A new methodology for an adaptive state observer design for a class of nonlinear systems with unknown parameters in unmeasured state dynamics

2016 ◽  
Vol 40 (4) ◽  
pp. 1297-1308 ◽  
Author(s):  
Nabil Oucief ◽  
Mohamed Tadjine ◽  
Salim Labiod
Keyword(s):  
Nonlinear Systems ◽  
Design Procedure ◽  
State Observer ◽  
Observer Design ◽  
Adaptive Observer ◽  
Linear Matrix ◽  
Unknown Parameters ◽  
Structural Requirement ◽  
Persistent Excitation ◽  
Adaptive State Observer

An adaptive state observer is an adaptive observer that does not require the persistent excitation condition to estimate the state. The usual structural requirement for designing this kind of observers is that the unknown parameters explicitly appear in the measured state dynamics. This paper deals with the problem of adaptive state observer synthesis for a class of nonlinear systems with unknown parameters in unmeasured state dynamics. The novelty of the proposed approach is that it requires neither a canonical form nor the approximation of some of the output’s time derivatives. Firstly, we establish a new matrix equality that characterizes the structure of almost all systems found in the very small literature dealing with this problem. Then, this equality is exploited in the construction of the adaptation law. This simplifies the design procedure and makes it very similar to the conventional adaptive state observer design procedure. The problem of finding the observer gains is expressed as a linear matrix inequalities optimization problem. Two examples are given to demonstrate the validity of the proposed scheme.

Robust H∞ gain neuro-adaptive observer design for nonlinear uncertain systems

2018 ◽  
Vol 41 (8) ◽  
pp. 2293-2309
Author(s):  
Krifa Abdelkader ◽  
Bouzrara Kais
Keyword(s):  
Nonlinear Approximation ◽  
The State ◽  
Observer Design ◽  
Adaptive Observer ◽  
Projection Algorithm ◽  
Linear Matrix ◽  
Positive Real ◽  
Unknown Parameters ◽  
Estimation Errors ◽  
Persistent Excitation

To guarantee convergent state estimates and exact approximations, it is highly desirable that observers can independently dominate the effects of unmodelled dynamics. Based on adaptive nonlinear approximation, this paper presents a robust H∞ gain neuro-adaptive observer (R H∞GNAO) design methodology for a large class of uncertain nonlinear systems in the presence of time-varying unknown parameters with bounded external disturbances on the state vector and on the output of the original system. The proposed R H∞GNAO incorporates radial basis function neural networks (RBFNNs) to approximate the unknown nonlinearities in the uncertain system. The weight dynamics of every RBFNN are adjusted online by using an adaptive projection algorithm. The asymptotic convergence of the state and parameter estimation errors is achieved by using Lyapunov cogitation under a well-defined persistent excitation condition, and without recourse to the strictly positive real condition. The repercussions of unknown disturbances are reduced by integrating an H∞ gain performance criterion into the proposed estimation approach. The condition imposed by this proposed observer approach, such that all estimated signals are uniformly ultimately bounded, is expressed in the form of the linear matrix inequality problem and warrants the demanded performances. To evaluate the performance of the proposed observer, various simulations are presented.

scholarly journals An adaptive observer design approach for a class of discrete-time nonlinear systems

2018 ◽  
Vol 28 (1) ◽  
pp. 55-67 ◽  
Author(s):  
Krishnan Srinivasarengan ◽  
José Ragot ◽  
Christophe Aubrun ◽  
Didier Maquin
Keyword(s):  
Parameter Estimation ◽  
Nonlinear Systems ◽  
Linear Systems ◽  
Discrete Time ◽  
Design Procedure ◽  
Observer Design ◽  
Joint Estimation ◽  
Adaptive Observer ◽  
Waste Water Treatment Plant ◽  
Joint State

AbstractWe consider the problem of joint estimation of states and some constant parameters for a class of nonlinear discrete-time systems. This class contains systems that could be transformed into a quasi-LPV (linear parameter varying) polytopic model in the Takagi-Sugeno (T-S) form. Such systems could have unmeasured premise variables, a case usually overlooked in the observer design literature. We assert that, for such systems in discrete-time, the current literature lacks design strategies for joint state and parameter estimation. To this end, we adapt the existing literature on continuous-time linear systems for joint state and time-varying parameter estimation. We first develop the discrete-time version of this result for linear systems. A Lyapunov approach is used to illustrate stability, and bounds for the estimation error are obtained via the bounded real lemma. We use this result to achieve our objective for a design procedure for a class of nonlinear systems with constant parameters. This results in less conservative conditions and a simplified design procedure. A basic waste water treatment plant simulation example is discussed to illustrate the design procedure.

scholarly journals Adaptive observer-based fault estimation for a class of Lipschitz nonlinear systems

2016 ◽  
Vol 26 (2) ◽  
pp. 245-259 ◽  
Author(s):  
Nabil Oucief ◽  
Mohamed Tadjine ◽  
Salim Labiod
Keyword(s):  
Nonlinear Systems ◽  
Transfer Functions ◽  
Matching Condition ◽  
Observer Design ◽  
Joint Estimation ◽  
Adaptive Observer ◽  
Fault Estimation ◽  
Linear Matrix ◽  
Lipschitz Nonlinear Systems ◽  
Observer Matching Condition

Abstract Fault input channels represent a major challenge for observer design for fault estimation. Most works in this field assume that faults enter in such a way that the transfer functions between these faults and a number of measured outputs are strictly positive real (SPR), that is, the observer matching condition is satisfied. This paper presents a systematic approach to adaptive observer design for joint estimation of the state and faults when the SPR requirement is not verified. The proposed method deals with a class of Lipschitz nonlinear systems subjected to piecewise constant multiplicative faults. The novelty of the proposed approach is that it uses a rank condition similar to the observer matching condition to construct the adaptation law used to obtain fault estimates. The problem of finding the adaptive observer matrices is formulated as a Linear Matrix Inequality (LMI) optimization problem. The proposed scheme is tested on the nonlinear model of a single link flexible joint robot system.

Nonlinear Adaptive Observer-Based Fault Diagnosis for Satellite Actuator

2012 ◽  
Vol 214 ◽  
pp. 851-855 ◽  
Author(s):  
Zhi Wang
Keyword(s):  
Observer Design ◽  
Adaptive Observer ◽  
Asymptotic Convergence ◽  
Sufficient Condition ◽  
Unknown Parameters ◽  
Adaptive Laws ◽  
Nonlinear Object ◽  
Adaptive State Observer ◽  
Simulation Results ◽  
Fault Mode

This paper studies the multi-structural fault mode of satellite actuators, and use numbers of unknown parameters as fault indicators. The problem of adaptive state observer design for nonlinear systems with unknown parameters is dealt with by applying Lypunov method. The nonlinear object is firstly linearized into Lipschitz system, and then by analyzing the sufficient condition for asymptotic convergence of the observer, the structure of observer and the adaptive laws for parameter estimation are given. Finally, the adaptive observer is employed to estimate the faults of satellite actuator. Numerical simulation results show that this method is effective and able to quickly detect faults.

A new robust observer design for nonlinear systems with application to fault diagnosis

2017 ◽  
Vol 40 (13) ◽  
pp. 3696-3708 ◽  
Author(s):  
Ammar Zemzemi ◽  
Mohamed Kamel ◽  
Ahmed Toumi ◽  
Mondher Farza
Keyword(s):  
Fault Diagnosis ◽  
Nonlinear Systems ◽  
Sliding Mode ◽  
Nonlinear Function ◽  
Design Procedure ◽  
Observer Design ◽  
Linear Matrix ◽  
Time Varying ◽  
System Nonlinearity ◽  
The Stability

This paper presents a robust fault diagnosis scheme for a class of uncertain nonlinear systems whose nonlinear function satisfies the Lipschitz condition with unmatched time-varying uncertainties, external disturbances and perturbed output. The design procedure combines the high robustness of the nonlinear unknown input observer with sliding-mode techniques in order to enhance the estimation qualities. The proposed design is derived and expressed as a linear matrix inequality optimization problem. Additionally, we have provided an approach to reduce conservatism in the derivation of the stability conditions. The effectiveness of this observer and the fault diagnosis scheme are shown by applying them to a single-link manipulator. Simulation results are presented to validate the proposed approach and show the robustness for the system nonlinearity and unmatched time-varying uncertainties.

Topology detection of a distribution network based on adaptive state observer

2021 ◽  
pp. 1-9
Author(s):  
Yong Xiao ◽  
Yonggang Zeng ◽  
Yun Zhao ◽  
Yuxin Lu ◽  
Weibin Lin
Keyword(s):  
Smart Grid ◽  
Distribution Network ◽  
Detection Algorithm ◽  
State Observer ◽  
Matlab Simulation ◽  
Unknown Parameters ◽  
State Observation ◽  
Observation Network ◽  
Topology Information ◽  
Adaptive State Observer

The traditional distribution network lacks real-time topology information, which makes the implementation of smart grid complicated. The smart grid needs to monitor and dispatch the grid to maintain the economic and safe operation of the system. In this paper, we propose a topology detection algorithm of the distribution network based on adaptive state observer. Based on the transient dynamic model of the distribution network, the line states of the distribution network are regarded as unknown parameters, a virtual adaptive state observation network is built, and the topology can be inferred by the changes of adaptive state parameters. Finally, the effectiveness of our algorithm is verified by the MATLAB simulation experiments.

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.

Adaptive observer design for a class of nonlinear systems. Application to speed sensorless induction motor

Automatica ◽  
2018 ◽  
Vol 90 ◽  
pp. 239-247 ◽  
Author(s):  
Mondher Farza ◽  
Mohammed M’Saad ◽  
Tomas Ménard ◽  
Ali Ltaief ◽  
Tarak Maatoug
Keyword(s):  
Nonlinear Systems ◽  
Induction Motor ◽  
Observer Design ◽  
Adaptive Observer ◽  
Speed Sensorless

Adaptive state observer for Lipschitz nonlinear systems

2013 ◽  
Vol 62 (4) ◽  
pp. 319-323 ◽  
Author(s):  
M. Ekramian ◽  
F. Sheikholeslam ◽  
S. Hosseinnia ◽  
M.J. Yazdanpanah
Keyword(s):  
Nonlinear Systems ◽  
State Observer ◽  
Lipschitz Nonlinear Systems ◽  
Adaptive State Observer
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