Fault detection for continuous‐time switched systems under asynchronous switching

In this paper, the problem of fault detection for continuous‐time switched systems under asynchronous switching is investigated. The designed fault detection filter is assumed to be asynchronous with the original systems. Attention is focused on designing a fault detection filter such that the estimation error between the residual and the fault is minimized in the sense of H _∞ norm. By employing piecewise Lyapunov function and average dwell time techniques, a sufficient condition for the existence of such a filter is exploited in terms of certain linear matrix inequalities. Finally, an example of a switched electrical circuit is provided to illustrate the effectiveness of the proposed approach. Copyright © 2013 John Wiley & Sons, Ltd.     

Robust Fault Detection for Switched Linear Systems With State Delays

This correspondence deals with the problem of robust fault detection for discrete-time switched systems with state delays under an arbitrary switching signal. The fault detection filter is used as the residual generator, in which the filter parameters are dependent on the system mode. Attention is focused on designing the robust fault detection filter such that, for unknown inputs, control inputs, and model uncertainties, the estimation error between the residuals and faults is minimized. The problem of robust fault detection is converted into an H _infin-filtering problem. By a switched Lyapunov functional approach, a sufficient condition for the solvability of this problem is established in terms of linear matrix inequalities. A numerical example is provided to demonstrate the effectiveness of the proposed method.     

基于异步切换多胞系统的网络化飞行器故障检测

本文研究了存在时变短时延和随机丢包的大包线网络化飞行器故障检测问题.首先,采用切换多胞系统描述飞行动态,并提出了一种局部重叠多胞划分方式以较低设计保守性.然后,借助泰勒级数展开和伯努利分布将时延和丢包转化为多胞系统参数,并构建了切换参数依赖故障检测滤波器.同时,考虑滤波器切换指令及多胞加权参数更新滞后引起的异步切换问题,基于切换参数依赖Lyapunov函数和平均驻留时间方法分析了系统的稳定性和l2性能,并以LMI形式给出了滤波器存在的充分条件.最后,以HiMAT(highly maneuverable technology)飞行器为例验证了所提方法的有效性.     

Simultaneous fault detection and control for switched systems with actuator faults

This paper is concerned with the fault detection and control problem for discrete-time switched systems. The actuator faults, especially ‘outage cases’, are considered. The detector/controller is designed simultaneously such that the closed-loop system switches under an average dwell time, and when a fault is detected, an alarm is generated and then the controller is switched to allow the norm of the states of the subsystem to increase within the acceptable limits. Thus, a switching strategy which combines average dwell time switching with event-driven switching is proposed. Under this switching strategy, the attention is focused on designing the detector/controller such that estimation errors between residual signals and faults are minimised for the fulfillment of fault detection objectives; simultaneously, the closed-loop system becomes asymptotically stable for the fulfillment of control objectives. A two-step procedure is adopted to obtain the solutions through satisfying a set of linear matrix inequalities. An example comprising of three cases is considered. Through these cases, it is demonstrated that the fault detection and control for switched systems using a two-stage switching strategy and asynchronous switching are feasible.     

基于局部交叠异步切换的网络控制系统故障检测

针对存在时变短时延和丢包的网络控制系统故障检测问题,将非线性对象建模为线性切换系统.考虑工程中存在的局部交叠切换律,将切换系统划分为若干局部交叠切换于系统.同时,考虑滤波器切换滞后引起的异步切换问题,进一步将系统增广为局部交叠异步切换系统.在此基础上,结合公共Lyapunov函数和平均驻留时间方法,以LMI形式给出检测滤波器设计方法.最后,通过某网络化飞行器的全包线飞行验证了所提出方法的有效性.     

Asynchronous fault detection filter design approach for discrete‐time switched linear systems

This paper is concerned with the problem of the fault detection filter design for discrete‐time switched linear systems with average dwell‐time. The designed fault detection filters are also switched systems, which are assumed to be asynchronously switched with the original switched systems. Improved results on the weighted l₂ performance and the H _? performance are first given, and the multiple Lyaounov‐like functions during matched period and unmatched period for the running time of one subsystem are used. By the aid of multiple Lyapunov‐like functions combined with Projection Lemma, the FD filters are designed such that the augmented systems under asynchronous switching are exponentially stable, and the residual signal generated by the filters achieves the weighted l₂‐gain for disturbances and guarantees the H _? performance for faults. Sufficient conditions are formulated by linear matrix inequalities, and the filter gains are characterized in terms of the solution of a convex optimization problem. Finally, examples are provided to demonstrate the effectiveness of the proposed design method. Copyright © 2012 John Wiley & Sons, Ltd.     

广义马尔科夫跳变系统的事件触发异步故障检测滤波

针对一类具有事件触发机制的离散时间广义马尔科夫跳变系统,解决了异步故障检测滤波问题。 提出了一种事件触发策略,实现了合理利用网络资源,降低通信负担的目的;考虑了系统模态和滤波器模态之间存在的异步现象,使用两种不同的马尔科夫链来分别表示系统模态和滤波器模态,并在此基础上提出了一种异步故障检测滤波器的设计方法。 通过将异步故障检测滤波器的设计问题与事件触发机制相结合,根据Lyapunov稳定性理论,给出了保证残差误差系统具有正则性、因果性和随机稳定的并且满足 性能的充分条件,通过求解一组特定的线性矩阵不等式,得到了期望的异步故障检测滤波器参数。 最后,通过一个仿真例子说明了所设计的异步故障检测滤波器的设计方法是有效的。     

Fault detection for discrete-time switched systems with interval time-varying delays

This paper investigates the problem of fault detection filter design for discrete-time switched systems with interval time-varying delays. The residual generator is constructed based on a mode-dependent fault detection filter, i.e., the designed fault detection filter is also a switched system as well. By constructing a novel switched Lyapunov functional, a new criterion is obtained for the residual system. Based on this, a sufficient condition for the existence of the above filter is established in terms of linear matrix inequalities (LMIs). The designed fault detection filter can guarantee the difference between the generated residual signal and the fault signal as small as possible. An example is provided to illustrate the effectiveness of the proposed method.     

Stabilisation of a class of positive switched nonlinear systems under asynchronous switching

This paper addresses the stabilisation problem for a class of positive switched nonlinear systems under asynchronous switching, which means that the switches between the candidate controllers and the system modes are not synchronous. The continuous and discrete cases are considered respectively. Sufficient conditions are firstly provided for the existence of the asynchronous switching controllers to guarantee the closed-loop system to be positive and exponentially stable, and the corresponding admissible switching signals are presented. As a special case, the stabilisation results for positive switched linear systems under asynchronous switching are provided accordingly. Finally, two numerical examples are given to illustrate the effectiveness of the proposed methods.     

Event‐triggered fault detection for switched systems with time‐varying sojourn probabilities

In this paper, a codesign strategy of an event‐triggered scheme and a fault detection filter (FDF) is developed for the networked switched systems with delayed measurements. A novel switching rule is proposed to better describe the switching behavior in a real system, under which the probability staying in each subsystem is time varying and results in a piecewise continuous system dynamics. An event‐triggered strategy based on the relative error with respect to the delayed measurement signal is established to reduce the communication burden. Our attention is concentrated on the construction of an event‐triggered fault detection technique for the proposed switched system with delayed measurements. Combining the stochastic analysis techniques and the average dwell time (ADT) method, a sufficient condition is obtained to guarantee the finite‐time boundedness of the generated residual system, the sensitivity of the residual signal to faults, and the disturbance attenuation of the switched system to external disturbances. Based on the established condition, a codesign strategy is developed to get the event‐triggered threshold and the FDF gain. Finally, two simulation results verify the effectiveness of the proposed design method.     

异步时滞切换正系统的有限时间镇定

研究异步切换下时滞切换正系统的有限时间控制问题,即针对控制器切换滞后于子系统切换形成的异步现象,基于平均驻留时间切换方法对切换正系统开展有限时间镇定研究.首先,将每个正子系统运行的区间划分为子系统与控制器匹配和失配区间,并构造多余正Lyapunov-Krasovskii泛函;其次,基于有限时间稳定理论,实现平均驻留时间切换律及异步时滞切换正系统有限时间镇定控制器的联合设计,并给出连续时间和离散时间两种情形下系统有限时间镇定的充分条件;最后,通过两个仿真例子验证所提出方法的有效性.     

Exponential H∞ Filtering for Discrete‐Time Switched State‐Delay Systems Under Asynchronous Switching

The exponential H_∞ filtering problem of discrete‐time switched state‐delay systems under asynchronous switching is considered in this paper. The objective is to design a full‐order or reduced‐order switched filter guaranteeing the exponential stability with the weighted H_∞ performance of the filtering error system. A sufficient condition for the exponential stability with the weighted H_∞ performance of the filtering error system is provided based on delay‐dependent multiple Lyapunov‐Krasovskii functionals. The gains of the filter can be obtained by solving a set of linear matrix inequalities. A numerical example is presented to demonstrate the effectiveness of the developed results.     

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.     

Stability Properties of Switched Nonlinear Delay Systems with Synchronous or Asynchronous Switching

This paper is concerned with the problem of input‐to‐state stability (ISS) for a class of switched nonlinear delay systems. The cases where the switching signal of the system and the switching signal of the corresponding controller are synchronous and asynchronous are both considered. To study two asynchronous switching signals in a unified framework, we adopt the technique of the merging switching signal. Based on a piecewise Lyapunov–Krasovskii functional method, some sufficient conditions are explicitly given to guarantee the ISS of the switched nonlinear delay system under the average dwell time scheme. Finally, a numerical example is presented to demonstrate the effectiveness of the proposed theory.     

基于转移依赖Lyapunov函数离散时间切换系统的异步$l_2-l_infty$滤波

主要研究离散时间切换系统在容许路径依赖混合驻留时间(AED-IDT)切换下异步$l_2-l_\infty$滤波器的设计问题.不同于以往的研究结果,提出一种异步转移依赖凸Lyapunov函数,得到了低保守性稳定性判据.所设计Lyapunov函数的创新之处在于其构建不再依赖系统模态,而是依赖当前激活的滤波器模态和刚刚运行结束的滤波器模态.鉴于所设计Lyapunov函数具有凸性质,这为所提出方法提升自由度和灵活性创造了空间.采用转移依赖凸Lyapunov函数和AED-IDT切换策略,能够得到保证滤波误差系统全局一致指数稳定,且具有$l_2-l_\infty$性能的充分条件.在此基础上,提出异步$l_2-l_\infty$滤波器的设计方法.最后,通过一个数值实例和一个切换RLC应用电路来验证所得结果的有效性,并经过仿真实验验证了所提出设计方法能够保证更紧的驻留时间界和较小的滤波误差结果.     

Asynchronous H∞ filtering for linear switched systems with average dwell time

This paper is concerned with the H_∞ filtering problem for a class of continuous-time linear switched systems with the asynchronous behaviours, where ‘asynchronous’ means that the switching of the filters to be designed has a lag to the switching of the system modes. By using the Lyapunov-like functions and the average dwell time technique, a sufficient condition is obtained to guarantee the asymptotic stability with a weighted H_∞ performance index for the filtering error system. Moreover, the results are formulated in the form of linear matrix inequalities that are numerical feasible. As a result, the filter design problem is solved. Finally, an illustrative numerical example is presented to show the effectiveness of the results.     

Robust Fault Detection for Discrete‐Time Nonlinear Impulsive Switched Systems

This paper deals with the problem of robust fault detection for discrete‐time nonlinear impulsive switched systems. The fault detection filter is used as the residual generator, in which the filter parameters are dependant on the system mode. Attention is focused on designing the robust fault detection filter. The problem of robust fault detection is converted into an H_∞‐filtering problem. A sufficient condition for the solvability of this problem is established by a convex optimization problem. A numerical example is provided to demonstrate the effectiveness of the proposed method.     

Exponential Stability and Asynchronous Stabilization of Switched Systems With Stable and Unstable Subsystems

This paper deals with the exponential stability and asynchronous stabilization of continuous‐time switched systems. By delicately constructed piecewise Lyapunov‐like functions and the minimum dwell time switching method, exponential stability of the switched systems with stable or unstable subsystems is obtained. Based on the result of the stability, the problem of controller design of the switched systems under asynchronous switching is also solved, and the delay that causes asynchronous phenomena can be unbounded. The stability results and control laws of the switched systems are formulated in the form of linear matrix inequalities that are numerically feasible. Finally, two illustrative numerical examples are presented to show the effectiveness of the obtained theoretical results.     

Simultaneous fault detection and control for switched LPV systems with inexact parameters and its application

This paper investigates the simultaneous fault detection and control problem for a switched linear parameter-varying (LPV) system. The inexact scheduling parameter-dependent fault detection filters and controllers are designed based on the output framework. To realise the detection and control goals, the inexact scheduling parameter-dependent sufficient LMI conditions are obtained by using multiple Lyapunov functions technique. A mode-dependent average dwell-time switching method is used, which is less strict than the general average dwell-time switching method. Simulation results on an aero-engine model show the feasibility and validity of the designed scheme.