scholarly journals Observer Design for One-Sided Lipschitz Nonlinear Systems Subject to Measurement Delays

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Sohaira Ahmad ◽  
Raafia Majeed ◽  
Keum-Shik Hong ◽  
Muhammad Rehan
Keyword(s):  
Nonlinear System ◽  
Nonlinear Systems ◽  
Time Lag ◽  
Time Derivative ◽  
Observer Design ◽  
Nonlinear Observer ◽  
Linear Matrix ◽  
Lipschitz Nonlinear Systems ◽  
System States ◽  
Lipschitz Systems

This paper presents a novel nonlinear observer-design approach to one-sided Lipschitz nonlinear systems in the presence of output delays. The crux of the approach is to overcome the practical consequences of time delays, encountered due to distant sensor position and time lag in measurement, for estimation of physical and engineering nonlinear system states. A Lyapunov-Krasovskii functional is employed, the time derivative of which is solved using Jensen’s inequality, one-sided Lipschitz condition, and quadratic inner-boundedness, and, accordingly, design conditions for delay-range-dependent nonlinear observer for delayed one-sided Lipschitz systems are derived. Further, novel solutions to the problems of delay-dependent observer synthesis of one-sided Lipschitz models and delay-range-dependent state estimation of linear and Lipschitz nonlinear systems are deduced from the present delay-range-dependent technique. An observer formulation methodology for retrieval of one-sided Lipschitz nonlinear-system states, which is robust againstL2norm-bounded perturbations, is devised. The resultant design conditions, in contrast to the conventional procedures, can be solved via less conservative linear matrix inequality- (LMI-) based routines that succeed by virtue of additional LMI variables, meaningful transformations, and cone complementary linearization algorithm. Numerical examples are worked out to illustrate the effectiveness of the proposed observer-synthesis approach for delayed one-sided Lipschitz systems.

LMI Enhanced Observer Design for Lipschitz Nonlinear Systems

2013 ◽  
Vol 756-759 ◽  
pp. 420-424
Author(s):  
Feng Qiao ◽  
Qing Ma ◽  
Feng Zhang ◽  
Hao Ming Zhao
Keyword(s):  
Nonlinear Systems ◽  
Observer Design ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Simulation Studies ◽  
Complex Issue ◽  
Lipschitz Nonlinear Systems ◽  
Satisfy Lipschitz Condition ◽  
The Relationship ◽  
Selection Of

Observer design for nonlinear systems has been an important and complex issue for decades. In this paper, considering a class of nonlinear systems which satisfy Lipschitz condition, a method for observer design is investigated based on Linear Matrix Inequality (LMI). This study focuses on the selection of gain matrices using LMI for two kinds of Lipschitz nonlinear systems, which are classified by the relationship between output and state. Simulation studies are made with Matlab/Simulink in this paper, and the simulation results verify the effectiveness of the proposed method.

Robust Observer Design for Lipschitz Nonlinear Systems With Parametric Uncertainty

2013 ◽  
Author(s):  
Yan Wang ◽  
David M. Bevly
Keyword(s):  
Nonlinear Systems ◽  
Vector Fields ◽  
Observer Design ◽  
Nonlinear Observer ◽  
Performance Criteria ◽  
Adaptation Algorithm ◽  
Algebraic Set ◽  
Observer Error ◽  
Robust Observer ◽  
Lipschitz Nonlinear Systems

This paper discusses optimal and robust observer design for the Lipschitz nonlinear systems. The stability analysis for the Lure problem is first reviewed. Then, a two-DOF nonlinear observer is proposed so that the observer error dynamic model can be transformed to an equivalent Lure system. In this framework, the difference of the nonlinear parts in the vector fields of the original system and observer is modeled as a nonlinear memoryless block that is covered by a multivariable sector condition or an equivalent semi-algebraic set defined by a quadratic polynomial inequality. Then, a sufficient condition for asymptotic stability of the observer error dynamics is formulated in terms of the feasibility of polynomial matrix inequalities (PMIs), which can be solved by Lasserre’s moment relaxation. Furthermore, various quadratic performance criteria, such as H2 and H∞, can be easily incorporated in this framework. Finally, a parameter adaptation algorithm is introduced to cope with the parameter uncertainty.

Observer Design for Lipschitz Nonlinear Systems with Output Uncertainty

2014 ◽  
Vol 533 ◽  
pp. 277-280
Author(s):  
Wei Zou ◽  
Yu Sheng Liu ◽  
Kai Liu
Keyword(s):  
Nonlinear Systems ◽  
Asymptotic Stability ◽  
Lyapunov Method ◽  
Observer Design ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Matrix Inequality ◽  
Output Uncertainty ◽  
Lipschitz Nonlinear Systems ◽  
Simulation Results

This paper presents an observer design for Lipschitz nonlinear systems with output uncertainty. By means of Lyapunov method as well as linear matrix inequality (LMI), the observer gain matrix is determined and a sufficient condition ensuring the asymptotic stability of the observer is proposed. Simulation results demonstrate the robustness of the proposed observer for output uncertainty.

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.

scholarly journals Robust Sensor Fault Reconstruction for Lipschitz Nonlinear Systems

2011 ◽  
Vol 2011 ◽  
pp. 1-17 ◽  
Author(s):  
M. J. Khosrowjerdi
Keyword(s):  
Observer Design ◽  
Nonlinear Observer ◽  
Disturbance Attenuation ◽  
Sensor Faults ◽  
Sensor Fault ◽  
Fault Reconstruction ◽  
Lipschitz Nonlinear Systems ◽  
Unknown Disturbances ◽  
Lipschitz Systems ◽  
Robust Nonlinear Observer

We extend existing theory on robust nonlinear observer design to the class of nonlinear Lipschitz systems where the systems are subject to sensor faults and disturbances. The designed observer is used for robust reconstruction of fault signals. Allowing bounded unknown disturbances to model system uncertainties, it is shown that by adjusting a design parameter we can trade off between fault reconstruction and disturbance attenuation. An LMI procedure solvable using commercially available softwares is presented. Two examples are presented to illustrate the application of the results.

Nonlinear observer based sliding mode control and oxygen fraction estimation for diesel engine

2017 ◽  
Vol 40 (7) ◽  
pp. 2227-2239 ◽  
Author(s):  
Haoping Wang ◽  
Qiankun Qu ◽  
Yang Tian
Keyword(s):  
Diesel Engine ◽  
Sliding Mode Control ◽  
Oxygen Concentration ◽  
Control Method ◽  
Sliding Mode ◽  
Observer Design ◽  
Nonlinear Observer ◽  
Linear Matrix ◽  
Model Based ◽  
Mode Control

In this paper, a nonlinear observer based sliding mode control (NOSMC) approach for air-path and a model-based observer for oxygen concentration in the diesel engine equipped with a variable geometry turbocharger and exhaust gas recirculation is introduced. We propose a less conservative observer design technique for Lipschitz nonlinear systems using Ricatti equations. The observer gains are obtained by solving the linear matrix inequality (LMI). Then a robust nonlinear control method, sliding mode control is applied for the states of intake and exhaust manifold pressure and compressor mass flow rate for the sake of the minimization of emissions. The proposed NOSMC controller is applied on a mean value model of turbocharged diesel engine. Besides this, a model-based observer is developed to estimate the oxygen concentration in the intake and exhaust manifolds owing to its significance in reducing emissions of diesel engines. The validation and efficiency of the proposed method are demonstrated by AMESim and Matlab/Simulink co-simulation results.

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.

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.

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