Asynchronous switching output feedback control of discrete-time switched linear systems

In this paper, the problem of dynamic output-feedback control synthesis is addressed for discrete-time switched linear systems under asynchronous switching. The proposed hybrid controller consists of a standard dynamic output-feedback switching control law and an impulsive reset law induced by controller state jumps. Using the average dwell time technique incorporating with multiple quadratic Lyapunov functions, the switching control synthesis conditions for asymptotic stability with guaranteed weighted ?₂-gain performance are derived as a set of linear matrix inequalities (LMIs). The proposed hybrid synthesis scheme advances existing design methods for output-feedback asynchronous switching control of switched linear systems in two important aspects: LMI formulation of the synthesis problem; and arbitrary order of the controller state. A numerical example is used to illustrate the effectiveness and advantages of the proposed design technique.     

A stability criterion for asynchronously switched linear systems via sampled‐data control

This paper considers an asynchronous problem for sampled‐data control of switched linear systems, which are described as switched linear systems with an input delay. To handle the problem, this paper proposes a stability criterion for the systems by constructing a novel Lyapunov‐Krasovskii functional dependent not on system modes but on controller modes. The functional continuously remains when the system modes are switched but discontinuously changes whenever the controller mode moves to the current system mode at the sampling instants. Furthermore, the functional is allowed to increase or decrease up to a certain level when the functional discontinuously changes and to increase up to a certain level when the system modes and the controller modes are asynchronous. Based on the functional, this paper derives an average dwell time associated with the interval of samplings and the incremental level of the functional for guaranteeing the stability of the systems. A numerical example illustrates the validation of the proposed method.     

Asynchronously switched control of switched linear systems with average dwell time

This paper concerns the asynchronously switched control problem for a class of switched linear systems with average dwell time (ADT) in both continuous-time and discrete-time contexts. The so-called asynchronous switching means that the switchings between the candidate controllers and system modes are asynchronous. By further allowing the Lyapunov-like function to increase during the running time of active subsystems, the extended stability results for switched systems with ADT in nonlinear setting are first derived. Then, the asynchronously switched stabilizing control problem for linear cases is solved. Given the increase scale and the decrease scale of the Lyapunov-like function and the maximal delay of asynchronous switching, the minimal ADT for admissible switching signals and the corresponding controller gains are obtained. A numerical example is given to show the validity and potential of the developed results.     

Model Predictive Control of Nonlinear Systems： Stability Region and Feasible Initial Control

This paper proposes a new method for model predictive control (MPC) of nonlinear systems to calculate stability region and feasible initial control profile/sequence, which are important to the implementations of MPC. Different from many existing methods, this paper distinguishes stability region from conservative terminal region. With global linearization, linear differential inclusion (LDI) and linear matrix inequality (LMI) techniques, a nonlinear system is transformed into a convex set of linear systems, and then the vertices of the set are used off-line to design the controller, to estimate stability region, and also to determine a feasible initial control profile/sequence. The advantages of the proposed method are demonstrated by simulation study.     

含时变时延的多智能体的包容控制器设计

针对一类含时变通讯时延的多智能体系统,基于时滞依赖法提出了其在有向网络拓扑下的一类包容控制器设计的方法,该设计能有效地驱使多智能体系统中所有跟随者的状态渐近一致地收敛到领导者运动过程中形成的几何凸包．结合李亚普诺夫稳定性理论和线性矩阵不等式（LMI）方法,推导了多智能体系统包容控制率存在的充分条件,并将包容控制器的设计最终转化成求解线性矩阵不等式可行解的问题．结果表明,该方法对多智能体系统中的时变通讯时延具有良好的补偿效果．最后通过仿真算例验证了此方法的有效性和可行性．     

Asynchronous Observer Design for Switched Linear Systems: A Tube-Based Approach

This paper proposes a tube-based method for the asynchronous observation problem of discrete-time switched linear systems in the presence of amplitude-bounded disturbances.Sufficient stability conditions of the nominal observer error system under mode-dependent persistent dwell-time(MPDT)switching are first established. Taking the disturbances into account, a novel asynchronous MPDT robust positive invariant(RPI) set and an asynchronous MPDT generalized RPI(GRPI)set are determined for the difference system between the nominal and disturbed observer error systems. Further, the global uniform asymptotical stability of the observer error system is established in the sense of converging to the asynchronous MPDT GRPI set, i.e., the cross section of the tube of the observer error system. Finally, the proposed results are validated on a space robot manipulator example.     

Asynchronous H ∞ Control for Positive Discrete-time Markovian Jump Systems

This paper deals with the asynchronous H∞ control for discrete-time positive Markovian jump systems (PMJSs). In previous results about PMJSs, asynchronous behaviors are always overlooked and the designed controller is based on the synchronization between the system modes and controller modes. Sufficient conditions for stochastic stability are proposed by the use of Lyapunov-Krasovskii functional. The asynchronous controller is designed to ensure the closed-loop system stochastically stable with a prescribed H∞ performance index. All the conditions are given in linear matrix inequality framework. Finally, a pest’s age-structured population dynamic model is illustrated to show the validity of the present design.     

Model predictive control for networked control systems

This paper investigates the problem of model predictive control for a class of networked control systems. Both sensor‐to‐controller and controller‐to‐actuator delays are considered and described by Markovian chains. The resulting closed‐loop systems are written as jump linear systems with two modes. The control scheme is characterized as a constrained delay‐dependent optimization problem of the worst‐case quadratic cost over an infinite horizon at each sampling instant. A linear matrix inequality approach for the controller synthesis is developed. It is shown that the proposed state feedback model predictive controller guarantees the stochastic stability of the closed‐loop system. Copyright © 2008 John Wiley & Sons, Ltd.     

基于静态输出反馈控制器的主动队列管理

利用李亚普诺夫函数对线性时滞系统的鲁棒稳定性进行了证明．给出了一种基于线性矩阵不等式（LMI）的参数判定依据,设计出了一种实现主动队列管理的静态输出反馈控制器（SOFC）．仿真结果表明,这种控制器具有良好的控制性能,并且在变化的网络环境下具有较强的鲁棒性．     

State and Mode Feedback Control for Discrete-time Markovian Jump Linear Systems With Controllable MTPM

In this note, the state and mode feedback control problems for a class of discrete-time Markovian jump linear systems (MJLSs) with controllable mode transition probability matrix (MTPM) are investigated. In most achievements, controller design of MJLSs pays more attention to state/output feedback control for stability, while the system cost in practice is out of consideration. In this paper, we propose a control mechanism consisting of two parts: finite-path-dependent state feedback controller design with which uniform stability of MJLSs can be ensured, and mode feedback control which aims to decrease system cost. Differing from the traditional state/output feedback controller design, the main novelty is that the proposed control mechanism not only guarantees system stability, but also decreases system cost effectively by adjusting the occurrence probability of system modes. The effectiveness of the proposed mechanism is illustrated via numerical examples.      

多阶段间歇过程鲁棒模糊预测异步切换控制EI北大核心CSCD

本文针对非线性多阶段间歇过程在切换瞬间存在异步切换的问题,提出了一种鲁棒模糊预测异步切换控制方法.该方法将非线性多阶段间歇过程表示为同步子系统和异步子系统的等效闭环扩展Takagi-Sugeno模糊模型,在此基础上给出了确保每个批次指数稳定和每个阶段渐近稳定的,基于线性矩阵不等式的稳定性条件以及不同情况运行时间的计算方法.根据运行时间采用超前切换思想,避免异步切换情况的出现,保证系统的稳定运行.仿真案例表明所设计的控制器是有效的和可行的.     

线性不确定中立型时滞系统的鲁棒二次性能

研究具有非匹配条件的范数有界线性不确定中立型时滞系统的稳定和二次性能控制问题．基于Lyapunov方法，提出了系统鲁棒渐近稳定并满足给定二次性能指标的时滞相关型条件，该条件等价干线性矩阵不等式(LMI)可解性问题，并根据LMI的可行解，构造了状态反馈控制器设计方法．     

一类基于观测器的非线性网络化控制系统的绝对稳定性

主要考虑了基于观测器的Lurie网络化控制系统的绝对稳定性问题. 由于采用了基于观测器的反馈控制器, 传感器到控制器的网络诱导时延和控制器到执行器的网络诱导时延不再能合并到一起处理. 首先通过状态增广方法将Lurie网络化控制系统建模为一个多时滞的Lurie系统, 然后利用Newton-Leibniz公式和添加自由权矩阵的方法给出了时滞依赖的稳定性条件. 在此基础上, 给出三种求解控制器和观测器增益矩阵的方法. 此外, 还分别给出了被控对象存在范数有界不确定性和结构不确定性时系统的鲁棒稳定性条件及鲁棒控制器设计方法, 所有得到的结果都是以线性矩阵不等式的形式给出的. 便于利用线性矩阵不等式工具包进行求解. 最后, 通过两个仿真算例说明了方法的可行性和有效性.     

基于分段模糊Lyapunov函数的模糊系统稳定性分析和保性能设计

针对一类 Takagi-Sugeno (T-S) 连续模糊系统, 在分析模糊系统前提规则结构信息的基础上, 研究了其稳定性和保性能设计问题. 通过将模糊 Lyapunov 函数 (FLF) 和分段二次 Lyapunov 函数 (PQLF) 结合, 构造出分段模糊 Lyapunov 函数 (PFLF), 并提出了一种新的并行分配补偿 (PDC) 控制器. 基于 PFLF 方法, 得到了线性矩阵不等式 (LMI) 形式的模糊系统分析与设计的求解方法. 该方法继承了 FLF 与 PQLF 的优点. 仿真实例表明: 该方法所得稳定性判据更为宽松, 具有更好的保性能控制效果.     

具有长时延和丢包的网络控制系统稳定性分析

针对同时出现长网络诱导时延和丢包的网络控制系统,研究了带不确定性的网络控制系统的稳定性问题。基于一定的数据包丢失率,系统被建模成带结构事件率约束的异步动态系统。利用李亚普诺夫方法和线性矩阵不等式相关知识,结合异步动态系统的稳定性理论,推出了使不确定网络控制系统指数稳定的充分条件,并给出了保证系统指数稳定的数据传输成功率满足范围;最后利用MATLAB仿真的数值例子验证了此方法的有效性和可行性。     

Set-point-related indirect iterative learning control for multi-input multi-output systems

A form of iterative learning control (ILC) is used to update the set-point for the local controller. It is referred to as set-point-related (SPR) indirect ILC. SPR indirect ILC has shown excellent performance: as a supervision module for the local controller, ILC can improve the tracking performance of the closed-loop system along the batch direction. In this study, an ILC-based P-type controller is proposed for multi-input multi-output (MIMO) linear batch processes, where a P-type controller is used to design the control signal directly and an ILC module is used to update the set-point for the P-type controller. Under the proposed ILC-based P-type controller, the closed-loop system can be transformed to a 2-dimensional (2D) Roesser s system. Based on the 2D system framework, a sufficient condition for asymptotic stability of the closed-loop system is derived in this paper. In terms of the average tracking error (ATE), the closed-loop control performance under the proposed algorithm can be improved from batch to batch, even though there are repetitive disturbances. A numerical example is used to validate the proposed results.     

自抗扰控制在永磁直线电机控制中的应用

针对在工业中广泛应用的PID控制器的特点及存在的问题做了分析,并介绍了自抗扰控制技术的原理、结构、以及控制器的设计.对一个永磁直线电机在考虑将电机耦合视为内扰及外部摩擦干扰情况下的具体实例给出了采用自抗扰控制技术的仿真结果.同时对简化的电机模型也给出了采用PID调节的仿真结果.结合仿真结果可以看到自抗扰控制器的抗干扰性和鲁棒性都优于经典PID控制器.     

等时切换下线性切换系统的稳定性及鲁棒稳定性研究-LMI方法

研究等时切换下线性切换系统的稳定性及鲁棒稳定性问题。文中首先提出等时切换的概念。然后利用LMI方法推导出等时切换下线性系统稳定及鲁棒稳定的充要条件，使用这两个充要条件可以将文中研究的复杂问题转化为相应的易处理的线性系统的问题，再利用线性系统已有的结论使问题得到解决。使用上述结果，本文为系统设计了鲁棒控制器。文中还给出实现线性切换系统等时切换的具体方法，这使等时切换方法可以真正应用于工程实践。大量仿真证实文中所提出的方法简洁、有效。     

Stability analysis of nonlinear systems in the presence of event-triggered impulsive control

This note puts forward continuous event-triggered impulsive control (CETIC) and dynamic event-triggered impulsive control (DETIC) to discuss a class of (integral) input-to-state stability (iISS, ISS) for nonlinear systems (NSs), where the impulse sequences are produced by certain predesigned event-triggering conditions. Different from traditionary event-triggered control (ETC), CETIC indicates that a controller will be stimulated only if the given state-dependent event condition is invoked. There exist no transfer of control between two continuous impulse triggered instants. Compared with the traditional static ETC, the DETIC can efficaciously lessen controller update and dramatically save energy at the same decay rate. In addition, all sample path solutions (SPS) for the system have the lowest time between events guaranteed to be positive. Utilizing CETIC strategy, we get some Lyapunov conditions to effectually avoid infinite triggering behavior and obtain the ISS-type stability of the investigative systems. Then, one applies the theoretical consequences to NSs and derive a class of ETC mechanism with impulsive control gains (ICG) by linear matrix inequalities (LMIs). Because of the existence of timer, the DETIC strategy naturally excludes Zeno phenomena. Furthermore, conclusions in this thesis permit the upper bound estimation for the differential Lyapunov function coefficient to be time-varying function instead of a constant in certain extant results, which means the criteria of the Lyapunov technique in this paper is less conservative and looser. Eventually, three examples with related simulations are demonstrated to indicate the rationalization and usefulness of our conclusion.     

积分二次约束线性系统的H∞控制器设计:一种LMI方法

基于动态耗散理论, 给出了具有积分二次约束线性系统稳定和具有L₂有限增益的充分条件. 导出了积分二次约束线性系统H_∞ 状态反馈和动态输出反馈降阶控制器的设计方法, 并转化为多个线性矩阵不等式, 利用LMI工具箱求解.