Design of unknown input observer with H∞ performance for linear time-delay systems

A unknown input observer (UIO) design for a class of linear time-delay systems when the observer error can't completely decouple from unknown input is dealt with. A sufficient condition to its existence is presented based on Lyapunov stability method. Design problem of the proposed observer is formulated in term of linear matrix inequalities. Two design problems of the observer with internal delay and without internal delay are formulated. Based on H∞ control theory in time-delay systems, the proposed observer is designed in term of linear matrix inequalities (LMI). A design algorithm is proposed. The effective of the proposed approach is illustrated by a numerical example.     

一类线性时滞系统的未知输入观测器设计

以一类线性时滞系统为研究对象,研究了当观测误差与未知输入完全解耦时的未知输入观测器设计问题。基于时滞系统Lyapunov稳定性方法,给出了指数稳定未知输入观测器的存在条件。基于这一条件,提出了含有内部时滞与不含有内部时滞两种观测器的设计问题。通过求解线性矩阵不等式给出了所提观测器的设计方法。给出了两种情形下的观测器设计算法。数值例子说明了提出的设计方法的有效性。     

基于未知输入观测器方法的非线性切换系统故障检测

基于非线性未知输入观测器方法对一类离散时间非线性切换系统的故障检测问题进行了研究。给出了两种不同结构的非线性未知输入观测器。针对每一种观测器都考虑了两种切换信号:任意时间切换信号和满足平均驻留时间的切换信号。在任意切换信号下,使用了切换Lyapunov函数的方法来设计非线性未知输入观测器的参数;在满足平均驻留时间切换信号下,使用了多Lyapunov函数方法进行观测器参数的设计。然后利用已知的非线性未知输入观测器,得到残差生成器,进而实现故障检测。通过数值仿真例子,验证了故障检测方法的有效性。     

Observer-based H∞ control over packet dropping networks

A new controller design problem of networked control systems with packet dropping is proposed. Depending on the place that the observer is put in the system, the network control systems with packet dropping are modeled as stochastic systems with the random variables satisfying the Bernoulli random binary distribution. The observer-based controller is designed to stabilize the networked system in the sense of mean square, and the prescribed H∞ disturbance attenuation level is achieved. The controller design problem is formulated as the feasibility of the convex optimization problem, which can be solved by a linear matrix inequality （LMI） approach. Numerical examples illustrate the effectiveness of the proposed methods.     

基于LMI的H_/H∞故障检测观测器设计

考虑未知输入信号的影响,研究了线性系统鲁棒故障检测观测器的设计问题。利用描述残差对故障灵敏度的H_指数和表示残差对未知输入鲁棒性的H∞范数,将鲁棒故障检测观测器的设计问题描述为基于H_/H∞的优化设计问题。利用线性矩阵不等式(linear matrix inequality, LMI)理论,给出故障检测观测器的存在条件,提出一种新的迭代LMI算法求解最优观测器增益。仿真结果表明,利用这种方法设计的故障检测观测器对故障的灵敏度高,对未知输入的鲁棒性强。     

H∞ fault estimation for a class of linear time-delay systems in finite frequency domain

This paper deals with the problem of H∞ fault estimation for linear time-delay systems in finite frequency domain. First a generalized coordinate change is applied to the original system such that in the new coordinates all the time-delay terms are injected by the system’s input and output. Then an observer-based H∞ fault estimator with input and output injections is proposed for fault estimation with known frequency range. With the aid of Generalized Kalman-Yakubovich-Popov lemma, sufficient conditions on the existence of the H∞ fault estimator are derived and a solution to the observer gain matrices is obtained by solving a set of linear matrix inequalities. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.     

H∞ fault estimation for a class of linear time-delay systems in finite frequency domain

This paper deals with the problem of H∞ fault estimation for linear time-delay systems in finite frequency domain. First a generalized coordinate change is applied to the original system such that in the new coordinates all the time-delay terms are injected by the system's input and output. Then an observer-based H∞ fault estimator with input and output injections is proposed for fault estimation with known frequency range. With the aid of Generalized Kalman-Yakubovich-Popov lemma, sufficient conditions on the existence of the H∞ fault estimator are derived and a solution to the observer gain matrices is obtained by solving a set of linear matrix inequalities. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.     

Delay-dependent robust H∞ control of convex polyhedral uncertain fuzzy systems

The robust H∞ control problem for a class of uncertain Takagi-Sugeno fuzzy systems with timevarying state delays is studied. The uncertain parameters are supposed to reside in a polytope. Based on the delay-dependent Lyapunov functional method, a new delay-dependent robust H∞ fuzzy controller, which depends on the size of the delays and the derivative of the delays, is presented in term of linear matrix inequalities （LMIs）. For all admissible uncertainties and delays, the controller guarantees not only the asymptotic stability of the system but also the prescribed H∞ attenuation level. In addition, the effectiveness of the proposed design method is demonstrated by a numerical example.     

New type of adaptive control for a class of distributed time-delay systems with adaptation regard to delay parameter

The problem on stabilization for the system with distributed delays is researched. The distributed time-delay under consideration is assumed to be a constant time-delay, but not known exactly. A design method is proposed for a memory proportional and integral (PI) feedback controller with adaptation to distributed time-delay. The feedback controller with memory simultaneously contains the current state and the past distributed information of the addressed systems. The design for adaptation law to distributed delay is very concise. The controller can be derived by solving a set of linear matrix inequalities (LMIs). Two numerical examples are given to illustrate the effectiveness of the design method.     

<Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> control for nonlinear stochastic Markov systems with time-delay and multiplicative noise

This paper is concerned with the H_∞ control problem for a class of nonlinear stochastic Markov jump systems with time-delay and system state-, control input- and external disturbancedependent noise. Firstly, by solving a set of Hamilton-Jacobi inequalities (HJIs), the exponential mean square H_∞ controller design of delayed nonlinear stochastic Markov systems is presented. Secondly, by using fuzzy T-S model approach, the H_∞ controller can be designed via solving a set of linear matrix inequalities (LMIs) instead of HJIs. Finally, two numerical examples are provided to show the effectiveness of the proposed design methods.     

Robust H∞ control for networked control systems

The robust H∞ control for networked control systems with both stochastic network-induced delay and data packet dropout is studied. When data are transmitted over network, the stochastic data packet dropout process can be described by a two-state Markov chain. The networked control systems with stochastic network-induced delay and data packet dropout are modeled as a discrete time Markov jump linear system with two operation modes. The sufficient condition of robust H∞ control for networked control systems stabilized by state feedback controller is presented in terms of linear matrix inequality. The state feedback controller can be constructed via the solution of a set of linear matrix inequalities. An example is given to verify the effectiveness of the method proposed.     

基于自适应未知输入观测器的多故障快速重构

针对一类非线性函数中耦合执行器故障的非线性动态系统, 提出一种基于自适应未知输入观测器的多故障快速重构方法, 通过引入比例项提高故障重构的快速性。首先, 将执行器故障进行解耦处理并构建包含传感器故障的增广系统。然后, 综合H_∞性能指标给出状态估计误差的稳定性证明。接着, 将观测器增益矩阵的求解转化为受线线矩阵不等式约束的非线性优化问题, 并实现执行器故障和传感器故障的多故障重构。最后, 结合单关节柔性机器人算例仿真验证了所提方法的有效性。     

一类非线性切换系统观测器设计的新方法

针对一类切换规则为时间依赖型的Lipschitz非线性切换系统,采用驻留时间方法研究了状态观测器设计问题.该切换系统同时含有可观测子系统与不可观测子系统,通过构造合适的Lyapunov函数,并利用矩阵不等式技术得到了保证状态观测器状态估计误差收敛的条件.并给出了观测器设计步骤.进一步,通过矩阵变换将观测器增益求解转化为LMI形式.最后给出了仿真算例说明了该设计方法的有效性.     

离散模糊时滞系统的鲁棒LQ/H∞非脆弱控制

针对一类由T-S模糊模型描述的不确定离散非线性时滞系统,讨论其在控制器存在可加性摄动情形下的鲁棒LQ/H_∞非脆弱控制问题。通过构造适当的Lyapunov函数,给出以线性矩阵不等式形式表示的系统时滞依赖稳定的充分条件以及相应的鲁棒LQ/H_∞非脆弱控制器设计方法。数值仿真表明,所构造的控制器不仅能够保证闭环模糊时滞系统的鲁棒渐近稳定性,还能使系统达到一定的H_∞干扰抑制水平。     

部分转移概率未知的Markov跳变系统鲁棒故障检测

针对部分转移概率未知的Markov跳变系统,研究了其鲁棒故障检测问题,设计了该系统的线性全阶鲁棒故障检测观测器。将自由连接权矩阵引入鲁棒故障检测观测器系统进行证明推导,极大地降低了固定连接权矩阵带来的保守性。通过构造Lyapunov函数,推导得出一系列线性矩阵不等式以确保鲁棒故障检测观测器系统随机渐近稳定。在此基础上,证明并给出了观测器存在的充分条件。进一步,优化所设计的观测器。数值仿真表明,所设计的鲁棒故障检测观测器不仅对故障具有较高的灵敏度,而且能确保对未知干扰输入有较强的鲁棒性。     

IMPROVED ROBUST H-INFINITY ESTIMATION FOR UNCERTAIN CONTINUOUS-TIME SYSTEMS

The design of full-order robust estimators is investigated for continuous-time polytopic uncertain systems. The main purpose is to obtain a stable linear estimator such that the estimation error system remains robustly stable with a prescribed H∞ attenuation level. Firstly, a simple alternative proof is given for an improved LMI representation of H∞ performance proposed recently. Based on the performance criterion which keeps the Lyapunov matrix out of the product of the system dynamic matrices, a sufficient condition for the existence of the robust estimator is provided in terms of linear matrix inequalities. It is shown that the proposed design strategy allows the use of parameterdependent Lyapunov functions and hence it is less conservative than the earlier results. A numerical example is employed to illustrate the feasibility and advantage of the proposed design.     

输入受限的参数摄动分段仿射系统鲁棒控制

研究了一类有输入约束和参数摄动的离散分段仿射系统的稳定性及其控制器的设计方法。提出了各分段仿射子系统离散时间状态集的椭圆集表示方法,结合Lyapunov意义的稳定约束,以LMIs形式给出了闭环分段仿射系统的鲁棒稳定充分条件和控制器的设计方法。同时将常见的输入约束转换成LMIs,通过LMIs的凸约束保证了求解控制器的可行性。最后通过仿真实例验证了所提方法的有效性。     

Design and simulation of fault diagnosis based on NUIO/LMI for satellite attitude control systems

This paper presents a scheme of fault diagnosis for flexible satellites during orbit maneuver. The main contribution of the paper is related to the design of the nonlinear input observer which can avoid false alarm arising from the disturbance from orbit control force. The effects of orbit control force on the fault diagnosis system for satellite attitude control systems, including the disturbing torque caused by the misalignments and the model uncertainty caused by the fuel consumed, are discussed, where standard Luenberger observer cannot work well. Then the nonlinear unknown input observer is proposed to decouple faults from disturbance. Besides, a linear matrix inequality approach is adopted to reduce the effect of nonlinear part and model uncertainties on the observer. The numerical and semi-physical simulation demonstrates the effectiveness of the proposed observer for the fault diagnosis system of the satellite during orbit maneuver.     

基于LMI的模糊控制器设计

对于许多实际的非线性系统,状态变量往往不能获取或难于测量。因此设计模糊状态观测器来估计状态变量是非常必要的。针对T-S模糊模型近似描述的非线性系统,提出了一种基于线性矩阵不等式(LMI)的具有区域极点配置功能的模糊控制器和模糊状态观测器的设计方法。首先利用并行分布补偿(PDC)设计思想和基于线性矩阵不等式(LMI)的极点配置理论,将闭环系统的全局渐进稳定性要求,性能指标及控制量约束条件统一到线性矩阵不等式框架内。然后求解线性矩阵不等式族获得控制器和观测器参数。最后将该设计方法应用于倒立摆的平衡控制中,通过仿真曲线可以看出该方法设计的控制器可使倒立摆稳定并满足指定的性能指标,因此该设计方法是有效的。     

Sliding mode H∞ control for a class of uncertain nonlinear state-delayed systems

A new proportional-integral (PI) sliding surface is designed for a class of uncertain nonlinear state-delayed systems. Based on this, an adaptive sliding mode controller (ASMC) is synthesized, which guarantees the occurrence of sliding mode even when the system is undergoing parameter uncertainties and external disturbance. The resulting sliding mode has the same order as the original system, so that it becomes easy to solve the H_∞ control problem by designing a memoryless H_∞ state feedback controller. A delay-dependent sufficient condition is proposed in terms of linear matrix inequalities (LMIs), which guarantees the sliding mode robust asymptotically stable and has a noise attenuation level γ in an H_∞ sense. The admissible state feedback controller can be found by solving a sequential minimization problem subject to LMI constraints by applying the cone complementary linearization method. This design scheme combines the strong robustness of the sliding mode control with the H_∞ norm performance. A numerical example is given to illustrate the effectiveness of the proposed scheme.