scholarly journals Unknown Input Observer Design for Fuzzy Bilinear System: An LMI Approach

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
D. Saoudi ◽  
M. Chadli ◽  
C. Mechmeche ◽  
N. Benhadj Braiek
Keyword(s):  
Nonlinear System ◽  
Fuzzy Model ◽  
Bilinear System ◽  
Observer Design ◽  
Fault Detection And Isolation ◽  
Linear Matrix ◽  
Unknown Input ◽  
Unknown Inputs ◽  
Bilinear Models ◽  
Bilinear Observer

A new method to design a fuzzy bilinear observer (FBO) with unknown inputs is developed for a class of nonlinear systems. The nonlinear system is modeled as a fuzzy bilinear model (FBM). This kind of T-S fuzzy model is especially suitable for a nonlinear system with a bilinear term. The proposed fuzzy bilinear observer subject to unknown inputs is developed to ensure the asymptotic convergence of the error dynamic using the Lyapunov method. The proposed design conditions are given in linear matrix inequality (LMI) formulation. The paper studies also the problem of fault detection and isolation. An unknown input fuzzy bilinear fault diagnosis observer design is proposed. This work is given for both continuous and discrete cases of fuzzy bilinear models. Illustrative examples are chosen to provide the effectiveness of the given methodology.

Robust Unknown Input Observer for Nonlinear Systems and Its Application to Fault Detection and Isolation

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
S. Mondal ◽  
G. Chakraborty ◽  
K. Bhattacharyya
Keyword(s):  
Fault Diagnosis ◽  
Nonlinear System ◽  
Fault Detection ◽  
Nonlinear Function ◽  
Fault Detection And Isolation ◽  
Linear Matrix ◽  
Unknown Input ◽  
Matrix Inequality ◽  
Unknown Input Observer ◽  
Linear Matrix Inequality Approach

A robust unknown input observer for a nonlinear system whose nonlinear function satisfies the Lipschitz condition is designed based on linear matrix inequality approach. Both noise and uncertainties are taken into account in deriving the observer. A component fault detection and isolation scheme based on these observers is proposed. The effectiveness of the observer and the fault diagnosis scheme is shown by applying them for component fault diagnosis of an electrohydraulic actuator.

Reduced-Order Observer Design for Discrete-Time Descriptor Systems With Unknown Inputs: An Linear Matrix Inequality Approach

2015 ◽  
Vol 137 (8) ◽  
Author(s):  
Shenghui Guo ◽  
Fanglai Zhu
Keyword(s):  
Linear Matrix Inequality ◽  
Discrete Time ◽  
Observer Design ◽  
Descriptor Systems ◽  
Linear Matrix ◽  
Unknown Input ◽  
Matrix Inequality ◽  
Reduced Order ◽  
Unknown Inputs ◽  
Reduced Order Observer

Reduced-order observer design methods for both linear and nonlinear discrete-time descriptor systems based on the linear matrix inequality (LMI) approach are investigated. We conclude that the conditions under which a full-order observer exists can also guarantee the existence of a reduced-order observer. By choosing a special reduced-order observer gain matrix, a reduced-order unknown input observer is proposed for linear system with unknown inputs, and then an unknown input reconstruction is provided for some special cases. We also extend above results to the cases of nonlinear systems. Finally, three numerical comparative simulation examples are given to illustrate the effectiveness and merits of proposed methods.

scholarly journals Decentralized Polynomial Observer Design for Discrete-Time Large-Scale Polynomial T-S Fuzzy System

2019 ◽  
Vol 2019 ◽  
pp. 1-12
Author(s):  
Seung-Hun Han ◽  
Van-Phong Vu ◽  
Manh-Son Tran
Keyword(s):  
Nonlinear System ◽  
Discrete Time ◽  
Fuzzy System ◽  
Large Scale ◽  
Observer Design ◽  
Unknown Input ◽  
New Approach ◽  
Unknown Inputs ◽  
Input Method ◽  
Takagi Sugeno

In this paper, a new approach for synthesizing a decentralized observer is proposed to estimate the unmeasurable states of a discrete-time large-scale nonlinear system. The large-scale nonlinear system in this study is modeled in terms of a set of discrete-time polynomial Takagi-Sugeno (T-S) fuzzy subsystems and interconnection terms. This modeling method will assist to reduce significantly the number of fuzzy rules. The interconnection terms are considered as the unknown inputs; then, the unknown input method is employed to design observer for this system. It should be emphasized that the interconnection parts in this paper are arbitrary and their effects are eliminated completely. On the basis of the Lyapunov methodology and SOS (Sum of Square) technique, the conditions for observer design expressed under the framework of SOS are derived in the main theorems. Finally, an illustrative example is presented to show the effectiveness and merit of the proposed method.

Unknown input fractional-order functional observer design for one-side Lipschitz time-delay fractional-order systems

2019 ◽  
Vol 41 (15) ◽  
pp. 4311-4321 ◽  
Author(s):  
Mai Viet Thuan ◽  
Dinh Cong Huong ◽  
Nguyen Huu Sau ◽  
Quan Thai Ha
Keyword(s):  
Time Delay ◽  
Nonlinear Systems ◽  
Fractional Order ◽  
Sufficient Conditions ◽  
Quadratic Function ◽  
Observer Design ◽  
Linear Matrix ◽  
Unknown Input ◽  
Functional Observer ◽  
The One

This paper addresses the problem of unknown input fractional-order functional state observer design for a class of fractional-order time-delay nonlinear systems. The nonlinearities consist of two parts where one part is assumed to satisfy both the one-sided Lipschitz condition and the quadratically inner-bounded condition and the other is not necessary to be Lipschitz and can be regarded as an unknown input, making the wider class of considered nonlinear systems. By taking the advantages of recent results on Caputo fractional derivative of a quadratic function, we derive new sufficient conditions with the form of linear matrix inequalities (LMIs) to guarantee the asymptotic stability of the systems. Four examples are also provided to show the effectiveness and applicability of the proposed method.

Fuzzy Observer Design for a Class of Uncertain Nonlinear System

2015 ◽  
Vol 740 ◽  
pp. 257-260
Author(s):  
Xian Jia Feng ◽  
Shu Li Guo ◽  
Li Na Han
Keyword(s):  
Nonlinear System ◽  
Magnetic Levitation ◽  
Fuzzy Model ◽  
Observer Design ◽  
Uncertain Nonlinear System ◽  
Adaptive Law ◽  
Levitation System ◽  
Magnetic Levitation System ◽  
Takagi Sugeno ◽  
Fuzzy State

In this paper, a fuzzy state observer with an appropriate adaptive law is developed for a class of uncertain nonlinear system. The uncertain nonlinear system is represented by Takagi-Sugeno (T-S) fuzzy model, and the adaptive law is derived based on Lyapunov synthesis approach. It is shown that under appropriate assumptions, the state error between plant system state and desired linear model state converges to zero as time increases. The results of numerical simulation and the experiment on the magnetic levitation system show the effectiveness of this approach.

Unknown Input Fault Detection and Isolation Observer Design for Neutral Systems

2016 ◽  
Vol 18 (5) ◽  
pp. 1825-1835 ◽  
Author(s):  
Aicha Elhsoumi ◽  
Saloua Bel Hadj Ali ◽  
Rafika El Harabi ◽  
Mohamed Naceur Abdelkrim
Keyword(s):  
Fault Detection ◽  
Observer Design ◽  
Fault Detection And Isolation ◽  
Unknown Input ◽  
Neutral Systems

scholarly journals Stable Fault Tolerant Controller Design for Takagi–Sugeno Fuzzy Model-Based Control Systems via Linear Matrix Inequalities: Three Conical Tank Case Study

Energies ◽  
2019 ◽  
Vol 12 (11) ◽  
pp. 2221 ◽  
Author(s):  
Himanshukumar R. Patel ◽  
Vipul A. Shah
Keyword(s):  
Nonlinear System ◽  
Nonlinear Systems ◽  
Control Systems ◽  
Linear Models ◽  
Fault Tolerant ◽  
Fuzzy Model ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Fuzzy Models ◽  
Takagi Sugeno

This paper deals with a methodical design approach of fault-tolerant controller that gives assurance for the the stabilization and acceptable control performance of the nonlinear systems which can be described by Takagi–Sugeno (T–S) fuzzy models. Takagi–Sugeno fuzzy model gives a unique edge that allows us to apply the traditional linear system theory for the investigation and blend of nonlinear systems by linear models in a different state space region. The overall fuzzy model of the nonlinear system is obtained by fuzzy combination of the all linear models. After that, based on this linear model, we employ parallel distributed compensation for designing linear controllers for each linear model. Also this paper reports of the T–S fuzzy system with less conservative stabilization condition which gives decent performance. However, the controller synthesis for nonlinear systems described by the T–S fuzzy model is a complicated task, which can be reduced to convex problems linking with linear matrix inequalities (LMIs). Further sufficient conservative stabilization conditions are represented by a set of LMIs for the Takagi–Sugeno fuzzy control systems, which can be solved by using MATLAB software. Two-rule T–S fuzzy model is used to describe the nonlinear system and this system demonstrated with proposed fault-tolerant control scheme. The proposed fault-tolerant controller implemented and validated on three interconnected conical tank system with two constraints in terms of faults, one issed to build the actuator and sond is system component (leak) respectively. The MATLAB Simulink platform with linear fuzzy models and an LMI Toolbox was used to solve the LMIs and determine the controller gains subject to the proposed design approach.

scholarly journals Unknown Input Observer Design for a Class of Linear Descriptor Systems

2021 ◽  
Vol 229 ◽  
pp. 01019
Author(s):  
Karim Bouassem ◽  
Abdellatif El Assoudi ◽  
Jalal Soulami ◽  
El Hassane El Yaagoubi
Keyword(s):  
Estimation Error ◽  
Lyapunov Theory ◽  
Observer Design ◽  
Descriptor Systems ◽  
Linear Matrix ◽  
Simultaneous Estimation ◽  
Unknown Inputs ◽  
Pilot Model ◽  
The Stability ◽  
Differential Part

This paper addresses the problem of unknown inputs observer (UIO) design for a class of linear descriptor systems. The unknown inputs affect both state and output of the system. The basic idea of the proposed approach is based on the separation between dynamic and static relations in the descriptor model. Firstly, the method used to separate the differential part from the algebraic part is developed. Secondly, an observer design permitting the simultaneous estimation of the system state and the unknown inputs is proposed. The developed approach for the observer design is based on the synthesis of an augmented model which regroups the differential variables and unknown inputs. The exponential stability of the estimation error is studied using the Lyapunov theory and the stability condition is given in term of linear matrix inequality (LMI). Finally, to illustrate the efficiency of the proposed methodology, a heat exchanger pilot model is considered.

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