Observer for nonlinear systems with unknown input using mean value theorem and genetic algorithm

2018 ◽  
Vol 39 (6) ◽  
pp. 1904-1915
Author(s):  
Ramzi Ben Messaoud ◽  
Salah Hajji
Keyword(s):  
Genetic Algorithm ◽  
Nonlinear Systems ◽  
Mean Value ◽  
Mean Value Theorem ◽  
Unknown Input

Nonlinear unknown input observer using mean value theorem and genetic algorithm

2019 ◽  
Vol 10 (02) ◽  
pp. 1950001 ◽  
Author(s):  
Ramzi Ben Messaoud
Keyword(s):  
Genetic Algorithm ◽  
Secure Communication ◽  
Estimation Error ◽  
Mean Value ◽  
Stability Study ◽  
Observer Design ◽  
Theoretical Development ◽  
Mean Value Theorem ◽  
Unknown Input ◽  
Unknown Input Observer

In this note, we consider a new unknown input observer design for nonlinear systems. The main idea consists in determining the estimation error and mean value theorem parameters ([Formula: see text]) to introduce them into proposed observer structure. This process is designed on the basis of mean value theorem and genetic algorithm. The stability study relies on the use of a classical quadratic Lyapunov function. The observer’s gains are determined systematically. For the validation of theoretical development proposed in this paper, we consider two practical realizations that deals with the secure communication problem.

scholarly journals Real Time Stabilization of Lipschitz Nonlinear Systems with Nonlinear Output

2020 ◽  
Vol 53 (4) ◽  
pp. 493-498
Author(s):  
Assem Thabet ◽  
Ghazi Bel Haj Frej ◽  
Noussaiba Gasmi ◽  
Brahim Metoui
Keyword(s):  
Nonlinear Systems ◽  
Real Time ◽  
Nonlinear Function ◽  
Mean Value ◽  
Mean Value Theorem ◽  
Linear Matrix ◽  
Linear Parameter ◽  
Linear Parameter Varying ◽  
Lipschitz Nonlinear Systems ◽  
Parameter Varying

This brief discusses a simple stabilization strategy for a class of Lipschitz nonlinear systems based on the transformation of nonlinear function to Linear Parameter Varying system. Due to the introduction of the Differential Mean Value Theorem (DMVT), the dynamic and output nonlinear functions are transformed into Linear Parameter Varying (LPV) functions. This allows to increase the number of decision variables in the constraint to be resolved and, then, get less conservative and more general Linear Matrix Inequality (LMI) conditions. The established sufficient stability conditions are in the form of LMI with the introduction of a cost control to ensure closed-loop stability. Finally, Real Time Implementation (RTI) using a DSP device (ARDUINO UNO R3) to a typical robot is given to illustrate the performances of the proposed method with a comparison to some existing results.

scholarly journals Adaptive Differentiator-Based Predefined-Time Control for Nonlinear Systems Subject to Pure-Feedback Form and Unknown Disturbance

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Man Yang ◽  
Qiang Zhang ◽  
Ke Xu ◽  
Ming Chen
Keyword(s):  
Nonlinear Systems ◽  
Control Method ◽  
Tracking Error ◽  
Nonlinear Function ◽  
Original System ◽  
Mean Value ◽  
Mean Value Theorem ◽  
Rbf Neural Networks ◽  
Feedback Form ◽  
Output Tracking Control

In this article, by utilizing the predefined-time stability theory, the predefined-time output tracking control problem for perturbed uncertain nonlinear systems with pure-feedback structure is addressed. The nonaffine structure of the original system is simplified as an affine form via the property of the mean value theorem. Furthermore, the design difficulty from the uncertain nonlinear function is overcome by the excellent approximation performance of RBF neural networks (NNs). An adaptive predefined-time controller is designed by introducing the finite-time differentiator which is used to decrease the computational complexity problem appeared in the traditional backstepping control. It is proved that the proposed control method guarantees all signals in the closed-loop system remain bound and the tracking error converges to zero within the predefined time. Based on the controller designed in this paper, the expected results can be obtained in predefined time, which can be illustrated by the simulation results.

scholarly journals Robust nonlinear observer design for actuator fault detection in diesel engines

2013 ◽  
Vol 23 (3) ◽  
pp. 557-569 ◽  
Author(s):  
Boulaid Boulkroune ◽  
Issam Djemili ◽  
Abdel Aitouche ◽  
Vincent Cocquempot
Keyword(s):  
Nonlinear Systems ◽  
Fault Detection ◽  
Estimation Error ◽  
Nonlinear Observer ◽  
Disturbance Attenuation ◽  
Mean Value Theorem ◽  
Unknown Input ◽  
Actuator Fault ◽  
Unknown Input Observer ◽  
Varying Coefficients

Abstract This paper is concerned with actuator fault detection in nonlinear systems in the presence of disturbances. A nonlinear unknown input observer is designed and the output estimation error is used as a residual for fault detection. To deal with the problem of high Lipschitz constants, a modified mean-value theorem is used to express the nonlinear error dynamics as a convex combination of known matrices with time-varying coefficients. Moreover, the disturbance attenuation is performed using a modified H∞ criterion. A sufficient condition for the existence of an unknown input observer is obtained using a linear matrix inequality formula, and the observer gains are obtained by solving the corresponding set of inequalities. The advantages of the proposed method are that no a priori assumption on the unknown input is required and that it can be applied to a large class of nonlinear systems. Performances of the proposed approach are shown through the application to a diesel engine model.

scholarly journals Adaptive Neural Control of Nonaffine Nonlinear Systems without Differential Condition for Nonaffine Function

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Chaojiao Sun ◽  
Bo Jing ◽  
Zongcheng Liu
Keyword(s):  
Nonlinear Systems ◽  
Neural Control ◽  
Tracking Error ◽  
Nonlinear Function ◽  
Mean Value ◽  
Mean Value Theorem ◽  
Adaptive Neural Control ◽  
Control Gain ◽  
Control Scheme ◽  
Nonaffine Nonlinear Systems

An adaptive neural control scheme is proposed for nonaffine nonlinear system without using the implicit function theorem or mean value theorem. The differential conditions on nonaffine nonlinear functions are removed. The control-gain function is modeled with the nonaffine function probably being indifferentiable. Furthermore, only a semibounded condition for nonaffine nonlinear function is required in the proposed method, and the basic idea of invariant set theory is then constructively introduced to cope with the difficulty in the control design for nonaffine nonlinear systems. It is rigorously proved that all the closed-loop signals are bounded and the tracking error converges to a small residual set asymptotically. Finally, simulation examples are provided to demonstrate the effectiveness of the designed method.

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