feasibility of the proposed distributed adaptive control strategy.     

Prescribed performance global stable adaptive neural dynamic surface consensus tracking control of stochastic multi-agent systems with hysteresis inputs and nonlinear dynamics

This paper focuses on the leader-following consensus control problem of stochastic multi-agent systems with hysteresis inputs and nonlinear dynamics. A leader-following consensus scheme is presented for stochastic multi-agent systems directions under directed graphs, which can achieve predefined synchronisation error bounds. By mainly activating an auxiliary robust control component for pulling back the transient escaped from the neural active region, a multi-switching robust neuro adaptive controller in the neural approximation domain, which can achieve globally uniformly ultimately bounded tracking stability of multi-agent systems recently. A specific Nussbaum-type function is introduced to solve the problem of unknown control directions. Using a dynamic surface control technique, distributed consensus controllers are developed to guarantee that the outputs of all followers synchronise with that of the leader with prescribed performance. Based on Lyapunov stability theory, it is proved that all signals in closed-loop systems are uniformly ultimately bounded and all the follower agents can keep consensus with the leader. Two simulation examples are provided to illustrate the effectiveness and advantage of the proposed control scheme.     

Cluster-delay consensus in multi-agent systems via pinning leader-following approach with intermittent effect

In this paper, the cluster consensus problem with delays of first-order nonlinear multi-agent systems is studied through pinning leader-following approach with periodic intermittent effect. The graph of the networked system is assumed to be directed and weakly connected. A new type of pinning consensus protocol with intermittent effect is designed according to the ways in which the agents link, specifically, the agents in each cluster are divided into three subsets due to the orientation of their topological degree, and each subset of agents is controlled by an individual law. A redefined notion on cluster consensus with two sorts of time delays is proposed in this article. Some consensus criteria are derived to guarantee that the agents in the same cluster asymptotically follow the virtual leader with a delay, while agents in different clusters reach consensus with delays via following their leaders. Some numerical simulations are given to illustrate the effectiveness of the theoretical results.     

受外界干扰的离散多智能体系统的均方有界一致性

对有外界干扰的二阶离散多智能体系统,研究了在马尔可夫切换拓扑结构下的均方有界一致性问题.首先,设计了一个带有智能体位置和速度信息的控制协议.其次,在随机有界干扰的情况下,借助于矩阵分析方法以及Lyapunov函数,得到了闭环系统实现均方有界一致所需的代数条件,同时给出了各智能体状态误差的上界.最后,数值仿真验证了理论结果的有效性.     

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.     

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.     

Consensus Seeking for Discrete-time Multi-agent Systems with Communication Delay

This paper studies the consensus problem for discrete-time multi-agent systems of first-order in the presence of constant communication delay. Provided that the agent dynamics is unstable and the network topology is undirected, effects of two kinds of communication delays on consensus are investigated. When the relative information is affected by delay, we show that the effect of delay can be alleviated by using the historical input information in the protocol design. On the other hand, if the communication delay only influences the actually transmitted information, sufficient condition admitting any large yet bounded delay for consensus is obtained, and the delay in this case is allowed to be unknown and time-varying. Finally, simulation results are provided to demonstrate the effectiveness of the theoretical results.      

Improved leaderless consenus criteria of networked multi-agent systems based on the sampled data

This paper is concerned with leaderless consensus of networked multi-agent systems with Lipschitz-type nonlinear dynamics based on the sampled data. By introducing a weighted average state of all nodes as the virtual leader, the error variables are defined as the distance between agents and the virtual leader. The improvements are done in two directions. First, several consensus conditions are derived by linear matrix inequalities based on Finsler's lemma instead of algebraic criteria based on the general algebraic connectivity. Finsler's lemma is utilised to deal with the linear dependence of the error variables. Second, a distributed event-triggered transmission strategy under the periodic sampling scheme is proposed to reduce the communication between agents and the control updates, which only need to check the event condition at each sampling instant, avoiding the continuous monitor. With the improved strategies, one theorem and two corollaries are derived and a co-design approach of the feedback gain and the event-triggered matrix is also presented. Finally, an example is provided to validate the effectiveness of the theoretical results.     

带虚拟领导者的多智能体系统的非光滑一致性

研究了在限制交互范围条件下具有一个虚拟领导者的二阶多智能体系统的一致性问题。假设多智能体系统中所有智能体均可以接收到领导者的信息，而智能体之间只有距离在一定范围内才可以进行相互通信。在相对状态反馈的线性一致性协议下，通过李雅普诺夫法，证明了该多智能体系统二阶一致性的充分条件。接着通过仿真实例验证了理论结果，并对该算法作出了总结。     

Adaptive output feedback consensus tracking for linear multi-agent systems with unknown dynamics

In this paper, the consensus tracking problem with unknown dynamics in the leader for the linear multi-agent systems is addressed. Based on the relative output information among the agents, decentralised adaptive consensus protocols with static coupling gains are designed to guarantee that the consensus tracking errors converge to a small neighbourhood around the origin and all the signals in the closed-loop dynamics are uniformly ultimately bounded. Moreover, the result is extended to the case with dynamic coupling gains which are independent of the eigenvalues of the Laplacian matrix. Both of the protocols with static and dynamic coupling gains are designed by using the relative outputs, which are more practical than the state-feedback ones. Finally, the theoretical results are verified through an example.     

Mean square consensus of multi-agent systems with multiplicative noises and time delays under directed fixed topologies

This paper investigates the mean square consensus problem of multi-agent systems impacted by the combined uncertainty of multiplicative noises and time delays. Considering general network under directed fixed topologies, we propose consensus protocol that take into account both the multiplicative noises and time delays. Using tools from stochastic differential delay equation (SDDE), martingale theory and stochastic inequality, we establish sufficient conditions and obtain the explicit consensus gain and delay upper bounds under which the proposed protocol leads to mean square consensus. In addition, we compare the impact of multiplicative and additive noise and reach the conclusion that multiplicative noises have the property of stabilizing effect. Simulations demonstrate the theoretical results.