奇异Markov跳跃系统的鲁棒故障检测

研究受L2有界未知输入影响的一类奇异Markov跳跃系统的鲁棒故障检测问题。采用基于观测器的故障检测滤波器（FDF）作为残差产生器,将故障检测滤波器的设计归结为随机意义下的H∞滤波问题。推导并证明了问题可解的充分条件,并通过求解线性矩阵不等式得到了故障检测滤波器参数矩阵的解。算例验证了所给算法的有效性。     

A Reduced-order Fault Detection Filter Design for Polytopic Uncertain Continuous-time Markovian Jump Systems with Time-varying Delays

In this article, the fault detection (FD) reduced-order filtering problem is investigated for a family of polytopic uncertain continuous-time Markovian jump linear systems (MJLSs) with time-varying delays. Under meeting the the premise of fault detection accuracy, the reduced order fault detection filters are desirable in applications where fast data processing and saving computing space are necessary. Then, by the aid of the Markovian Lyapunov-Krasovskii functional and convex polyhedron techniques, some novel time-varying delays and polytopic uncertain sufficient conditions are proposed to insure the existence of the FD reduced-order filter. Finally, a simulated continuous stirred tank reactor process example is provided to verify the feasibility of the proposed methodology.     

时滞离散马尔可夫跳跃系统的鲁棒故障检测

研究具有状态时滞离散马尔可夫跳跃系统的鲁棒故障检测问题．基于依赖于系统模态的滤波器构造残差产生系统,利用H∞控制理论将故障检测滤波器的设计归结为H∞滤波问题,应用线性矩阵不等式技术得到了此类系统的故障检测滤波器存在的充分条件．数值仿真表明所提方法是可行的．     

延迟不确定马尔科夫跳变系统的执行器和传感器故障同时估计方法

针对具有参数不确定和延迟环节的马尔科夫跳变系统,在状态转移概率矩阵（Transition probability matrix,TPM）不确定的情形下,讨论了其执行器和传感器故障同时估计的方法.通过扩展系统状态,将系统转换为一个具有马尔科夫跳变参数的广义描述系统,基于此广义描述系统设计马尔科夫跳变观测器实现对其状态和传感器故障的估计.与此同时,还设计了一组自适应律对执行器故障进行在线调节.通过求解一组线性矩阵不等式最优化问题,得到观测器存在的充分条件.最后,针对两个数值实例,验证了所设计方法的有效性.     

线性离散马尔科夫跳跃系统最优故障检测

本文研究线性离散马尔科夫跳跃系统的最优故障检测问题。通过设计基于观测器的故障检测滤波器作为残差产生器,将滤波器的设计问题归结为随机意义下H_/H或H/H性能指标优化问题。基于算子优化方法,通过解耦合Riccati方程得到上述问题的统一解。算例验证所提方法的有效性。     

一类马尔可夫跳跃线性系统的FDF设计

研究受L2范数有界未知扰动影响的一类马尔可夫跳跃线性系统的基于观测器的故障诊断滤波器设计问题.应用H∞优化技术,给出并证明了随机稳定并满足一定性能指标的残差产生系统的存在条件.通过求解线性矩阵不等式可求得故障诊断滤波器设计的解析解.     

Robust Stochastic Stability and Control for Uncertain Singular Markovian Jump Systems with Multiplicative Noise

This paper focuses on the problems of robust stability and stabilization and robust control for uncertain singular Markovian jump systems with (x,v)‐dependent noise. The parameter uncertainties appearing in state, input, disturbance as well as diffusion terms are assumed to be time‐varying but norm‐bounded. Based on the approach of generalized quadratic stability, the memoryless state feedback controller is designed for the robust stabilization problem, which ensures that the resulting closed‐loop system has an impulse‐free solution and is asymptotically stable in the mean square. Furthermore, the results of robust control problem are derived. The desired state feedback controller is presented, which not only meets the requirement of robust stabilization but also satisfies a prescribed performance level. The obtained results are formulated in terms of strict LMIs. What we have obtained can be viewed as corresponding extensions of existing results on uncertain singular systems. A numerical example is finally given to demonstrate the application of the proposed method.     

Stochastic Stability and Stabilization of Singular It ‐type Markovian Jump Systems with Uncertain Transition Rates: An LMI Approach

This paper investigates the stochastic stability and stabilization for a class of singular stochastic systems of Itô‐type with Markovian switching, the transition rates (TRs) in the jumping processes are uncertain. The aims are to establish sufficient conditions to ensure the considered system to be stochastically stable in the mean square sense, which is supported by a detailed proof of existence and uniqueness of the system solution, and to propose a controller such that the system can be stabilizable. The controller is first proposed and has advantage over traditional ones, the controller gain matrices are obtained by solving a strict linear matrix inequality (LMI). Finally, a numerical example is provided to illustrate the validity of the obtained methodology.     

Markovian跳变不确定分布参数系统随机稳定性分析

研究了一类具有Markovian跳变的不确定分布参数系统的随机稳定性问题。基于线性矩阵不等式方法,通过构造适当的随机Lyapunov泛函,计算弱无穷小算子,利用Green公式及Schur补引理,系统随机稳定的充分条件以一组线性矩阵不等式给出。线性矩阵不等式很容易通过MATLAB中的LMI工具箱进行求解。该充分条件便于工程实际应用。最后,构建仿真模型验证了该方法的有效性。     

Reliable Dissipative Control for a Class of Uncertain Singular Markovian Jump Systems via Hybrid Impulsive Control

In this paper, the problem of robust normalization and reliable dissipative control is investigated for a class of uncertain singular Markovian jump systems with actuator failures. The uncertainties exhibit in both system matrices and transition rate matrix of the Markovian chain. A new impulsive and proportional–derivative control strategy is presented. The gain matrices of the impulsive control part can be obtained together with the design approach. Moreover, the dissipative control results obtained in this paper include the results of H‐infinity and passive control as special cases. Finally, two numerical examples are provided to illustrate the effectiveness and applicability of the proposed methods.     

广义马氏跳变系统在一般转移速率下的控制器设计

针对转移概率不能精确获得并且部分未知的广义马氏跳变系统, 分别讨论在模态依赖控制器和模态独立控制器条件下的系统镇定问题. 与现有结果相比, 所提研究方法具有较小的保守性, 能够有效地解决实际问题. 首先, 运用自由权矩阵方法, 得到了广义马氏跳变系统在转移速率满足上述一般条件时系统随机容许的充分条件. 在此基础上, 以线性矩阵不等式(Linear matrix inequality, LMI)的形式分别给出了模态依赖和模态独立控制器的求解条件. 最后, 通过数值算例验证设计方法的有效性和优越性.     

具有马氏跳跃参数的切削加工系统控制问题研究

以单刀具垂直切削加工系统为研究对象, 引入了变进给量控制方法, 建立了具有Markov跳跃参数的时变时滞跳跃系统模型. 通过对系统的随机稳定性分析, 给出了使系统呈均方意义下指数稳定的充分条件, 同时研究了在系统参数矩阵和状态转移率非精确可知情形下的鲁棒稳定性条件, 并讨论了时变时滞参数对系统状态变量指数衰减速率的影响关系. 最后以仿真算例说明了本文所提方案的有效性.     

马尔可夫跳变系统基于观测器的有限时间容错控制

针对具有一般不确定转移速率的单边Lipschitz Markovian跳变系统,设计了有限时间故障估计观测器和容错控制器.首先,提出一种自适应的有限时间故障估计观测器,它对未知输入具有鲁棒性,能够同时估计出系统的状态、执行器故障和传感器故障,并确保了误差系统的H_∞有限时间有界.然后,基于所估计的状态和执行器故障,提出一种有限时间故障容错控制方法确保闭环系统H_∞有限时间有界.通过线性矩阵不等式的形式,给出了所设计的有限时间观测器和控制器存在的充分条件.最后,通过一个仿真实例,验证了所提方法的有效性.     

Sliding Mode Control for Markovian Jump Systems with Generalized Switching

In this paper, the sliding mode control (SMC) problem for continuous‐time Markovian jump systems (MJSs) is considered, in which the transition rate matrix (TRM) is partially unknown and uncertain. Firstly, the sliding mode surface S(t) = 0 is designed, which is mode‐dependent. Therefore, is used instead of in the SMC algorithm. Via adopting a linear matrix inequality (LMI) approach, sufficient conditions are proposed to ensure that the reduced order system is exponentially stable in mean square. Furthermore, the reduced order system is completely insensitive to the external disturbance. Secondly, SMC law is designed correspondingly which dominated by a Markov process. It could drive the state trajectories onto the specified sliding mode surface in finite time quickly and maintain them on the surface in subsequently time. Thirdly, a new term in will be introduced in the designed SMC and should be handled by a new approach. Finally, a numerical example is provided to show the effectiveness of the proposed method.     

不确定广义跳变时滞系统的鲁棒指数稳定性

讨论不确定广义跳变时滞系统的鲁棒指数稳定性问题. 利用线性矩阵不等式(LMI)技术给出一个时滞区间依赖条件保证标称系统正则、无脉冲且均方指数稳定. 同时该准则也被推广至不确定系统. 数值例子说明本文的结果改进了已有的结论.     

不确定短时延网络控制系统的故障检测

针对远程被控对象为线性模型,且网络诱导时延小于一个采样周期的一类网络控制系统(NCS),假设可能发生执行器故障,对系统进行故障检测。将随机时延对系统的影响转化为未知有界条件下的不确定项,建立了系统的离散数学模型。按照时延补偿策略设计了系统的故障观测器,并基于Lyapunov稳定性定理和线性矩阵不等式理论,推导出了整个观测器系统全局渐近稳定的充分条件。仿真例子验证了方法的有效性。     

Stability and Stabilization for Discrete-time Markovian Jump Stochastic Systems with Piecewise Homogeneous Transition Probabilities

International Journal of Control, Automation and Systems - In this paper, the stability and stabilization problems for discrete-time Markovian jump stochastic systems with time-varying transition...     

二维FM系统的同时故障检测与控制

本文研究二维Fornasini-Marchesini (FM)系统的同时故障检测与控制问题.针对故障和干扰的有限频特性, 设计满足有限频性能指标的故障检测滤波器/控制器, 在实现故障检测目标的同时兼顾控制性能.借助于二维广义KYP引理, 将有限频性能指标转化为矩阵不等式条件.在此基础上, 采用构造切平面的方法以及两步算法解决设计过程中出现的非凸问题.最后, 将所提出的方法应用于带钢轧制过程以验证其有效性.     

Robust Output Feedback Stabilization for Uncertain Discrete-Time Fuzzy Markovian Jump Systems With Time-Varying Delays

This paper provides a delay-dependent approach to the design of fuzzy dynamic output feedback controllers for uncertain discrete-time fuzzy Markovian jump systems with interval time-varying delays. First, by a fuzzy-basis-dependent and mode-dependent Lyapunov functional, a stochastic stability condition is derived by using the Finsler's lemma. Second, in terms of linear matrix inequalities (LMIs), a delay-dependent sufficient condition is presented, under which there exists a fuzzy output feedback controller such that the resulting closed-loop system is robustly stochastically stable. A desired controller can be constructed when these LMIs are feasible. Finally, the effectiveness of the proposed design method is demonstrated by a simulation example.