时变时滞连续切换奇异系统的一致有限时间稳定分析

讨论一类含有时变时滞的连续时间切换奇异系统的一致有限时间稳定、有限时间有界和状态反馈镇定问题. 在给定任意的切换规则下, 运用多Lyapunov 函数和平均驻留时间方法设计使得闭环系统一致有限时间稳定和有限时间有界的状态反馈控制器, 同时给出基于线性矩阵不等式表示的控制器存在的充分条件. 最后通过数值算例表明了所提出方法的合理性和有效性.

     

切换自治系统的动态输出反馈镇定

本文研究离散时间切换线性自治系统的输出反馈镇定问题. 在切换系统可观测的假设下, 设计具有多线性 时变增益的动态观测器, 实现有限时间状态估计. 在此基础上, 设计多路径动态输出反馈切换策略, 实现闭环系统指 数收敛.     

一类不确定切换奇异时滞系统的时滞依赖鲁棒镇定

针对一类不确定切换奇异时滞系统,对其鲁棒镇定问题进行了研究.首先利用多李亚普诺夫泛函方法和线性矩阵不等式工具,通过引入适当的自由权矩阵,在适当的切换律下,给出了基于严格线性矩阵不等式表示的标称自治切换奇异系统正则、无脉冲且渐近稳定的时滞依赖条件;然后基于此条件,通过设计相应的状态反馈子控制器,得到了保证闭环系统对所有允许的不确定性是正则、无脉冲且渐近稳定的时滞依赖条件,同时给出了子控制器的显示表达式.数值算例表明该方法的有效性.     

一类时滞切换系统的鲁棒控制

研究一类状态矩阵和控制输入矩阵同时具有不确定项的线性时滞切换系统的鲁棒控制器的设计问题。,利用多Lyapunov函数方法设计出状态反馈的鲁棒控制器,并设计出切换策略,证明闭环系统在给定的切换策略下在其平衡点处的渐近稳定性。最后通过MATLAB中的LMI工具箱进行仿真,仿真结果验证结论的有效性。     

离散线性切换系统的一致有限时间稳定分析和反馈控制及其在网络控制系统中的应用

研究了一类离散线性切换系统的一致有限时间稳定性分析和反馈镇定．基于线性矩阵不等式技术,给出了在任意切换信号作用下,离散线性切换系统有限时间稳定和有限时间有界的充分条件,并给出了离散线性切换控制系统一致有限时间状态反馈控制器的设计方法．将上述分析结果应用于一类丢包有界的网络控制系统,得到了保证其有限时间稳定的反馈控制器．最后,通过两个数值仿真例子验证了所提方法的有效性．     

基于LMI的不确定切换系统极点配置

研究了一类不确定线性切换系统基干状态反馈的援点配置和LMI方法问题。此类切换系统不仅具有未知但有界的结构不确定性,而且具有外部扰动。利用公共Lyapunov函数,得到一稳定切换控制策略来保证:(1)备线性子系统的特征值位于左半复平面的选定圆内,(2)最小化闭环切换系统的扰动衰减水平。在各子系统不稳定的前提下,设计切换系统的状态反馈控制器,使得在任意切换策略下系统的闭环极点配置在左半复平面,且具有良好的扰动衰减水平,系统渐近稳定。得到了切换系统可状态反馈镇定的充分条件,然后用易于求解的线性矩阵不等式形式表示出结果;最后通过仿真验证所设计的切换系统在状态反馈控制器下渐近稳定,且具有良好的投点配置和最小γ衰减水平。     

一类不确定切换系统的鲁棒状态反馈镇定

研究了一类扰动项不满足匹配条件的不确定切换系统的鲁棒镇定问题.在每个子系统均不能镇定的情况下,利用完备性条件和多李雅普诺夫函数方法,分别得到了不确定切换系统可镇定的充分条件.状态矩阵和控制输入矩阵同时带有时变、未知且有界的不确定性,基于凸组合技术和LMI方法,设计出鲁棒状态反馈控制器及相应的切换策略,使得闭环系统在其平衡点处是渐近稳定的.最后仿真结果表明所设计的控制器及切换策略的正确有效性.     

时滞系统的输出反馈滑模控制的一种奇异系统方法

利用一种奇异系统方法讨论了时滞系统的输出反馈滑模控制问题. 时滞系统的非线性项满足范数有界约束.首先,将滑动模态与线性切换面作为一个奇异时滞系统,基于奇异时滞系统的稳定性理论, 给出滑动模态稳定及切换面存在的线性矩阵不等式(Linear matrix inequality, LMI)充分条件.然后,给出使得系统闭环渐近稳定的静态输出反馈滑模控制器的设计方法,此控制器保证闭环 系统有限时间到达切换面.最后,用数值算例验证本文方法的有效性和正确性.     

一类切换时滞奇异系统的状态反馈H∞控制*

研究一类由任意有限多个时滞奇异子系统组成的切换系统的状态反馈H∞控制问题。利用Lyapunov函数方法和凸组合技术,给出由矩阵不等式表示的控制器存在的充分条件,并设计了相应的子控制器和切换规则。采用变量替代方法,将该矩阵不等式转换为一组线性矩阵不等式(LMIs),最后给出一个求解状态反馈控制器增益矩阵的仿真算例。研究结果表明,通过切换,闭环系统在整个状态空间上的每个点都满足H∞性能,并不要求每个子系统在整个状态空间上都满足H∞性能,甚至也不要求其渐进稳定。     

一类切换线性奇异系统的状态反馈H∞控制*

研究了一类由任意多个子系统组成的线性切换奇异系统的状态反馈H∞控制问题。采用共同Lyapunov函数方法和凸组合技术,给出由矩阵不等式表示的使闭环系统渐近稳定且满足H∞性能的控制器存在的充分条件, 并设计了相应的子控制器和切换策略。采用矩阵变换,将矩阵不等式等价转换为一组线性矩阵不等式。数值算例说明了所提方法的有效性和可行性。     

Observer‐Based Reliable Control for Discrete‐Time Switched Linear Systems with Faulty Actuators

This paper deals with the issue of reliable control for discrete‐time switched linear systems with faulty actuators by utilizing a multiple Lyapunov functions method and estimate state‐dependent switching technique. A solvability condition for the reliable control problem is given in terms of matrix inequality with an extra matrix variable. This condition allows the reliable control problem for each individual subsystem to be unsolvable. For each subsystem of such a switched system, we design an observer and an observer‐based controller. A switching rule depending on the observer state is designed which, together with the controllers, can guarantee the stability of the closed‐loop switched system for all admissible actuator failures. The observers, controllers, and switching law are explicitly computed by solving linear matrix inequalities (LMIs). The proposed design method is illustrated by two numerical examples.     

Periodic stabilizability of switched linear control systems

Stabilizability via direct/observer-based state feedback control for discrete-time switched linear control systems (SLCSs) is investigated in this paper. For an SLCS, the control factors are not only the control input but also the switching signal, and they need to be designed in order to stabilize the system. As a result, stabilization design for SLCSs is more complicated than that for non-switched ones. Differently from the existing approaches, a periodic switching signal and piecewise constant linear state feedback control are adopted to achieve periodic stabilizability for such systems. It is highlighted that multiple feedback controllers need to be designed for one subsystem. For discrete-time SLCSs, it is proved that reachability implies periodic stabilizability via state feedback. A necessary and sufficient criterion for periodic stabilizability is also established. Two stabilization design algorithms are presented for real application. Moreover, it is proved that reachability and observability imply periodic stabilizability via observer-based feedback for discrete-time SLCSs. Periodic detectability, as the dual concept of periodic stabilizability, is discussed and the stabilization design algorithms via observer-based feedback are presented as well.     

一类离散时间切换混杂系统鲁棒控制

由于切换规则的存在使得切换混杂控制系统的稳定性研究变得极为复杂,如何针对给定的系统设计适当的控制器和切换规则没有统一的方法.本文考虑一类线性不确定离散时间切换混杂系统的鲁棒二次镇定和渐近镇定问题.利用公共李雅普诺夫函数方法和多李雅普诺夫函数方法,分别设计了切换混杂系统鲁棒状态反馈控制器和鲁棒输出反馈控制器,保证了切换混杂系统的二次稳定性和渐近稳定性.仿真结果验证了所提算法的正确有效性.     

Adaptive stabilization of a class of uncertain switched nonlinear systems with backstepping control

In this paper, we focus on the problem of adaptive stabilization for a class of uncertain switched nonlinear systems, whose non-switching part consists of feedback linearizable dynamics. The main result is that we propose adaptive controllers such that the considered switched systems with unknown parameters can be stabilized under arbitrary switching signals. First, we design the adaptive state feedback controller based on tuning the estimations of the bounds on switching parameters in the transformed system, instead of estimating the switching parameters directly. Next, by incorporating some augmented design parameters, the adaptive output feedback controller is designed. The proposed approach allows us to construct a common Lyapunov function and thus the closed-loop system can be stabilized without the restriction on dwell-time, which is needed in most of the existing results considering output feedback control. A numerical example and computer simulations are provided to validate the proposed controllers.     

一类线性切换系统的事件触发输出调节问题

通过设计事件触发状态反馈控制器,研究一类线性切换系统的输出调节问题.相比于时间触发控制,事件触发控制可显著地降低控制任务执行的次数.由于事件触发时刻与切换时刻的相互混合,导致切换系统控制器的设计十分困难.本文通过给出事件触发机制、状态反馈控制器和满足平均驻留时间的切换信号联合设计的方案,得到系统输出调节问题可解的充分条件.非共同坐标变换突破原有各子系统的调节器方程组具有共同解的限制.此外,为了避免Zeno现象,给出相邻事件触发间隔时间存在一个正下界.最后,应用切换RLC电路系统进行仿真验证结论的有效性.     

Backstepping design for global stabilization of switched nonlinear systems in lower triangular form under arbitrary switchings

This paper is concerned with the global stabilization problem for switched nonlinear systems in lower triangular form under arbitrary switchings. Two classes of state feedback controllers and a common Lyapunov function (CLF) are simultaneously constructed by backstepping. The first class uses the common state feedback controller which is independent of switching signals; the other class utilizes individual state feedback controllers for the subsystems. As an extension of the designed method, the global stabilization problem under arbitrary switchings for switched nonlinear systems in nested lower triangular form is also studied. An example is given to show the effectiveness of the proposed method.     

Robust exponential stabilization for network-based switched control systems

It has become a common practice to employ networks in control systems for connecting controllers and sensors/actuators on controlled plants and processes. A network-based switched control system, as a special case of networked control systems, is studied. Such a system is represented with network-induced delays and packet dropout as a switched delay system. Sufficient conditions for robust exponential stability are derived for a class of switching signals with average dwell time. A stabilization design for continuous-time, linear switched plant with nonlinear perturbation under a given communication network via a hybrid state feedback controller is proposed. A hybrid controller design is network-dependent and given in terms of linear matrix inequalities.     

基于牵制控制的切换布尔网络的分布式集合镇定

切换布尔网络是一种典型的网络化控制系统, 在基因调控、信息安全、人工智能、电路设计等领域具有重 要应用. 本文基于牵制控制方法, 研究切换布尔网络在任意切换下的分布式集合镇定问题. 首先, 利用矩阵半张量积 方法,得到切换布尔网络的代数形式. 其次, 基于代数形式, 提出构造性的算法来实现切换布尔网络在牵制控制的 作用下任意切换集合镇定, 并设计出状态反馈牵制控制器. 再次, 利用逻辑矩阵分解技术和分布式控制方法, 设计任 意切换下切换布尔网络的分布式集合镇定控制器, 并提出分布式控制器存在的充分条件. 文中给出3个例子来说明 所获得结果的有效性.     

Nonfragile robust exponential stabilization of nonlinear uncertain switched systems with actuator saturation

For nonlinear uncertain switched systems, the problem of how to overcome the controller vulnerability is studied when the actuator saturation is considered. The sufficient condition for guaranteeing nonfragile robust exponential stabilization of the system is derived by using the method of minimum dwell time. Then, a switching law and the nonfragile state feedback controllers are designed such that the closed-loop system can be robustly exponentially stabilized at the origin. Next, when some scalar parameters of the closed-loop system are given, the design issue of the nonfragile state feedback controllers, which aim at enlarging the estimation of domain of attraction for closed-loop system, is transformed into a convex optimization issue with linear matrix inequalities (LMI) constraints. Finally, an example is given to verify the effectiveness of the proposed method.