含时延约束的多智能体系统二分一致性

针对多智能体系统中信息交互存在通信时延这一约束,在无向符号图拓扑结构下分别研究了含固定时延和时变时延的一阶多智能体系统二分一致性问题。通过设计相应的控制协议,使得该系统收敛到两个模值相同但符号不同的状态。在稳定性分析中,利用广义Nyquist准则的方法,得到含固定时延多智能体系统实现二分一致性的充分条件;对含时变时延系统构造包含三重积分项的Lyapunov函数,利用积分不等式和线性矩阵不等式理论,并结合自由矩阵的方法得到含时变时延多智能体系统实现二分一致性的充分条件。最后,数值仿真验证了所得结论的有效性和正确性。     

一类多时变时延异质多智能体系统的组一致性

研究了一类由一阶和二阶智能体组成的异质多智能体系统的组一致性问题．首先,在多时变时延异质系统中设计了实现静态组一致的控制算法;其次,运用稳定性理论和线性矩阵不等式,分别给出了无时延、同时具有通信与输入时延的异质多智能体系统实现组一致性的充分条件;再次,通过求解一组可行的线性矩阵不等式,得到了输入时延的容许上界,并得出了通信时延与异质多智能体系统的组一致性无关的结论;最后,仿真结果验证了理论结果的有效性．     

基于观测器的线性时变时滞多智能体系统一致性

针对系统状态不可测和具有通信时延的线性多智能体系统,提出一种基于观测器的一致性控制算法.设计观测器用于解决智能体状态不可测的问题,在观测器的基础上,提出一种控制协议来实现带时变时延的线性多智能体系统一致性.利用模型转换的方式将原系统转换为新的模型系统,在此基础上,构造Lyapunov-Krasovskii函数并分析系统稳定性,通过求解线性矩阵不等式获取控制器系数矩阵.最后通过Matlab数值仿真验证所提出方法的有效性.     

具有随机多跳时变时延的多航天器协同编队姿态一致性

针对存在随机多跳时变时延的多航天器协同编队的姿态一致性问题,本文设计了可消除随机多跳时变时延影响并能够实现多航天器协同编队姿态角速度一致及姿态角有效跟踪的静态控制器.首先基于有向图论推导出领航者一跟随者误差系统的动态方程,然后通过构造合适的Lyapunov函数将误差系统调节器问题转化为了线性矩阵不等式解的存在性问题,其次通过求解线性矩阵不等式完成了协同编队姿态控制系统的静态控制器设计.理论分析表明,所设计的控制器能够有效消除随机多跳时变时延影响,实现了多航天器协同编队的姿态一致性.数值仿真验证了所提方法的正确性和有效性.     

带有参数摄动的网络化控制系统非脆弱H_∞控制

针对带有时变传输时延的网络化系统中控制器参数存在随机摄动问题,设计了一种非脆弱H_∞控制器。利用Lyapunov稳定性理论和线性矩阵不等式方法,得到了非脆弱H_∞控制器存在的充分条件,通过求解线性矩阵不等式得到该控制器增益。所设计的控制器在容许的随机参数摄动和有界时变时延下,能保证闭环网络化控制系统的稳定性和预定的H_∞性能指标。仿真例子验证了方法的有效性。     

具有时变时延的网络化LPV系统的容错控制

针对一类具有时变时延以及Lipschitz非线性项的网络化线性参数变化系统,研究了系统中存在外部扰动、执行器和传感器同时发生随机故障时的容错控制问题。用Bernoulli分布序列描述执行器和传感器发生的随机故障,利用自由权矩阵方法处理时变时延。根据Lyapunov-Krasovskii稳定性定理和线性矩阵不等式（LMI）方法求出◢H◣▼∞▽容错控制器存在的充分条件,然后通过利用近似基函数和网格化技术将无限维的LMI求解问题转换为有限维的LMI问题,得到了相应的容错控制器增益。最后,通过数值仿真验证了所设计方法的有效性。     

不确定多智能体互联动态系统分布式鲁棒H∞协同控制

研究一类具有时延和切换拓扑的不确定多智能体互联系统的分布式协同控制问题,提出一类分布式鲁棒H∞协同控制器.该控制器能够在满足期望的H∞性能指标的前提下,使得所有智能体鲁棒地跟踪虚拟Leader.针对所提出的分布式H∞协同控制器,借助Lyapunov-Krasovskii泛函,利用线性矩阵不等式,推导出一系列充分(必要)条件,并且在通信拓扑连通的前提条件下,给出整个闭环系统的稳定性证明.仿真实例表明了所提出方法的有效性.     

基于连续时间模型的多智能体系统采样数据一致性

讨论了一般线性模型的多智能体系统具有时变采样间隔的采样数据一致性问题.首先基于连续时间模型,利用采样数据的离散时间特性分析时变采样间隔允许的上界.由于不考虑采样间隔之间的状态,Lyapunov函数仅需要在每个采样时刻保证递减.由此得到了一个利用线性矩阵不等式求解更低保守性的时变采样间隔上界的方法.接着通过参数化矩阵变量得到了基于线性矩阵不等式的控制器设计方法.最后数值仿真展示了理论结果的正确性.     

变采样网络控制系统的最优保性能控制

针对具有时变有界采样周期和时延的网络控制系统,首先将其建模成一类离散动态区间系统.在此基础上,对一个给定的二次型性能指标,研究了系统的保性能控制问题,基于线性矩阵不等式(LMI)给出最优保性能控制器设计方法.利用LMI工具箱,求解十分方便.仿真结果表明该方法的有效性.     

具有时变采样周期的网络控制系统的H∞控制

研究了具有时变采样周期的网络控制系统的H∞鲁棒控制器设计问题．提出了基于变采样周期的切换方法（采样周期在有限集合内切换），并利用该方法将存在时变采样周期、长时延以及丢包的网络控制系统建模为切换系统．在此基础上，通过把一个非凸的可行性问题转化为受线性矩阵不等式约束的多目标优化问题，研究了网络控制系统的H∞控制器设计方法．仿真结果验证了基于采样周期切换的H∞控制器设计方法的有效性．     

Improved stability criterion and its applications in delayed controller design for discrete-time systems

This paper is concerned with the problem of delay-dependent stability analysis for discrete-time systems with interval-like time-varying delays and the problem of stabilization for discrete-time linear systems via time-delayed controllers. The first problem is solved by applying a novel Lyapunov functional, and an improved delay-dependent stability criterion is obtained in terms of a linear matrix inequality. Based on this, a sufficient condition for the solvability of the second problem is presented. The reduced conservatism of the proposed stability result is shown through a numerical example, while the applicability of the time-delayed controller design method is demonstrated by an inverted pendulum system.     

带时变时延的网络化控制系统控制器设计方法

为带时变时延的网络化控制系统提出了一种新的状态反馈控制器的设计方法.根据控制系统的时滞相关稳定性条件来设计确保网络化控制系统稳定性的控制器,并以线性矩阵不等式的形式描述.该方法可进一步扩展到解决鲁棒控制问题.最后的仿真实例表明了该方法的有效性.     

Delay-dependent robust stabilisation for a class of fuzzy bilinear systems with time-varying delays in state and control input

The stabilisation problem for a class of Takagi–Sugeno (TS) fuzzy bilinear systems (FBSs) with time-varying state and input delays is investigated in this article. A fuzzy controller is designed to stabilise TS FBSs with time-varying state and input delays via the parallel distributed compensation method. Based on a Lyapunov–Krasoviskii function, the delay-dependent stabilisation conditions are proposed in terms of a linear matrix inequality to guarantee the asymptotic stabilisation of time-delay FBSs with disturbance input. Two numerical examples with delays in the state and input are given to demonstrate that the proposed stability condition is less conservative than some existing results. Finally, the validity and applicability of the proposed control scheme are successfully demonstrated in the control of a Van de Vusse reactor with delay.     

Delay-range-dependent robust 2D iterative learning control for batch processes with state delay and uncertainties

This paper proposes the design of the integrated output feedback and iterative learning control (ILC) for batch processes with uncertain perturbations and interval time-varying delays, where the main idea is to transform the design into a robust delay-range-dependent H_∞ control of a 2D system described by a state-space model with varying delays. A sufficient criterion for delay-dependent H_∞ noise attenuation is derived through linear matrix inequality (LMI) by introducing a comprehensive 2D difference Lyapunov–Krasovskii functional candidate and adding a differential inequality to the difference in the Lyapunov function for the 2D system. Based on the criterion obtained, the delay-range-dependent output feedback controller combined with ILC is then developed. The developed system ensures that the closed-loop system for all admissible uncertainties is asymptotically stable and has a prescribed H_∞ performance level in terms of the LMI constraint. The controller is obtained by solving an LMI optimization problem with simple calculations and less constraint conditions. Moreover, the conditions can also be directly extended from delay-range-dependent to general delay-dependent stability. Applications in injection velocity control demonstrate the effectiveness and feasibility of the proposed method.     

线性时滞系统的时滞相关鲁棒控制

讨论了同时具有输入时滞与状态时滞的线性系统的时滞相关鲁棒控制问题.将矩阵分解思想应用于线性时滞系统的控制综合,借助于积分不等式,利用Lyapunov_Krasovskii泛函方法,得到了系统经无记忆状态反馈后可镇定的、基于LMI的时滞相关条件.既不要对原系统进行模型变换,也不要对交叉项进行界定.最后的实例说明了本文方法的有效性.     

不确定线性多时变时滞系统的时滞相关鲁棒控制

提出一种积分不等式新方法，讨论不确定线性多时变时滞系统的鲁棒稳定性以及鲁棒稳定化问题，首先利用Park不等式建立了基于二次型项的积分不等式，利用这一不等式获得了系统基于LMI的时滞相关、时滞导数相关鲁棒稳定条件；然后利用这一条件给出了时滞状态反馈控制器的一种新的设计方法，数值例子说明了所得结论具有较小的保守性。     

线性多时滞不确定离散时间线性系统的时滞相关H∞控制

讨论了线性多时滞不确定离散时间线性系统的时滞相关H_∞控制问题．首先,建立了一个基于二次型项的有限和不等式．然后,利用这一不等式,采用Lyapunov-Krasovskii泛函方法,获得了系统不仅内部稳定而且具有给定的H_∞性能的时滞相关条件,同时以LMI的形式给出了无记忆H_∞控制器的设计方法．最后,数值例子说明了本文方法的有效性．     

Observer-based adaptive iterative learning control for nonlinear systems with time-varying delays

An observer-based adaptive iterative learning control (AILC) scheme is developed for a class of nonlinear systems with unknown time-varying parameters and unknown time-varying delays. The linear matrix inequality (LMI) method is employed to design the nonlinear observer. The designed controller contains a proportional-integral-derivative (PID) feedback term in time domain. The learning law of unknown constant parameter is differential-difference-type, and the learning law of unknown time-varying parameter is difference-type. It is assumed that the unknown delay-dependent uncertainty is nonlinearly parameterized. By constructing a Lyapunov-Krasovskii-like composite energy function (CEF), we prove the boundedness of all closed-loop signals and the convergence of tracking error. A simulation example is provided to illustrate the effectiveness of the control algorithm proposed in this paper.     

Robust mixed H 2 /H ∞ control of time-varying delay systems

This paper describes the mixed H 2 /H X controller design method of linear systems with time-varying delays in both state and control input. More specifically, the proposed mixed H 2 /H X controller minimizes the H 2 performance measure when satisfying a prescribed H X norm bound on the closed loop system. The sufficient conditions for the existence of controller, the mixed H 2 /H X controller design method and the upper bound of performance measure are presented using the linear matrix inequality (LMI) technique. Also, all solutions including controller gain and the upper bound of performance measure are obtained simultaneously. Furthermore, the proposed controller design method can be easily extended into the problem of robust mixed H 2 /H X controller design method for parameter uncertain systems with time-varying delays in both state and control input.     

Passivity-based decentralized stabilization of multi-agent systems with uncertainty and mixed delays

In this paper, we investigate a decentralized stabilization problem of uncertain multi-agent systems with mixed delays including discrete and distributed time-varying delays based on passivity stability. We design a decentralized state-feedback stabilization scheme such that the family of closed-loop feedback subsystems enjoys the delay-dependent passivity stability for each subsystem. Then, by employing a new Lyapunov-Krasovskii function, a linear matrix inequality （LMI） approach is developed to establish the delay-dependent criteria for the passivity stability of multi-agent systems. The sufficient condition is given for checking the passivity stability. The proposed LMI result is computationally efficient. An example is given to show the effectiveness of the method.