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Asymptotic state estimation for linear systems with sensor and actuator faults

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Science China(Information Sciences) 2019年第11期62卷 106-120页

作者： Chun-Hua XIE Hui YANG Dianhui WANG Zhe LI School of Electrical and Automation Engineering East China Jiaotong University Key Laboratory of Advanced Control & Optimization of Jiangxi Province Department of Computer Science and Information Technology La Trobe University College of Electrical and Information Engineering Hunan University

This paper investigates the asymptotic state estimation problem for linear systems with sensor and actuator faults, where the faults are modeled via multiple modes. For the case of sensor faults, we first introduce a new notion of detectability, i.e., detectability of system against sensor faults. The notion helps to address the question of whether it is possible to asymptotically estimate the system state by using the control input and system output, irrespective of which mode the system is in and what values the fault signals are.A necessary and sufficient condition for the system to be detectable against sensor faults is given, and then two switched observers are proposed for asymptotic state estimation with the help of maximin strategy. For the system with ? fault modes, we provide the explicit form of the switched observer, which is based on a bank of ?(?+1)/2 Luenberger-like or sliding-mode observers. Furthermore, extensions to the case of sensor and actuator faults are further studied. Finally, a simulation example of a reduced-order aircraft system is provided to show the effectiveness of the proposed approaches.

关键词： asymptotic state estimation observer linear systems sensor faults actuator faults

CONVERGENCE DOMAINS OF AOR TYPE ITERATIVE MATRICES FOR SOLVING NON-HERMITIAN linear systems

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Journal of Computational Mathematics 2004年第6期22卷 817-832页

作者： LiWang LSEC ICMSECAcademyofMathematicsandSystemSciencesChineseAcademyofSciencesBeijing100080China

We discuss AOR type iterative methods for solving non-Hermitian linear systems based on Hermitian splitting and skew-Hermitian splitting. Convergence domains of iterative matrices are given and optimal parameters are investigated for skew-Hermitian splitting. Numerical examples are presented to compare the effectiveness of the iterative methods in different points in the domain. In addition, a model problem of three-dimensional convection-diffusion equation is used to illustrated the application of our results.

关键词： Convergence AOR type iterative methods Skew-Hermitian splitting Hermitian splitting linear systems

Some Open Problems on Simultaneous Stabilization of linear systems

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Journal of systems Science & Complexity 2016年第2期29卷 289-299页

作者： LI Wang WANG Long YU Wensheng Shanghai Key Laboratory of Trustworthy Computing East China Normal UniversityShanghai 200062China. Intelligent Control Laboratory College of EngineeringPeking UniversityBeijing 100871China. College of Electronic Engineering Beijing University of Posts and TelecommunicationsBeijing 100876China.

Simultaneous stabilization of linear systems is a fundamental issue in the system and control theory, and is of theoretical and practical significance. In this paper, the authors review the recent research progress and the state-of-art results on simultaneous stabilization of single-input single-output linear time-invariant systems. Especially, the authors list the ever best results on the parameters involved in the well known ＂French Champagne Problem＂ and ＂Belgian Chocolate Problem＂ from the point of view of mathematical theoretical analysis and numerical calculation. And the authors observed that Boston claimed the lower bound of 5 can be enlarged to 0.976461 in 2012 is not accurate. The authors hope it will inspire further study on simultaneous stabilization of several linear systems.

关键词： Belgian Chocolate problem French Champagne Problem linear systems simultaneous stabilization.

Observer design for matrix second order linear systems with uncertain disturbance input-a parametric approach

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Journal of systems Engineering and Electronics 2006年第4期17卷 811-816,823页

作者： Wu Yunli Li Zhibin Duan Cruangren National Laboratory of Space Intelligent Control Technology Beijing Inst. of Control Engineering Beijing 100080P.R.China Centre of Control Theory and Guidance Technology Harbin Inst. of Technology Harbin 150001P.R.China

A simple parametric approach to design a full-order observer for matrix second-order linear systems with uncertain disturbance input in the matrixsecond-order framework is proposed. The basic idea is to minimize the H2 norm of the transfer function from disturbance to estimation error using the design degrees of freedom provided by a parametric approach in the observer design. Besides the design parameters, the eigenvalues of the closed-loop system are also optimized within desired regions on the left-half of the complex plane. Using the proposed approach, additional specifications can be easily achieved. A spring-mass system is using to show the effect of the proposed approaches.

关键词： linear systems uncertain disturbance input observers parametric approach optimization.

POSITIVE DEFINITE AND SEMI-DEFINITE SPLITTING METHODS FOR NON-HERMITIAN POSITIVE DEFINITE linear systems

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Journal of Computational Mathematics 2016年第3期34卷 300-316页

作者： Na Huang Changfeng Ma School of Mathematics and Computer Science Fujian Normal University Fuzhou 350117 China

In this paper, we further generalize the technique for constructing the normal （or pos- itive definite） and skew-Hermitian splitting iteration method for solving large sparse non- Hermitian positive definite system of linear equations. By introducing a new splitting, we establish a class of efficient iteration methods, called positive definite and semi-definite splitting （PPS） methods, and prove that the sequence produced by the PPS method con- verges unconditionally to the unique solution of the system. Moreover, we propose two kinds of typical practical choices of the PPS method and study the upper bound of the spectral radius of the iteration matrix. In addition, we show the optimal parameters such that the spectral radius achieves the minimum under certain conditions. Finally, some numerical examples are given to demonstrate the effectiveness of the considered methods.

关键词： linear systems Splitting method Non-Hermitian matrix Positive definitematrix Positive semi-definite matrix Convergence analysis.

Stochastic Gradient Descent for linear systems with Missing Data

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Numerical Mathematics(Theory,Methods and Applications) 2019年第1期12卷 1-20页

作者： Anna Ma Deanna Needell Claremont Graduate University ClaremontCA 91711USA University of California Los AngelesLos Angeles CA 90095USA

Traditional methods for solving linear systems have quickly become imprac-tical due to an increase in the size of available *** massive amounts of data is further complicated when the data is incomplete or has missing *** this work,we address the obstacles presented when working with large data and incom-plete data *** particular,we propose to adapt the Stochastic Gradient Descent method to address missing data in linear *** proposed algorithm,the Stochastic Gradient Descent for Missing Data method(mSGD),is introduced and theoretical convergence guarantees are *** addition,we include numerical experiments on simulated and real world data that demonstrate the usefulness of our method.

关键词： linear systems missing data iterative methods least squares problems

ANALYSIS OF A MECHANICAL SOLVER FOR linear systems OF EQUATIONS

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Journal of Computational Mathematics 2001年第1期19卷 9-14页

作者： Luis Vazquez (Dept. Matematica Aplicada, Facultad de Informatica, Universidad Complutense, 28040-Madrid, Spain ) Salvador Jimenez (Dept. Matematica y Fisica Aplicadas, Universidad Alfonso X E1 Sabio, Avda. Universidad 1, 28691-Villanueva de la Canada, Mad Universidad Complutense 西班牙 28040- Universidad Alfonso X E1 Sabio 西班牙 128691

In this contribution we analyse some fundamental features of an iterative method to solve systems of linear equations, following the approve introduced in a previous work[l]. Such questions range from optimal parameters and initial conditions to comparison with other methods. An interesting result is that a priori we can give an estimation of the number of iterations to get a given accuracy.

关键词： Iterative method linear systems Classical dynamics.

Mean square stability of discrete-time linear systems with random impulsive disturbances

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Science China(Information Sciences) 2023年第6期66卷 297-298页

作者： Jiamei LONG Yuqian GUO Weihua GUI School of Automation Central South University

Dear editor,In the real world,many dynamic processes may experience abrupt state [1] or parameter changes. Mathematically,these abrupt changes of state can be modeled as ideal impulsive effects. And also,the moments a... 详细信息

关键词： linear systems

A new stability analysis and controller design method for discrete-time linear systems with saturation nonlinearities

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控制理论与应用（英文版） 2011年第4期9卷 604-610页

作者： Wei GUAN Guanghong YANG School of Automation Shenyang Aerospace UniversityShenyang Liaoning 1 10136China CollegeofInformationScienceandEngineering NortheasternUniversityShenyangLiaoning110004China

The problems of stability analysis and controllers design for discrete-time linear systems subject to state saturation nonlinearities are investigated in this paper. Both full state saturation and partial state saturation are considered. It is well known to all that the controller design problem under state saturation is very difficult and complex to deal with. In order to overcome the difficulty, a new and tractable system is constructed, and it can be proved that the constructed system is with the same domain of attraction as the original system. With the aid of this property, to estimate the domain of attraction of the original system, an LMI-based method is presented for estimating the domain of attraction of the origin for the new constructed system under state saturation. Further, two optimization algorithms are developed for constructing dynamic output-feedback controllers and state feedback controllers, respectively, which guarantee that the domain of attraction of the origin for the closed-loop system is as ＇large＇ as possible. An example is provided to demonstrate the effectiveness of the new method.

关键词： State saturation linear systems LMIs