Practical time‐varying formation tracking for high‐order nonlinear multiagent systems with multiple leaders based on the distributed disturbance observer

Practical time‐varying formation tracking analysis and design problems for high‐order nonlinear multiagent systems with directed interaction topologies are investigated by using the distributed disturbance observer, where the time‐varying formation tracking error can be controlled within an arbitrarily small bound. Different from the previous work, there exists a predefined time‐varying formation formed by the states of the followers and the formation tracks the convex combination of the states of the leaders with unknown control inputs. Besides, the leaders can be multiple, and the dynamics of each follower has heterogeneous nonlinearity and disturbance. First, a distributed disturbance observer‐based practical time‐varying formation tracking protocol is constructed using neighboring relative information, where only a part of the followers, which are named as well‐informed ones, are required to obtain the information of the multiple leaders. The proposed protocol can process the heterogeneous nonlinearity, the disturbance of each follower, and the unknown control inputs of the leaders simultaneously. Then, an algorithm with 2 steps is presented to design the practical time‐varying formation tracking protocol by solving an algebraic Riccati equation and an algebraic equation, where the time‐varying formation tracking feasibility condition is introduced. Moreover, the stability of the closed‐loop multiagent system under the proposed protocol is proved by using the properties of the Laplacian matrix and the Lyapunov stability theory. Finally, a numerical simulation example is provided to illustrate the effectiveness of the obtained theoretical results.     

Distributed Time-Varying Formation Tracking Analysis and Design for Second-Order Multi-Agent Systems

Distributed time-varying formation tracking analysis and design problems for second-order multi-agent systems with one leader are studied respectively, where the states of followers form a predefined time-varying formation while tracking the state of the leader. Different from the previous results on formation tracking control, the formation for the followers can be described by specified time-varying vectors and the trajectory of the leader can also be time-varying. A distributed formation tracking protocol is constructed using only neighboring relative information. Necessary and sufficient conditions for second-order multi-agent systems with one leader to achieve time-varying formation tracking are proposed by utilizing the properties of the Laplacian matrix, where the formation tracking feasibility constraint is also given. An approach to design the formation tracking protocol is proposed by solving an algebraic Riccati equation. The presented results can be applied to deal with the target enclosing problems and consensus tracking problems for second-order multi-agent systems with one target/leader. An application in the target enclosing of multiple vehicles is provided to demonstrate the effectiveness of the theoretical results.     

Homogeneous finite-time consensus tracking of high-order-integrator agents by parametric approach

Finite-time consensus tracking of high-order-integrator multi-agent systems (MAS) is investigated under an undirected topology. When the leader's control input is known to all followers, the homogeneous finite-time control for a high-order integrator is extended to a distributed protocol for the corresponding MAS, and a set of control gains are found by the parametric approach for robust control, such that the multiple agents are simultaneously stabilised in finite time by keeping all characteristic polynomials Hurwitz. When it is only known to the leader's neighbouring followers, a distributed observer is presented for each follower to estimate it in finite time, and the combined observer-based protocol achieves finite-time consensus tracking in a fully distributed fashion. Simulation examples illustrate the effectiveness of the proposed scheme.     

基于观测器的多智能体系统一致性控制与故障检测

针对一类受到未知干扰的非线性多智能体系统,提出了一种鲁棒一致性控制与故障检测算法.首先,针对每个智能体系统设计了一个未知输入非线性观测器.然后,基于观测器的状态估计信息,设计了鲁棒一致性控制协议.控制协议保证了给定的干扰抑制性能指标.接着,考虑智能体出现故障的情形,采用自适应阈值法,提出了一种分布式故障检测算法.最后,以多个直流电机驱动的单摆系统为例进行了仿真实验,仿真结果表明了一致性控制与故障检测算法的有效性.     

Formation Control for Nonlinear Multi-agent Systems with Linear Extended State Observer

This paper investigates the formation control problem for nonlinear multi-agent systems with a virtual leader. A distributed formation control strategy based on linear extended state observer (LESO) is proposed under the hypothesis that velocity of the agent's neighbors could not be measured. Some sufficient conditions are established to ensure that the nonlinear multi-agent systems form a predefined formation with switching topology when the nonlinear function is known. Moreover, the tracking errors are bounded with external disturbance. Lastly, a numerical example with different scenarios is presented to demonstrate the validity of the obtained results.      

异构集群系统分布式自适应输出时变编队跟踪控制

提出了一种能够解决高阶异构集群系统输出时变编队跟踪问题的控制方法. 集群系统中的智能体分为领导者和跟随者, 领导者和跟随者的动力学模型可以完全不同. 跟随者的输出在跟踪领导者输出的同时保持时变编队实现协同运动. 考虑了领导者存在已知或未知控制输入、领导者和跟随者均存在未知扰动、有向通信拓扑存在切换等多种因素并存的情况, 结合观测器理论、自适应控制理论和滑模控制理论设计了完全分布式的输出时变编队跟踪控制协议, 摆脱了对领导者控制输入上界值、与通信拓扑相关的拉普拉斯矩阵的特征值以及时变编队函数等全局信息的依赖. 利用Lyapunov理论证明了在有向拓扑切换条件下异构集群系统的闭环稳定性. 最后通过数值仿真对理论结果的有效性进行了验证.     

一阶多智能体受扰系统的自抗扰分布式优化算法

研究一类具有未知外部干扰的一阶多智能体系统的分布式优化问题.在分布式优化任务中,每个智能体只被容许利用自己的局部目标函数和邻居的状态信息,设计一个分布式优化算法,使全局目标函数取得最小值,其中全局目标函数是所有局部目标函数之和.针对该问题,首先提出由扩张状态观测器和优化算法组成的自抗扰分布式优化算法.其次,在Lyapu...     

高阶不确定非线性系统的线性自抗扰控制

针对一类具有内部动态和外部扰动未知的SISO高阶非线性系统,提出一种通用的线性自抗扰控制方案.该方案基于单参数调节的高增益观测器思想,分别设计线性跟踪微分器、线性扩张状态观测器和线性状态误差反馈控制律.利用Lagrange中值定理和Cauchy-Schwarz不等式将系统总扰动的微分值转化为关于系统估计和跟踪误差的函数,可以解决因系统控制增益未知所导致的控制量微分值难以预先确定的问题.在此基础上,基于Lyapunov稳定性定理证明闭环系统误差信号有界,并进一步分析得到系统估计和跟踪误差与控制器参数的定量关系,即都可以随观测器增益的增大而达到无限小.仿真比较结果验证了所提出方案的有效性,与韩式自抗扰控制方案相比,该方案结构简单,调节参数少,易于工程实现.     

单向通信拓扑领航者动态未知线性多智能体系统的协同迭代学习控制（英文）

This paper considers the cooperative tracking of linear multi-agent systems with a dynamic leader whose input information is unavailable to any followers. Cooperative iterative learning controllers, based on the relative state information of neighboring agents, are proposed for tracking the dynamic leader over directed communication topologies. Stability and convergence of the proposed controllers are established using Lyapunov-Krasovskii functionals. Furthermore, this result is extended to the output feedback case where only the output information of each agent can be obtained. A local observer is constructed to estimate the unmeasurable states. Then, cooperative iterative learning controllers, based on the relative observed states of neighboring agents,are devised. For both cases, it is shown that the multi-agent systems whose communication topologies contain a spanning tree can reach synchronization with the dynamic leader, and meanwhile identify the unknown input of the dynamic leader using distributed iterative learning laws. An illustrative example is provided to verify the proposed control schemes.     

单向通信拓扑领航者动态未知线性多智能体系统的协同迭代学习控制

研究单向通信拓扑领航者动态未知线性多智能体系统的协同跟踪问题.基于邻居的相对状态信息,设计了分布式迭代学习控制律实现对领航者的协同跟踪控制,采用Lyapunov-Krasovskii函数分析闭环系统的稳定性与收敛性.进而,将状态反馈结论拓展到输出反馈,通过构造局部观测器估计不可量测的状态信息,采用估计的相对状态信息设计了分布式迭代学习控制器.对于以上两种情形,多智能体系统在通讯拓扑含有生成树的条件下能够实现与领航者的状态同步,同时,所设计的分布式迭代学习律能够对领航者未知输入进行精确估计.仿真实例验证了所提方法的有效性.     

Distributed Fault-Tolerant Consensus Tracking of Multi-Agent Systems Under Cyber-Attacks

This paper investigates the distributed fault-tolerant consensus tracking problem of nonlinear multi-agent systems with general incipient and abrupt time-varying actuator faults under cyber-attacks. First, a decentralized unknown input observer is established to estimate relative states and actuator faults. Second, the estimated and output neighboring information is combined with distributed fault-tolerant consensus tracking controllers. Criteria of reaching leader-following exponential consensus tracking of multi-agent systems under both connectivity-maintained and connectivity-mixed attacks are derived with average dwelling time, attack frequency, and attack activation rate technique, respectively. Simulation example verifies the effectiveness of the fault-tolerant consensus tracking algorithm.      

Disturbance rejection based tracking control design for fuzzy switched systems with time-varying delays and disturbances

The disturbance rejection and tracking problem of T-S fuzzy switched systems with uncertainties, input time-varying delays and disturbances is addressed in this article. For that cause, a modified repetitive control protocol based on the improved-equivalent-input-disturbance (IEID) estimator and extended Smith predictor approach has been proposed, which guarantees the perfect disturbance estimation and tracking performances with high precision. Specifically, by incorporating the transfer function of main feedback path in conventional Smith predictor block, the input time-varying delays are effectively compensated. In the direction of estimating the disturbances, an active disturbance rejection technique called IEID estimator approach is precisely considered. By exploiting the output of the IEID estimator and parallel distributed compensation strategy, the fuzzy rule based modified repetitive control system is formulated. Further, by making use of Lyapunov method together with average dwell-time approach, a set of sufficient conditions in the form of matrix inequalities are established. More respectively, by solving the developed matrix inequalities, the controller and observer gain matrices are determined. At last, the method proposed in this work is validated in terms of presenting the simulation results of two numerical examples, including boiler-turbine system.     

Leader–follower consensus of linear multi-agent systems with unknown external disturbances

This paper addresses the leader–follower consensus tracking problem for multi-agent systems with identical general linear dynamics and unknown external disturbances. First, a distributed extended state observer is proposed, where both the local states and disturbance of each agent are estimated simultaneously by using the relative output information between neighbors. Then a consensus algorithm is proposed for each agent based on the relative estimated states between neighbors and its own disturbance estimate. It is shown that, with the proposed observer-based consensus algorithm, the leader–follower consensus problem can be solved. Finally, we present a simulation example to demonstrate the effectiveness of the proposed algorithm.     

Observer-based prescribed-time consensus control for heterogeneous multi-agent systems under directed graphs

This work studies the prescribed-time robust consensus tracking problem of heterogeneous multi-agent systems over directed graphs. Aiming at multi-agent systems with a static leader and only matched disturbances, a distributed observer-based consensus algorithm is developed, to ensure that the tracking errors converge to zero accurately in prescribed time. For the case of multi-agent systems with a dynamic leader and mismatched/matched disturbances, an adaptive strategy based on a distributed observer and a disturbance observer is designed by the dynamic damping reciprocal technology. Such strategy can avoid the numerical singularity, adapt to the situation that the upper bounds of the disturbances are unknown, and assure that the tracking errors converge to an adjustable neighborhood of zero within prescribed time. Finally, simulations are given to verify the effectiveness of the proposed control strategies.     

带有输入时滞的领导跟随系统扰动抑制一致性

针对一类受到外部干扰且有输入时滞的多智能体系统,讨论了在固定有向拓扑下的领导跟随扰动抑制一致性问题。首先,对于存在外部干扰的多智能体系统,给出分布式状态观测器,使得每个智能体的系统状态和外部干扰被同时估计。其次,基于截取预测方法,利用邻居智能体相对输出信息获得的状态估计和自身干扰估计为每个智能体设计一致性协议。然后,用Lyapunov-Krasovskii理论对系统的观测性和稳定性进行分析,获得满足多智能体系统稳定的充分条件,并将控制器增益和观测器增益求解转化为求解线性矩阵不等式(LMIs)的形式。最后,通过一个仿真例子来验证所得结果的可行性和有效性。     

Robust time‐varying formation design for multiagent systems with disturbances: Extended‐state‐observer method

Robust time‐varying formation design problems for second‐order multiagent systems subjected to external disturbances are investigated. First, by constructing an extended state observer, the disturbance compensation is estimated, which is a critical term in the proposed robust time‐varying formation control protocol. Then, an explicit expression of the formation center function is determined and impacts of disturbance compensations on the formation center function are presented. With the formation feasibility conditions, robust time‐varying formation design criteria are derived to determine the gain matrix of the formation control protocol by utilizing the algebraic Riccati equation technique. Furthermore, the tracking performance and the robustness property of multiagent systems are analyzed. Finally, the numerical simulation is provided to illustrate the effectiveness of theoretical results.     

Event-triggered based bearing-only formation control for nonlinear multi-agent with unknown disturbance

This article delves into the bearing-only formation tracking control problem of nonlinear multi-agent systems with unknown disturbances and unmodeled dynamics, wherein the distributed control solely utilizes the relative bearing information of its neighbors. Firstly, a disturbance observer combined with a neural network is proposed to eliminate the impact of unknown disturbances and unmodeled dynamics. Additionally, a pioneering event-triggered based backstepping control approach is put forth for the formation tracking control problem of nonlinear multi-agent systems, which economizes on communication bandwidth and computing resources by decreasing the update frequency of the controller. Finally, using the Lyapunov method, it is demonstrated that all signals of the control system are bounded, and the convergence errors are confined to a small neighborhood of the origin while excluding the “Zeno behavior” phenomenon through rigorous proof.     

Observer-based distributed coordinated tracking control for multiple simple-pendulum network systems with time-varying delays

For networked control systems consisting of multiple simple-pendulums driven by corresponding DC motors with time-varying communication and input delays, a distributed coordinated controller via observer-based output feedback is designed to solve the tracking problem under both fixed and jointly-connected switching topologies. Firstly, the linearized dynamic model for multiple nonlinear simple-pendulum network systems with DC motors is presented, and the distributed coordinated tracking problem considering time-varying input delays is mathematically described. Then the distributed observer-based tracking control protocol with time-varying communication and input delays is proposed, and simultaneously, both the observer gain and feedback gain are designed. Two examples are simulated to demonstrate consensus tracking for three types of states, i.e., swing angles, angular velocities of multiple simple-pendulums and armature currents of DC motors can be completed utilizing the developed coordinated tracking control with fixed and jointly connected topologies.     

Decentralised consensus-based formation tracking of multiple differential drive robots

This article investigates the control problem for formation tracking of multiple nonholonomic robots under distributed manner which means each robot only needs local information exchange. A class of general state and input transform is introduced to convert the formation-tracking issue of multi-robot systems into the consensus-like problem with time-varying reference. The distributed observer-based protocol with nonlinear dynamics is developed for each robot to achieve the consensus tracking of the new system, which namely means a group of nonholonomic mobile robots can form the desired formation configuration with its centroid moving along the predefined reference trajectory. The finite-time stability of observer and control law is analysed rigorously by using the Lyapunov direct method, algebraic graph theory and matrix analysis. Numerical examples are finally provided to illustrate the effectiveness of the theory results proposed in this paper.     

Cooperative output regulation of heterogeneous multi-agent systems based on passivity

This paper investigates the problem of cooperative output regulation of heterogeneous linear multi-agent systems. A passive framework is presented for the stabilisation analysis of cooperative output regulation, which can overcome the difficulty caused by the fact that the global dynamics of heterogeneous multi-agent systems depends on the global communication structure. An adaptive distributed observer is proposed to estimate the state of the exosystem, and the proposed distributed observer is independent of any global information of the communication graph. Based on passivity design and adaptive distributed observer, both a distributed state feedback and a distributed output feedback protocol are designed for output synchronisation of heterogeneous multi-agent systems. The gain matrices of the distributed protocols and observers are obtained by a Riccati equation design approach. Furthermore, sufficient local conditions for solving the problem of cooperative output regulation of heterogeneous multi-agent systems are presented. Finally, numerical simulation results are given to illustrate the effectiveness of the proposed distributed control schemes.