scholarly journals Computer Algorithms of a General Class of Time-Variant Nonlinear Systems and a Nonlinear Observer

2005 ◽  
Vol 41 (3) ◽  
pp. 210-215
Author(s):  
Kazuo KOMATSU ◽  
Hitoshi TAKATA
Keyword(s):  
Nonlinear Systems ◽  
General Class ◽  
Nonlinear Observer ◽  
Computer Algorithms

scholarly journals A Continuous-Discrete Finite Memory Observer Design for a Class of Nonlinear Systems: Application to Fault Diagnosis

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Tingting Zhang ◽  
Frédéric Kratz ◽  
Yunhui Hou ◽  
Vincent Idasiak
Keyword(s):  
Nonlinear Systems ◽  
Control Charts ◽  
Nonlinear Dynamical Systems ◽  
Approximation Error ◽  
Time Instant ◽  
Fault Isolation ◽  
Observer Design ◽  
Nonlinear Observer ◽  
Prediction Algorithm ◽  
Finite Memory

This paper aims to develop a continuous-discrete finite memory observer (CD-FMO) for a class of nonlinear dynamical systems modeled by ordinary differential equations (ODEs) with discrete measurements. The nonlinear systems under consideration are at least locally Lipschitz, which guarantees the existence and uniqueness of solution at each time instant. The proposed nonlinear observer uses a finite number of collected measurements to estimate the system state in the presence of measurement noise. Besides, a one-step prediction algorithm incorporated with an iterative-update scheme is performed to solve the integral problem caused by system nonlinearity, and an analysis of the numerical integration approximation error is given. The properties of estimation performance have been further proved in deterministic case and been analyzed by Monte Carlo simulation in stochastic cases. It is worth noting that the presented method has a finite-time convergence, while most nonlinear observers are usually asymptotically convergent. Another advantage of CD-FMO is that it has no initial value problem. For the application purpose, residuals are generated to implement fault detection cooperated with Cumulative Sum (CUSUM) control charts, while a bank of CD-FMOs is adopted to realize fault isolation for different sensor and actuator faults of the considered nonlinear robotic arm. The robustness and effectiveness of the proposed approach are illustrated via the simulation results.

A Distributed Nonlinear Observer Design Method for Output Estimation in Nonlinear Systems

2011 ◽  
Author(s):  
Javad Mohammadpour ◽  
Ali Hooshmand ◽  
Heidar Malki ◽  
Karolos Grigoriadis ◽  
Robert Provence
Keyword(s):  
Nonlinear Systems ◽  
Design Method ◽  
Observer Design ◽  
Nonlinear Observer

Robust dynamic sliding mode observer design for a class of nonlinear systems

2020 ◽  
pp. 014233122095220
Author(s):  
Mahnoosh Shajiee ◽  
Seyed Kamal Hosseini Sani ◽  
Mohammad Bagher Naghibi-Sistani ◽  
Saeed Shamaghdari
Keyword(s):  
Nonlinear Systems ◽  
Sliding Mode ◽  
Lipschitz Constant ◽  
Design Procedure ◽  
Sliding Mode Observer ◽  
Observer Design ◽  
Nonlinear Observer ◽  
Dynamical Structure ◽  
Additional Degree ◽  
The Stability

In this paper, a novel method for the design of robust nonlinear observer in the [Formula: see text] framework for Lipschitz nonlinear systems is proposed. For this purpose, a new dynamical structure is introduced that ensures the stability of observer error dynamics. Design innovation is the use of dynamic gain in the sliding mode observer. The additional degree of freedom provided by this dynamic formulation is exploited to deal with the nonlinear term. The performance of this stable [Formula: see text] observer is better than conventional static gain observers and the dynamic Luenberger observer. The compensator is designed in such a way that, while ensuring the stability of the closed-loop system, it prevents performance loss in the presence of the nonlinearities. By the proposed approach, the observer is robust to nonlinear uncertainties because of increasing the Lipschitz constant. Also, the design procedure in the presence of system and measurement noises is addressed. Finally, the simulation of our methodology is conducted on a nonlinear system to illustrate the advantage of this work in comparison with other observers.

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