Distributed output regulation for linear multi-agent systems with communication delays

In this paper, a distributed output regulation approach is presented for the cooperative control of linear multi-agent systems in the presence of communication delays. Both dynamic state and output feedback control laws are designed for achieving the property of output regulation. Sufficient conditions for the existence of these control laws are provided in terms of linear matrix inequalities. Simulation results are given to support the efficiency of the proposed distributed output regulation approach.     

Distributed event-triggered output regulation of multi-agent systems

Motivated by the future use of embedded microprocessors with limited resources and limited computational resources, the distributed output regulation with event-driven strategies problem of linear multi-agent systems is considered in this paper. The main task is to design distributed feedback by employing event-triggered technique for multi-agent systems such that all agents can track an active leader, and/or distributed disturbance rejection. Both leader and disturbance are generated by some external system (exosystem). Both distributed static and dynamic feedback with event-triggered strategy are constructed here. Then, the input-to-state stability of the closed-loop multi-agent system is analysed. Finally, a numerical example is given to validate the proposed control.     

Distributed formation output regulation of switching heterogeneous multi-agent systems

In this article, the distributed formation output regulation problem of linear heterogeneous multi-agent systems with uncertainty under switching topology is considered. It is a generalised framework for multi-agent coordination problems, which contains or concerns a variety of important multi-agent problems in a quite unified way. Its background includes active leader following formation for the agents to maintain desired relative distances and orientations to the leader with a predefined trajectory, and multi-agent formation with environmental inputs. With the help of canonical internal model we design a distributed dynamic output feedback to handle the distributed formation output regulation problem.     

Robust cooperative control for multi-agent systems via distributed output regulation

Robust cooperative control for multi-agent systems is considered in this paper, under the framework of the distributed output regulation problem. With some fundamental assumptions, two necessary and sufficient conditions are given for the distributed output regulation problem to be solvable. The algorithm of designing the robust distributed control law is provided, with the help of internal models. It is shown that this robust controller is effective in a neighborhood of the nominal system, which is tolerant of system uncertainties.     

Distributed robust control of linear multi-agent systems with parameter uncertainties

This article considers the distributed robust control problems of uncertain linear multi-agent systems with undirected communication topologies. It is assumed that the agents have identical nominal dynamics while subject to different norm-bounded parameter uncertainties, leading to weakly heterogeneous multi-agent systems. Distributed controllers are designed for both continuous- and discrete-time multi-agent systems, based on the relative states of neighbouring agents and a subset of absolute states of the agents. It is shown for both the continuous- and discrete-time cases that the distributed robust control problems under such controllers in the sense of quadratic stability are equivalent to the H _∞ control problems of a set of decoupled linear systems having the same dimensions as a single agent. A two-step algorithm is presented to construct the distributed controller for the continuous-time case, which does not involve any conservatism and meanwhile decouples the feedback gain design from the communication topology. Furthermore, a sufficient existence condition in terms of linear matrix inequalities is derived for the distributed discrete-time controller. Finally, the distributed robust H _∞ control problems of uncertain linear multi-agent systems subject to external disturbances are discussed.     

Cooperative global output regulation of heterogeneous second-order nonlinear uncertain multi-agent systems

In this paper, we study the cooperative global output regulation problem for a class of heterogeneous second order nonlinear uncertain multi-agent systems. We first introduce a type of distributed internal model that converts the cooperative global output regulation problem into the global robust stabilization problem of the so-called augmented multi-agent system. Then we further globally stabilize this augmented multi-agent system via a distributed state feedback control law, thus leading to the solution of the original problem. A special case of our result leads to the solution of the global leader-following consensus problem for the second order nonlinear multi-agent systems without satisfying the global Lipschitz condition.     

非线性多智能体磁滞系统的分布式输出反馈渐近一致控制

针对一类具有磁滞输入且状态未知的非线性多智能体系统,本文提出了一种基于领导者–跟随者的分布式输出反馈渐近一致自适应控制方案.首先,构造了具有动态高增益的K-滤波器以估计多智能体系统的未知状态.然后,采用一种新型的动态面控制策略设计控制器.不同于传统动态面控制策略所采用的一阶低通滤波器,本文设计了含正时变积分函数的非线性...     

Distributed consensus control of nonlinear multi-agent systems with sensor uncertainty

This article focuses on the distributed consensus control problem for nonlinear multi-agent systems subject to sensor uncertainty. To be specific, we study nonlinear multi-agent systems of lower or upper triangular structure with unknown growth rate and sensor uncertainty. A new time-varying gain approach is proposed to construct observers as well as distributed output-feedback controllers. By selecting suitable design parameters, the leader-follower consensus of nonlinear multi-agent systems is achieved. Different from the existing results, a time-varying function in a logarithmic form is introduced to deal with unknown growth rate. Moreover, a monotonically increasing time-varying function is constructed to cope with uncertain sensor sensitivity. Two simulation examples are provided to demonstrate the effectiveness of the proposed distributed consensus control algorithms.     

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.     

Cooperative output regulation of multi-agent systems with switched leader dynamics

In this paper, the cooperative output regulation problem for heterogeneous multi-agent systems is addressed by considering a switched leader dynamics. The switched leader dynamics consists of multiple linear models and a switching rule governing the switches among them. A switched leader is capable of generating various sophisticated reference signals for more complicated multi-agent coordination tasks. A novel distributed hybrid impulsive switching control scheme is proposed to achieve cooperative output regulation. Distributed switching stability is established using the average dwell-time technique with multiple Lyapunov functions. Moreover, the associated distributed control synthesis conditions are formulated in terms of linear matrix inequalities plus linear matrix equations. As a result, both switching rules for the leader and distributed switching protocols for the followers can be jointly synthesised via efficient semi-definite programming. An example has been used to demonstrate the effectiveness of the proposed approach.     

有限时间内异构多智能体系统的协同输出调节

针对异构多智能体系统有限时间输出调节问题,本文提出了分布式有限时间状态观测器控制算法和相应的输出反馈控制策略.应用图论、Lyapunov稳定性理论证明了所设计的观测器能够在有限时间内估计出外部系统状态,同时可以保证系统在有限时间内的稳定性,很好的解决了当部分跟随者无法获取外部命令时的有限时间输出调节问题.最后,通过MATLAB数值仿真验证了该协议的有效性和正确性,仿真结果表明系统除了在有限时间内获得更快的收敛速度外,还具有良好的暂态性能.     

Probabilistic output admissible set for systems with time-varying uncertainties

This paper considers time-varying uncertain constrained systems, and develops a method for computing a probabilistic output admissible (POA) set. This set consists of the initial states probabilistically assured to satisfy the constraint. The time-invariant counterpart has already been investigated in Hatanaka and Takaba [Computations of probabilistic output admissible set for uncertain constrained systems, Automatica 44 (2) (2008), to appear]. We first define the POA set for time-varying uncertainties with finite dimensional probability space. Then, we show that an algorithm similar to Hatanaka and Takaba [Computations of probabilistic output admissible set for uncertain constrained systems, Automatica 44 (2) (2008), to appear] provides the POA set also in the time-varying case, as long as an upper bound of a what we call future output admissibility (FOA) index is available. We moreover present two methods for computing the upper bound of the FOA index: probabilistic and deterministic methods. A numerical simulation demonstrates the effectiveness of our algorithm.     

基于事件触发非线性多智能体系统的固定时间一致性

本文研究了在有向拓扑下,带有非线性动力学多智能体系统的固定时间一致性问题.提出了一种新的基于事件触发机制的非线性控制策略,对于每个智能体给出了基于状态信息的事件触发条件,当状态误差满足所给条件时才触发事件,能有效的减小系统的能量耗散和控制器的更新频次.利用Lyapunov稳定性理论和代数图论,证明在该控制策略下,多智能体系统在固定时间能实现领导跟随一致性,且不存在Zeno行为.相较于有限时间一致性策略,采用固定时间一致性策略系统的收敛时间不再依赖于系统的初始状态.最后,仿真实例验证了理论结果的有效性.     

Distributed fuzzy adaptive event-triggered finite-time consensus tracking control for uncertain nonlinear multi-agent systems with asymmetric output constraint

This article investigates the consensus problem for uncertain nonlinear multi-agent systems (MASs) with asymmetric output constraint. Different from BLF-based constraint consensus tracking control, a novel approach based on nonlinear state-dependent function is proposed to solve the asymmetric output constraint, which need not convert output constraint into tracking error bound. First-order sliding mode differentiator is incorporated into each step of backstepping control design to reduce computation burden. Further, in combination of proposed event-triggered mechanism based on time-varying threshold, a distributed fuzzy adaptive event-triggered finite-time consensus method is developed. It can ensure that the consensus tracking error tends to a small neighbor in a finite time and the asymmetric output constraint of each subsystem is not violated. Two simulations are given to demonstrate the effectiveness of control method.     

带有输出约束条件的随机多智能体系统容错控制

在有向通讯拓扑图下,针对一类具有输出约束和执行器偏差增益故障的非严格反馈随机多智能体系统,提出一种自适应神经网络容错控制设计方案.采用神经网络逼近未知非线性函数,构造障碍李雅普诺夫函数处理系统的输出约束问题,以反步法和动态面技术为框架,结合Nussbaum函数设计自适应神经网络容错控制方法.基于李雅普诺夫稳定性理论,证明所有跟随者输出与领导者输出达到一致,闭环系统的所有信号依概率半全局一致最终有界且系统输出限制在给定紧集内.论文最后通过仿真实验验证所给出控制方案的有效性.     

Distributed consensus for discrete-time heterogeneous multi-agent systems

This paper studies the consensus problem for a class of discrete-time heterogeneous multi-agent systems. Two kinds of consensus algorithms will be considered. The heterogeneous multi-agent systems considered are converted into equivalent error systems by a model transformation. Then we analyse the consensus problem of the original systems by analysing the stability problem of the error systems. Some sufficient conditions for consensus of heterogeneous multi-agent systems are obtained by applying algebraic graph theory and matrix theory. Simulation examples are presented to show the usefulness of the results.     

Flocking with connectivity preservation for disturbed nonlinear multi-agent systems by output feedback

This paper considers the problem of flocking with connectivity preservation for a class of disturbed nonlinear multi-agent systems. In order to deal with the nonlinearities in the dynamic of all agents, some auxiliary variables are introduced into the state observer for stability analysis. By proposing a bounded potential function and using adaptive theory, a novel output feedback consensus algorithm is developed to guarantee that the states of all agents achieve flocking with connectivity preservation.     

具Frobenius有界不确定性广义系统的鲁棒稳定性

研究了具Frobenius有界不确定性广义系统的稳定与鲁棒镇定问题. 通过对代数Riccati不等式或代数Riccati方程的求解, 获得了不确定广义系统广义二次稳定的充要条件, 使得对所有容许的不确定参数, 系统是稳定, 正则和无脉冲. 而且, 根据一类矩阵方程, 构造了使不确定广义系统鲁棒镇定的状态反馈控制器的设计方法. 实例说明了上述方法的有效性.     

离散多智能体有限时间Q学习协同输出调节

针对离散多智能体系统输出调节,提出了一种基于Q学习的最优控制策略。对于传统多智能体系统的输出调节,获取系统的精确动力学模型并依此求得其HJB方程的解为主要障碍。该策略通过智能体之间的局部通信,在不依赖系统动态模型的前提下实现了对每个智能体输出的全局最优控制。为实现对系统响应速率的优化,提出了一种新的有限时间局部误差公式,不仅保证了算法原有的全局最优性能,而且将输出同步时间缩短了近50%,并对所提算法的稳定性进行了分析。仿真结果表明,该策略在避免建立复杂系统模型和求解离散HJB方程的前提下实现了对系统的最优控制,采用更新后的有限时间局部误差公式有效缩短了收敛时间。     

H 2 input load disturbance rejection controller design for synchronised output regulation of time-delayed multi-agent systems with frequency domain method

An analytical H ₂ input load disturbance rejection (ILDR) controller design approach is presented for the synchronised output regulation (SOR) of homogeneous time-delayed multi-agent systems. First, a closed-loop multi-input multi-output framework with transfer functions is introduced, and an SOR condition is given. Second, the decomposition method is utilised to simplify the analysis of internal stability and H ₂ performance index of the whole system to a set of independent optimisation problems with respect to the eigenvalues of the topology matrix. Finally, for each decomposed subsystem, the H ₂ optimal ILDR controller can be computed from all the stabilising controllers. By comparison with the conventional given-structured controllers, the contributions of the new approach are that the design procedure is calculated analytically for multi-agent systems with input disturbances, and a simple quantitative tuning way is developed to trade-off the nominal performance and robustness. The simulation example shows the effective ILDR capability of the proposed control strategy.