Simultaneous reduced-order control and fault detection for discrete-time switched systems with relaxed persistent dwell time regularity

This paper focuses on the problem of simultaneous control and fault detection (FD) for discrete-time switched systems. The main goal is to develop a control/detection unit (CDU) associated with a switching law to control the system and detect faults simultaneously. When the switched systems are with partial measurable states, we directly use these states to construct partial control and FD signals. Next, the reduced-order CDU is designed to generate the other control and FD signals. Compared with existing results based on full-order CDU, the proposed results lead to less conservatism and reduce design complexity. The switching law is constructed in the frame of persistent dwell time (PDT) switching. A novel switching number constraint condition is introduced, which further relaxes the restrictions on the dwell time of switching processes of PDT. The less restriction on dwell time degrades the performance requirement of each subsystem and upgrades the degree of freedom for switching law design. Based on the proposed results, a class of nonweighted performance indexes is introduced to characterize the fault sensitivity and robustness. Finally, the effectiveness of the proposed method is illustrated by an example.     

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.     

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.     

A fault tolerant control framework for periodic switched non-linear systems

An observer-based fault tolerant control (FTC) framework is proposed for a class of periodic switched non-linear systems (PSNS) without full state measurements. Two kinds of faults are considered: continuous faults that affect each mode during its dwell period; and discrete faults that affect the switching sequence. Under the average dwell time scheme, the proposed FTC framework can maintain the stability of overall PSNS in spite of these two kinds of fault. A switched reluctance motor example is taken to illustrate the efficiency of the proposed method.     

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.     

Fault detection and isolation for discrete-time switched linear systems based on average dwell-time method

This article is concerned with the problem of fault detection and isolation (FDI) for discrete-time switched linear systems based on the average dwell-time method. The proposed FDI framework consists of a bank of FDI filters, which are divided into N groups for N subsystems. The FDI filters belonging to one group correspond to the faults for a subsystem, and generate a residual signal to guarantee the fault sensitivity performance for the subsystem, the fault attenuation performance for other subsystems and the disturbance attenuation performance for all subsystems. Different form employing the weighting matrices to restrict the frequency ranges of faults for each subsystem, the finite-frequency H _? performance for switched systems is first defined. Sufficient conditions are established by linear matrix inequalities (LMIs), and the filter gains are characterised in terms of the solution of a convex optimisation problem. Two examples are used to demonstrate the effectiveness of the proposed design method.     

Stabilisation analysis for switched neutral systems based on sampled-data control

In this paper, the problem of stabilisation analysis for switched neutral systems based on sampled-data control and average dwell time approach is investigated. Delay-dependent stabilisation results are derived in terms of linear matrix inequalities by constructing piecewise Lyapunov–Krasovskii functional based on the Wirtinger's inequality. Also, the controller gain matrix is designed by applying an input-delay approach. Further convex combination technique and some integral inequalities are used to derive less conservative results. The effectiveness of the derived results is validated through numerical examples.     

Weighted control with ‐stability constraint for switched positive linear systems

This paper is concerned with the problem of control with ‐stability constraint for a class of switched positive linear systems. The ‐stability means that all the poles of each subsystem of the resultant closed‐loop system belong to a prescribed disk in the complex plane. A sufficient condition is derived for the existence of a set of state‐feedback controllers, which guarantees that the closed‐loop system is not only positive and exponentially stable with each subsystem ‐stable but also has a weighted performance for a class of switching signals with average dwell time greater than a certain positive constant. Both continuous‐time and discrete‐time cases are considered, and all of the obtained conditions are formulated in terms of linear matrix inequalities, whose solution also yields the desired controller gains and the corresponding minimal average dwell time. Numerical examples are given to illustrate the effectiveness of the presented approach.Copyright © 2012 John Wiley & Sons, Ltd.     

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 control and fault detection for continuous‐time switched systems subject to a dwell time constraint

This paper is concerned with the simultaneous robust control and fault detection problem for continuous‐time switched systems subject to a dwell time constraint. To meet the control and detection objectives under the constraint, the controller/detectors matching different time intervals are first constructed in an output feedback framework. A state‐dependent switching law that obeys the dwell time constraint is then designed such that the closed‐loop switched system is asymptotically stable and also with the robust and detection performance. Further, the proposed switching law is dependent only on the partial measurable states of the closed‐loop system, which is applicable when the states of system mode are fully unavailable. Thus, our result extends the existing ones in state‐dependent switching and state‐feedback frameworks. Finally, a numerical example is given to illustrate the effectiveness of the proposed method. Copyright © 2015 John Wiley & Sons, Ltd.     

切换系统的同时故障估计与容错控制

当切换系统发生故障时,通常需要依次进行故障诊断和容错控制.为了提高切换系统故障诊断的可靠性和容错控制的及时性,本文提出一种同时故障估计与容错控制方法.针对满足平均驻留时间约束的线性切换系统,首先建立了基于状态观测器的同时故障估计与容错控制器,并将其设计问题转化为了加权H∞性能指标下增广误差系统的多目标求解问题.然后使用平均驻留时间技术和多Lyapunov函数方法设计了故障估计与容错控制器的参数,又通过松弛矩阵方法进一步得到了保守性较低的结果.最后,利用一个例子对本文所提方法进行了仿真,证实了该方法的有效性.     

Event-triggered simultaneous fault detection and tracking control for multi-agent systems

The main aim of this study is to design distributed simultaneous fault detection and control units for multi-agent systems subject to limited communication and energy resources. For this purpose, each agent is equipped with a single module that generates both the residual signal for the fault detection task, as well as the control input of each agent for the tracking objective. To reduce the communication among the agents, an event-triggered data transmission paradigm is considered by using a dynamic triggering rule which results in higher data transmission reduction in comparison with the static triggering condition. Moreover, the proposed dynamic observer-based structure for the detector-controller module provides more degrees of freedom compared to the static Luenberger observer. The design parameters are obtained by solving a multi-objective optimisation problem considering the fault detection, tracking, and communication objectives. Simulation results illustrate the effectiveness and capabilities of the proposed method.     

Fault detection for output feedback control systems with actuator stuck faults: A steady‐state‐based approach

The paper studies the fault detection problem for output feedback control systems with bounded disturbances and nonzero constant reference inputs. A steady‐state‐based approach is proposed which can be used to detect small actuator stuck faults including actuator outage (the stuck value is zero). These small stuck faults, especially the outage faults, cannot be detected effectively using the existing techniques. A dynamic output feedback controller and a weighting matrix are designed simultaneously. The dynamic output feedback controller stabilizes the closed‐loop system for both fault‐free and faulty cases and attenuates the effects of disturbances. By manipulating the steady‐state values of system states with the detection weighting matrix, a residual is then generated, through which actuator stuck faults including actuator outages can be detected effectively. Simulation results are included to demonstrate our design procedure. Copyright © 2009 John Wiley & Sons, Ltd.     

High-order repetitive control for discrete-time linear switched systems

This paper is concerned with the design of a high-order repetitive control (RC) law for a class of discrete-time linear switched systems with repetition-varying reference trajectories. First, a high-order RC law, which embeds the characteristic of known variation of the reference trajectories, is proposed to the system, and a two-dimensional (2D) model is presented to describe the control and learning actions of the repetitive control system by using the lifting technique. By choosing appropriate multiple Lyapunov–Krasovskii functions, sufficient conditions for asymptotic stability of the 2D system are derived in the form of a set of linear matrix inequalities. Finally, an example is given to illustrate the effectiveness of the proposed results.     

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.     

任意相对阶下非线性切换系统的事件触发漏斗控制

针对一类具有任意相对阶且带有部分非输入到状态稳定逆动态的非线性切换系统, 提出一种动态事件触 发漏斗跟踪控制方案. 首先, 引入一个虚拟输出将任意相对阶的非线性切换系统转换为相对阶为一的非线性切换系 统. 其次, 设计各子系统的事件触发漏斗控制器和切换的动态事件触发机制, 解决候选事件触发漏斗控制器和子系 统之间的异步切换问题, 所提方案消除已有文献中为所有子系统设计共同控制器带来的保守性. 在一类具有平均驻 留时间切换信号的作用下, 保证切换闭环系统的所有信号都是有界的, 且跟踪误差一直在预设的漏斗内演化, 并排 除采样中的奇诺现象. 最后, 一个仿真例子验证方案的实用性和有效性.     

Input‐to‐state stability of switched nonlinear systems with delay in the active mode detection

A switched nonlinear system subject to disturbances is considered in this paper. The switching signal admits an average dwell time and a state feedback control depending on the system operating modes, detected with a maximum time delay, is applied to the system. In this framework, the input‐to‐state stability problem of the closed‐loop system is addressed. Based on some established existence conditions of mode‐dependent Lyapunov‐like functions, the values of the maximum time delay and the average dwell time that allow to achieve the input‐to‐state stability of the closed‐loop system are determined. In order to obtain more tractable results, the existence conditions of the mode‐dependent Lyapunov‐like functions are given in terms of sum‐of‐squares programming in the case of polynomial nonlinearities. In the linear case, they are expressed in terms of linear matrix inequalities and a procedure for the synthesis of the mode‐dependent controller is provided in this situation. The established theoretical results are illustrated through a control problem of a building ventilation system and a switched control problem of a vehicle suspension system.     

Fault detection for switched nonlinear systems under asynchronous switching

Asynchronous switching between switched system and associated filter or controller frequently occurs in several applications. In this article, the fault detection problem for a class of switched nonlinear systems with asynchronous switching is addressed. To model the switched system behaviour under asynchronous switching, two working modes are adopted to facilitate the studies on the issue. Then, based on average dwell time approach, a fault detection filter is developed via solving LMIs. Furthermore, it is proved that the fault detection problem under synchronous switching is only a particular case of our results for asynchronous switching. Finally, a numerical example is given to illustrate the effectiveness of proposed results.     

带有执行器故障的网络控制系统的自适应容错H_∞控制

针对带有执行器故障的网络控制系统, 提出了一种自适应容错控制方法. 首先基于最近提出的一种新的网络诱导时滞模型, 设计了状态反馈形式的自适应容错控制器. 然后以线性矩阵不等式的形式给出了控制器存在的充分条件. 该条件不仅保证了系统在执行器故障和正常情形下均能达到稳定, 而且使得其H∞性能最优. 最后通过一个数值例子证明了所提方法的有效性.     

Adaptive iterative learning control for switched nonlinear continuous-time systems

In this paper, an adaptive iterative learning control (ILC) method is proposed for switched nonlinear continuous-time systems with time-varying parametric uncertainties. First, an iterative learning controller is constructed with a state feedback term in the time domain and an adaptive learning term in the iteration domain. Then a switched nonlinear continuous-discrete two-dimensional (2D) system is built to describe the adaptive ILC system. Multiple 2D Lyapunov functions-based analysis ensures that the 2D system is exponentially stable, and the tracking error will converge to zero in the iteration domain. The design method of the iterative learning controller is obtained by solving a linear matrix inequality. Finally, the efficacy of the proposed controller is demonstrated by the simulation results.