Adaptive containment control of second-order multi-agent systems with nonlinear dynamics and multiple input-bounded leaders

This paper considers the adaptive containment control problem of second-order multi-agent systems with inherent nonlinear dynamics. In particular, the leaders’ control inputs are nonzero, bounded, and not available to any follower. Based on the relative states among neighbouring agents, a discontinuous adaptive protocol is first proposed to ensure that the containment errors of each follower converge to zero asymptotically, i.e. the states of the followers asymptotically converge to the convex hull spanned by those of the leaders. To eliminate the chattering effect caused by the discontinuous protocol, a continuous adaptive protocol is further designed based on the boundary layer technique and the σ-modification technique. Numerical examples are provided to demonstrate the effectiveness of our theoretical results.     

Dynamic-estimator-based adaptive secure containment control for constrained nonlinear multi-agent systems under denial-of-service attacks

This article concentrates upon the adaptive secure containment control problem for a class of uncertain nonlinear multi-agent systems with the output constraint requirements under denial-of-service (DoS) attacks. At first, to overcome the difficulty that the tracking performance of the nonlinear multi-agent systems under the DoS attacks is disturbed seriously, a novel adaptive secure containment control approach is presented by applying a DoS attacks detection mechanism and introducing the barrier Lyapunov functions, which enables the system to achieve the security control objective that the output of each agent eventually converges to the convex hull spanned by the dynamic leaders' outputs, while never violating the output constraints. Then, a state estimator is designed, which reconstructs the immeasurable states of the multi-agent systems and approximates the completely unknown nonlinearities arising from the agents. In addition, the dynamic surface control technique is used to solve the “explosion of complexity” problem. It is demonstrated that the proposed anti-attack controller ensures that all the signals of the closed-loop system are semi-globally uniformly ultimately bounded. Finally, a simulation example is provided to illustrate the effectiveness of the theoretical results.     

带强连通分支的多智能体系统可控包含控制

研究有强连通子图拓扑结构的有向多智能体系统领导者选择及可控包含控制问题.根据网络拓扑结构,智能体被分为两类:单元智能体和一般智能体.首先设计强连通子图中个体组成的单元智能体的一致性协议实现各个单元的一致;后由单元智能体和一般智能体构成新的拓扑结构,结合复杂网络可控性理论与二分图最大匹配算法确定满足网络可控的最少领导者集合,并为所有智能个体设计相应的控制协议,驱使跟随者渐近收敛到多个领导者组成的动态凸包中,从而实现网络的可控包含控制.仿真结果验证了理论分析的正确性.     

Nonfragile containment control of nonlinear multi-agent systems via a disturbance observer-based approach

In this article, we consider the nonfragile containment control problem of nonlinear multi-agent systems (MASs) with exogenous disturbance where the communication links among agents under consideration is directed. Firstly, based on relative output measurements between the agent and its neighbors, a disturbance observer-based control protocol is proposed to solve the containment control problem of MASs with inherent nonlinear dynamics and exogenous disturbances. Secondly, because of the additional tuning of parameters in the real control systems, uncertainties in the designing of observer and controller gains always occur, and as a result, an output feedback controller with disturbance rejection is conceived and the containment control problem of nonlinear MASs with nonfragility is thoroughly investigated. Then, depending on matrix transformation and inequality technique, sufficient conditions of the designed controller gains exist, which is derived from the asymptotic stability analysis problem of some containment error dynamics of MASs. Finally, two simulation examples are exploited to illustrate the effectiveness of the proposed techniques.     

Multi-stage dynamic event-triggered containment control of nonlinear multi-agent systems with input-bounded leaders and time-varying delay

This article immerses in the event-triggered containment control problem for a Lipschitz-like nonlinear multi-agent system with multiple active leaders. First, two event-triggered mechanisms with internal dynamic variables are designed in both sensor-observer (S-O) and controller-actuator (C-A) channels to monitor data transmission and reduce communication burden. Second, an observer is constructed with the aid of the output information to estimate the states that cannot be acquired directly. Then, a control protocol considering time-varying communications delays is proposed based on the observer. Third, the boundedness analysis of the containment error system is constructed by Lyapunov stability theory, the sufficient conditions are given in light of strict feasible LMIs. Finally, the validity of the proposed controller is verified by two simulations.     

Event-triggered containment control for multi-agent systems under hybrid cyber attacks

This paper studies event-triggered containment control problem of multi-agent systems (MASs) under deception attacks and denial-of-service (DoS) attacks. First, to save limited network resources, an event-triggered mechanism is proposed for MASs under hybrid cyber attacks. Different from the existing event-triggered mechanisms, the negative influences of deception attacks and DoS attacks are considered in the proposed triggering function. The communication frequencies between agents are reduced. Then, based on the proposed event-triggered mechanism, a corresponding control protocol is proposed to ensure that the followers will converge to the convex hull formed by the leaders under deception attacks and DoS attacks. Compared with the previous researches about containment control, in addition to hybrid cyber attacks being considered, the nonlinear functions related to the states of the agents are applied to describe the deception attack signals in the MAS. By orthogonal transformation of deception attack signals, the containment control problem under deception attacks and DoS attacks is reformulated as a stability problem. Then, the sufficient conditions on containment control can be obtained. Finally, a set of simulation example is used to verify the effectiveness of the proposed method.     

Distributed adaptive containment control for high-order nonlinear multi-agent systems

This paper considers the adaptive containment control of high-order nonlinear multi-agent systems with nonlinear parameterisation. Without imposing any conditions on the unknown nonlinearities and unknown parameters, the distributed controllers are constructed recursively with only neighbours’ information by using the backstepping design method. Under the assumption that the leaders set is globally reachable, it is shown that all the signals of the closed-loop systems are global uniformly ultimately bounded (UUB), and all the followers will exponentially converge to the convex hull spanned by the dynamic leaders with adjustable tracking errors. Finally, two simulation examples demonstrate the effectiveness of the control scheme.     

多智能体网络系统的自适应协调控制

为实现多智能体网络系统的协调控制,设计了一种新型的带有自适应协调器的控制器.基于动态图建立了多智能体网络系统的模型,并考虑了系统的非线性互联和不可避免存在的时变时滞.应用分布式控制策略,设计了自适应参数估计的协调器,用于调节智能体之间的互联强度,使网络达到稳定的预设水平.并基于Lyapunov-Kra-sovskii泛函和自适应动态偏差反馈控制技术,根据拉萨尔不变集原理证明了偏差控制系统的渐近收敛性.这种控制方法,可在系统参数不确定的情况下,同时完成参数估计和协调控制.所设计的控制律和自适应律简单,易于实现,仿真示例验证了所提方法的有效性.     

多智能体系统自适应跟踪控制

基于带有非线性动态的二阶多智能体系统,研究了在有动态领导者条件下的跟踪一致性问题。假设跟随者只能获取邻居智能体的相对状态信息,只有一部分跟随者可以获得领导者的位置和速度信息,领导者的控制输入非零且不被任何一个跟随者可知。在通信拓扑为无向连通图的条件下,为了避免全局信息的不确定性,设计了分布式自适应控制协议。将系统的一致性问题转化为误差系统的一致性问题,通过Lyapunov稳定性理论和矩阵理论分析得到了该协议使系统达到一致的充分条件。最后用仿真例子证明了设计方法的有效性。     

Robust output regulation for containment control of heterogeneous discrete-time nonlinear multi-agent systems

ABSTRACT

In existing researches on containment control of heterogeneous multi-agent systems (MASs), the solution is usually dependent on the solvability of regulator equations. However, the closed-form solution of many nonlinear regulator equations of systems is rarely obtained. Towards this end, in this paper the containment control problem of heterogeneous discrete-time nonlinear MASs subject to parameter uncertainties is considered, and the power series approach is adopted to solve complex regulator equations by decomposing them into a series of solvable linear equations. Then, a distributed robust control law based on internal model principle is presented by utilising the solution of the linear equations. Theoretical analysis shows that under certain assumptions asymptotic containment control is achieved for the heterogeneous discrete-time nonlinear MASs with sufficiently small parameter perturbations. Finally, a numerical simulation is implemented to verify the proposed control law.     

Command-filter-based distributed containment control of nonlinear multi-agent systems with actuator failures

In this paper, the problem of distributed containment fault-tolerant control for a class of nonlinear multi-agent systems in strict-feedback form is studied. The considered nonlinear multi-agent systems are subject to unknown nonlinear functions and actuator faults with loss of effectiveness and lock-in-place. By resorting to the universal approximation capability of fuzzy logical systems, the command filtered backstepping technique and nonlinear fault-tolerant control theory, distributed controllers are designed recursively. From the Lyapunov stability theory, it is proved that all signals of the resulting closed-loop systems are cooperatively semi-globally uniformly ultimately bounded and the containment errors converge to a small neighbourhood of origin by properly tuning the design parameters. Finally, a numerical example is provided to show the effectiveness of the proposed control method.     

Event-triggered distributed containment control of heterogeneous linear multi-agent systems by an output regulation approach

In this paper, the event-triggered distributed containment control of heterogeneous linear multi-agent systems in the output regulation framework is studied. The leaders are treated as exosystems and the containment control problem will be converted into an output regulation problem. An event-triggered protocol is then designed for each follower by the output information of neighbours. It is proved that the followers can asymptotically converge to the dynamic convex hull spanned by multiple leaders under the designed protocol and triggered strategy. Furthermore, it is shown that the proposed protocol and triggered condition can exclude Zeno behaviour, so the feasibility of the control strategy is verified. Finally, a numerical simulation is given to illustrate the effectiveness of the proposed protocol.     

无需相对速度信息的多Euler-Lagrange 系统自适应神经网络包含控制

对含有模型非线性不确定性和外部扰动的多Euler-Lagrange 系统的分布式协调包含控制问题进行研究. 考虑通讯拓扑为有向图, 所有领航者均为动态, 且各智能体间相对速度信息不可测情况. 首先, 选取相对速度作为辅助变量, 引入低通滤波器进行估计; 然后, 采用神经网络方法逼近并补偿非线性不确定性, 提出一种分布式自适应包含控制律, 并应用Lyapunov 稳定性理论证明闭环系统的包含误差一致最终有界; 最后, 通过仿真算例验证了所提出的控制律的有效性.

     

多智能体系统的有限时间包含控制研究

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.     

Adaptive containment control of heterogeneous high-order fully actuated multi-agent systems

In this article, the distributed containment control schemes are presented for a class of nonlinear heterogeneous high-order fully actuated multi-agent systems. First, for each follower, the reference trajectory generator is constructed by using the output information of the neighbor agents. Then, the distributed containment controllers are designed for the system with known nonlinear system function matrices and control gain matrices. Further, since the existence of modeling errors and other uncertain factors, the obtained system model is often not accurate enough, that is, the system function matrix and control gain matrix are actually unknown nonlinear matrices. To tackle these obstacles, we employ the radial basis function neural network method to approximate the unknown nonlinear system function matrices and skillfully construct the controllers combined with the adaptive technology to eliminate the effects of the unknown control gain matrices. The developed control strategies can guarantee that the containment control can be realized and the containment errors can be adjusted to arbitrary precision. In the end, the simulation results on the electromechanical system and robotic system demonstrate the availability and effectiveness of the provided schemes.     

Neuroadaptive containment control of nonlinear multiagent systems with input saturations

This paper investigates the output containment tracking problem of nonlinear multiagent systems with mismatched uncertain dynamics and input saturations. A neural network–based distributed adaptive command filtered backstepping (CFB) scheme is given, which can guarantee that the containment tracking errors reach to the desired neighborhood of origin and all signals in the closed‐loop system are bounded. Note that error compensation system and virtual control laws established in CFB only use local information, so the given scheme is completely distributed. Moreover, the applied sliding mode differentiator (SMD) can make the outputs of SMD fast approximate the virtual signal and its derivative at each step of backstepping, which can further improve the control quality. Finally, a simulation example is given to show the effectiveness of the proposed scheme.     

Event-based containment control for multi-agent systems with packet dropouts

This paper is concerned with the event-triggered containment control for stochastic multi-agent systems subject to packet dropouts. The adopted event-triggered protocol is with absolutely triggered conditions catering for the requirement of real-time to an extreme. In light of such a protocol, a novel definition of containment control in mean-square sense, named as χ-containment, is proposed to better describe the tracking dynamics of followers. Based on relative measurement outputs, the purpose of this paper is to design an output-feedback controller such that all followers converge into the convex hull spanned by leaders. First, with the help of the property of the Laplacian matrix, the containment control problem is transformed to an easily setting step by step. Then, sufficient conditions with the form of matrix inequalities are derived to guarantee the desired χ-containment which depends on the initial values and the event-triggered thresholds. By introducing a free matrix combined with an orthogonal basis of the null space of control matrix, the controller gain can be obtained by solving a set of linear matrix inequalities. Finally, a simulation example is given to verify the effectiveness of the designed control protocol.     

Observer-based event-triggered containment control of multi-agent systems with time delay

This paper studies the containment control of general linear multi-agent systems with or without time delay. The observer-based event-triggered control schemes will be considered. For the conventional distributed containment control protocol, we will not update the relative state continuously, i.e. the relative state will be updated by some events which happen intermittently. A completely decentralised event trigger will be designed for leader–follower systems. Under the proposed protocol, if we design some appropriate feedback gain matrices, all followers will asymptotically converge to the convex hull spanned by the dynamic leaders. Numerical simulations are also provided and the results show highly consistent with the theoretical results.     

分数阶时滞非线性多智能体系统的自适应控制

针对分数阶多智能体系统中存在时滞和非线性特性, 时滞往往会引起控制系统的性能下降甚至出现系统 不稳定等问题, 提出了一种含时滞非线性的分数阶多智能体系统自适应控制方法. 对于多智能体系统的控制协议, 设计了基于领导者和相邻智能体状态信息的自适应控制协议, 减小了过大常数控制增益带来的能源浪费. 对于一 致性, 利用图论基础、分数阶Halanay不等式稳定性定理、Kronecker积和Schur补引理, 获得了分数阶时滞非线性多 智能体系统的LMI一致性条件. 仿真结果验证了本文算法的正确性和有效性. 由于整数阶系统是分数阶系统的特殊 形式, 本文结论可以直接推广到整数阶多智能体系统中.