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.     

Disturbance observer–based consensus tracking for nonlinear multiagent systems with switching topologies

This paper considers the leader‐follower consensus tracking problem for nonlinear multiagent systems with external disturbances and switching topologies. A distributed disturbance observer is constructed to estimate the disturbances suffered by the followers. Then, a distributed consensus protocol is proposed for the consensus tracking problem with disturbance rejection under a fixed directed topology based on the disturbance observer. Next, this result is extended to the case in which the switching communication topology only frequently but not always contains a directed spanning tree. By selecting the parameters appropriately such that the communication time satisfies various preset conditions, it is theoretically proven that the consensus tracking with disturbance rejection can also be achieved by the multiagent systems. Finally, a simulation example is presented to demonstrate the performance of the proposed control scheme.     

Robust consensus tracking for a class of heterogeneous second‐order nonlinear multi‐agent systems

This paper deals with the robust consensus tracking problem for a class of heterogeneous second‐order nonlinear multi‐agent systems with bounded external disturbances. First, a distributed adaptive control law is proposed based on the relative position and velocity information. It is shown that for any connected undirected communication graph, the proposed control law solves the robust consensus tracking problem. Then, by introducing a novel distributed observer and employing backstepping design techniques, a distributed adaptive control law is constructed based only on the relative position information. Compared with the existing results, the proposed adaptive consensus protocols are in a distributed fashion, and the nonlinear functions are not required to satisfy any globally Lipschitz or Lipschitz‐like condition. Numerical examples are given to verify our proposed protocols. Copyright © 2014 John Wiley & Sons, Ltd.     

具有非匹配扰动的非线性变参数系统模型参考跟踪控制

本文研究了一类含有非匹配扰动的非线性变参数系统的跟踪控制问题.首先,设计非线性扰动观测器用于估计系统所受到的未知扰动.其次,在前馈–反馈跟踪控制器中引入扰动补偿控制项,提出一种基于扰动观测器的跟踪控制策略.利用依赖于状态和时变参数的线性矩阵不等式,导出保证闭环系统输入–状态稳定的充分条件,进而运用平方和凸优化技术解析地构造出扰动观测器和跟踪控制器.通过理论证明,所设计的控制策略能够实现非线性变参数系统输出对参考模型输出的跟踪,消除输出通道中非匹配扰动的影响.最后,由数值仿真例子验证了所提方法的有效性.     

Output Consensus of Heterogeneous Linear Multi‐agent Systems Subject to Different Disturbances

This paper investigates the output consensus problem of heterogeneous linear multi‐agent systems with individual agents subject to different disturbances. A distributed control law based on internal reference models and dynamic output feedback is presented for output consensus. It is shown that the embedded internal reference models of agents can achieve consensus to a common trajectory which is determined by the underlying system topology and the initial states of the internal reference models. Then a necessary and sufficient condition is presented for output consensus of heterogeneous linear multi‐agent systems. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed control laws.     

基于干扰观测器的二阶多智能体系统模型参考一致性

针对受到外部干扰影响的二阶多智能系统, 提出一种新型干扰观测器的设计方案.在只有部分智能体能接收到参考模型信 号的条件下, 研究受到不同外系统生成干扰信号影响的二阶多智能体系统模型参考一致性问题.针对干扰信号由线性外系统和非线性外系 统生成的情况, 分别设计干扰观测器.进一步提出分布式控制协议, 所提出的一致性协议可以有效地抑制干扰, 最终实现多智能体 系统的模型参考一致性.仿真算例验证了所提出方法的有效性.     

Robust Consensus Tracking Control of Uncertain Multi-Agent Systems With Local Disturbance Rejection

In this paper, a new distributed consensus tracking protocol incorporating local disturbance rejection is devised for a multi-agent system with heterogeneous dynamic uncertainties and disturbances over a directed graph. It is of two-degree-of-freedom nature. Specifically, a robust distributed controller is designed for consensus tracking, while a local disturbance estimator is designed for each agent without requiring the input channel information of disturbances. The condition for asymptotic di...     

Optimal tracking control for discrete-time systems with multiple input delays under sinusoidal disturbances

This study researches the tracking control problem for discrete-time systems with multiple input delays affected by sinusoidal disturbances. This study is organized around the expression of sinusoidal and disturbances and the delay-free transformation. First, based on the periodic characteristic of the sinusoidal disturbance, the sinusoidal disturbances are considered as the output of an exosystem. By proposing a discrete variable transformation, the discrete-time system with multiple input delays and the quadratic performance index are transformed into equivalent delay-free ones. Then, by constructing an augmented system that comprises the states of the exosystems of sinusoidal disturbances, the reference input, and the delay-free transformation systems, the original tracking problem is transformed into the optimal tracking problem for a delay-free system with respect to the simplified performance index. The optimal tracking control (OTC) law is obtained from Riccati and Stein equations. The existent and uniqueness of the optimal control law is proved. A reduced-order observer is constructed to solve the problem of physically realizable for the items of the reference input and sinusoidal disturbances. Finally, the feasibility and effectiveness of the proposed approaches are validated by numerical examples.     

Practical time-varying formation tracking for high-order nonlinear multi-agent systems based on the distributed extended state observer

Practical time-varying formation tracking analysis and design problems for high-order nonlinear multi-agent systems are investigated, where the time-varying formation tracking error is controlled within an arbitrarily small bound. The states of followers form a predefined time-varying formation while tracking the state of the leader with unknown control input. Besides, the dynamics of each agent has heterogeneous nonlinearity and disturbance. First, a distributed extended state observer is constructed to estimate the follower's nonlinearity and disturbance, and the leader's unknown control input simultaneously. A protocol based on the distributed extended state observer is proposed. Second, sufficient conditions for the multi-agent systems to achieve the practical time-varying formation tracking under the protocol are presented by using the Lyapunov stability theory. Third, an approach is derived to design the proposed protocol by solving a linear matrix inequality. Finally, numerical simulation results are given to illustrate the effectiveness of the theoretical results.     

Nonlinear internal model based attitude tracking and disturbance rejection

In this paper, we consider the attitude tracking and disturbance rejection problem of rigid spacecraft, which is subject to some disturbances generated by nonlinear exosystems. A new nonlinear internal model is designed to manipulate the uncertainties caused by external disturbances, which includes the linear internal model as a special case. A numerical example is given to illustrate the theoretical result presented in the paper. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

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.     

Robust Tracking Control for Self-balancing Mobile Robots Using Disturbance Observer

In this paper, a robust tracking control scheme based on nonlinear disturbance observer is developed for the self-balancing mobile robot with external unknown disturbances. A desired velocity control law is firstly designed using the Lyapunov analysis method and the arctan function. To improve the tracking control performance, a nonlinear disturbance observer is developed to estimate the unknown disturbance of the self-balancing mobile robot. Using the output of the designed disturbance observer, the robust tracking control scheme is presented employing the sliding mode method for the selfbalancing mobile robot. Numerical simulation results further demonstrate the effectiveness of the proposed robust tracking control scheme for the self-balancing mobile robot subject to external unknown disturbances.      

Observer‐based consensus of second‐order multi‐agent system with fixed and stochastically switching topology via sampled data

This paper addresses the distributed observer‐based consensus problem of second‐order multi‐agent systems via sampled data. Firstly, for the case of fixed topology, a velocity‐independent distributed control law is proposed by designing a distributed observer to estimate the unavailable velocity, then a sufficient and necessary condition of consensus on design parameters and sampling period is obtained by using the matrix analysis method. Secondly, for the case of stochastically switching topology, a sufficient and necessary condition of mean square consensus is also proposed and proven, and an algorithm is provided to design the parameters in the consensus protocol. Two simulation examples are given to illustrate the effectiveness of the proposed consensus algorithms. Copyright © 2012 John Wiley & Sons, Ltd.     

Robust fault detection in linear systems based on PI observers

A parametric approach for robust fault detection in linear systems with unknown disturbances is presented. The residual is generated using full-order proportional-integral (PI) observers. The approach is based on a result for PI observer design recently proposed. In terms of the design degrees of freedom provided by the parametric PI observer design and a group of introduced parameter vectors, a sufficient and necessary condition for PI observer design with disturbance decoupling is established. By properly constraining the design parameters according to this proposed condition, the effect of the disturbance to the residual signal is decoupled, and a simple algorithm is presented. The presented approach offers all the degrees of design freedom. A numerical example illustrates the effect of the proposed approach.     

有向图中基于扰动观测器的线性多智能体系统一致性

在有向图中,针对多智能体系统中智能体动力学存在扰动的情形,研究了系统的一致性问题.每个智能体的动力学模型为存在未知外部扰动的一般线性系统.在有向图是强连通的条件下,通过设计一种基于扰动观测器的分布式算法,实现了存在未知扰动的线性多智能体系统的一致性.最后通过仿真验证所提算法的有效性.     

Robust adaptive tracking control for a class of mechanical systems with unknown disturbances under actuator saturation

A robust adaptive tracking control scheme is presented for a class of multiple‐input and multiple‐output mechanical systems with unknown disturbances under actuator saturation. The unknown disturbances are expressed as the outputs of a linear exogenous system with unknown coefficient matrices. An adaptive disturbance observer is constructed for the online disturbance estimation. An actuator saturation compensator is introduced to attenuate the adverse effects of actuator saturation. The adaptive backstepping method is then applied to design the robust adaptive tracking control law. It is proved that the designed control law makes the system outputs track the desired trajectories and guarantees the global uniform ultimate stability of the closed‐loop control system. Simulations on a two‐link robotic manipulator verify the effectiveness of the proposed control scheme.     

Flatness-based linear output feedback control for disturbance rejection and tracking tasks on a Chua's circuit

A linear output feedback controller is developed for trajectory tracking problems defined on a modified version of Chua's circuit. The circuit modification considers the introduction of a flat input, i.e. a suitable external control input channel guided by (a) the induction of the flatness property on a measurable output signal of the circuit and (b) the physical viability of the control input. A linear active disturbance rejection control based on a high-gain linear disturbance observer, is implemented on a laboratory prototype. We show that the state-dependent disturbance can be approximately, but arbitrarily closely, estimated through a linear high-gain observer, called a generalised proportional integral (GPI) observer, which contains a linear combination of a sufficient number of extra iterated integrals of the output estimation error. Experimental results are presented in the output reference trajectory tracking of a signal generated by an unrelated chaotic system of the Lorenz type. Laboratory experiments illustrate the proposed linear methodology for effectively controlling chaos.     

适应扰动的无人直升机姿态跟踪控制

无人直升机在实际飞行过程中,会受到阵风等外界因素的干扰,并且模型不确定性也会对控制效果带来不利影响.为应对这些挑战,本文设计了一种基于扩张状态观测器的自抗扰反步控制器.首先,建立了无人直升机姿态动力学模型.随后,引入扩张状态观测器,用以实时观测由外界扰动和模型不确定性组成的总和扰动.观测得到的总和扰动估计值与基于Lyapunov函数的反步法控制器控制算法相结合,用以消除总和扰动的影响,使得无人直升机在各种飞行条件下均能对运动指令进行快速和准确的跟踪.最后,仿真研究和飞行实验验证了该控制律的有效性.与同等条件下的PID控制器相比,该控制律表现出更优的飞行性能.     

基于参考模型的扰动观测器控制系统

为了补偿控制系统的未知动态和外部扰动,论文提出一种基于参考模型的扰动观测器控制系统.首先,分析了二阶理想参考模型控制系统的设计,并通过闭环传递函数证明了参考模型控制系统的稳定性.然后,设计了二阶系统扰动观测器和基于参考模型的扰动观测器控制律,分析了二阶闭环控制误差系统收敛性.并推广到n阶控制系统,证明了n阶闭环控制误差...