ON THE DIFFERENCE BETWEEN BOUNDED JACOBIAN AND LIPSCHITZ OBSERVERS FOR NONLINEAR ESTIMATION APPLICATIONS

2017 ◽  
Vol 41 (3) ◽  
pp. 395-415
Author(s):  
Gridsada Phanomchoeng ◽  
Rajesh Rajamani
Keyword(s):  
Convex Combination ◽  
Estimation Error ◽  
Lipschitz Constant ◽  
Longitudinal Velocity ◽  
Nonlinear Estimation ◽  
Velocity Estimation ◽  
Observer Design ◽  
Mean Value Theorem ◽  
Varying Coefficients ◽  
Time Varying Coefficients

This paper examines the performance of bounded Jacobian and Lipschitz observer design techniques for nonlinear estimation applications. The bounded Jacobian observer technique utilizes the mean value theorem to express the nonlinear estimation error dynamics as a convex combination of known matrices with time varying coefficients. The Lipschitz based observers are the most popular observer design technique used for nonlinear systems. But they are derived from more conservative Lipschitz conditions on the nonlinearity. Both observers are evaluated for longitudinal velocity estimation, vehicle roll angle estimation, and estimation in a polynomial nonlinear system with a large Lipschitz constant. The results show that the bounded Jacobian observer is the more appropriate observer for these problems.

scholarly journals Vehicle Velocity Estimation Fusion with Kinematic Integral and Empirical Correction on Multi-Timescales

Energies ◽  
2019 ◽  
Vol 12 (7) ◽  
pp. 1242
Author(s):  
Jiangyi Lv ◽  
Hongwen He ◽  
Wei Liu ◽  
Yong Chen ◽  
Fengchun Sun
Keyword(s):  
Autonomous Vehicles ◽  
Estimation Error ◽  
Longitudinal Velocity ◽  
Estimation Method ◽  
Velocity Estimation ◽  
Model Parameters ◽  
Lateral Velocity ◽  
Empirical Correction ◽  
Vehicle Velocity ◽  
Wide Range

Accurate and reliable vehicle velocity estimation is greatly motivated by the increasing demands of high-precision motion control for autonomous vehicles and the decreasing cost of the required multi-axis IMU sensors. A practical estimation method for the longitudinal and lateral velocities of electric vehicles is proposed. Two reliable driving empirical judgements about the velocities are extracted from the signals of the ordinary onboard vehicle sensors, which correct the integral errors of the corresponding kinematic equations on a long timescale. Meanwhile, the additive biases of the measured accelerations are estimated recursively by comparing the integral of the measured accelerations with the difference of the estimated velocities between the adjacent strong empirical correction instants, which further compensates the kinematic integral error on short timescale. The algorithm is verified by both the CarSim-Simulink co-simulation and the controller-in-the-loop test under the CarMaker-RoadBox environment. The results show that the velocities can be accurately and reliably estimated under a wide range of driving conditions without prior knowledge of the tire-model and other unavailable signals or frequently changeable model parameters. The relative estimation error of the longitudinal velocity and the absolute estimation error of the lateral velocity are kept within 2% and 0.5 km/h, respectively.

New Nonlinear Takagi–Sugeno Vehicle Model for State and Road Curvature Estimation via a Nonlinear PMI Observer

2014 ◽  
Vol 23 (2) ◽  
pp. 155-170
Author(s):  
Zedjiga Yacine ◽  
Dalil Ichalal ◽  
Naima Ait Oufroukh ◽  
Said Mammar ◽  
Said Djennoune
Keyword(s):  
Estimation Error ◽  
Longitudinal Velocity ◽  
Multiple Integral ◽  
Lyapunov Theory ◽  
Observer Design ◽  
Force Model ◽  
Vehicle Model ◽  
Lateral Dynamics ◽  
Bounded Error ◽  
Takagi Sugeno

AbstractThe present article deals with an observer design for nonlinear vehicle lateral dynamics. The contributions of the article concern the nonconsideration of any force model and the consideration that the longitudinal velocity is time varying, which is more realistic than the assumption that it is constant. The vehicle model is then represented by an exact Takagi–Sugeno (TS) model via the sector nonlinearity transformation. A proportional multiple integral (PMI) observer based on the TS model is designed to estimate simultaneously the state vector and the unknown input (lateral forces and road curvature). The convergence conditions of the estimation error are expressed under LMI formulation using the Lyapunov theory, which guaranties a bounded error. Simulations are carried out for comparison between the conventional PI observer, the enhanced PI observer, and the PMI observer. Finally, experimental results are provided to illustrate the performances of the proposed PMI observer.

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.

Observer Design for Non-Uniform Sampled Systems Using Gain-Scheduling

2014 ◽  
Author(s):  
Omid Bagherieh ◽  
Behrooz Shahsavari ◽  
Ehsan Keikha ◽  
Roberto Horowitz
Keyword(s):  
Kalman Filter ◽  
Hard Disk Drives ◽  
Gain Scheduling ◽  
Observer Design ◽  
Time Varying ◽  
Time Intervals ◽  
Varying Coefficients ◽  
Regular Time ◽  
Time Varying Coefficients ◽  
Sampled Systems

In non-uniform sampled systems, the measurements are arriving at irregular time intervals. However, the control is updated at regular time intervals. An observer is required to obtain the estimate of the states during the control update times. We evaluate two observer designs: A Kalman filter and a gain-scheduling observer. The Kalman filter has the optimal performance. However, it is computationally expensive. In contrast, a recent gain-scheduling synthesis technique [1] can be used to design a time varying observer, whose time varying coefficients are a function of the measured sampling time variations. This observer is suboptimal, but it has significantly less computational complexity as compared to the Kalman filter, which makes it feasible to implement. Simulations are conducted for a self servo writing process in hard disk drives, in order to evaluate performance of H2 gain-scheduling observer design.

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 The VIT Transform Approach to Discrete-Time Signals and Linear Time-Varying Systems

Eng ◽  
2021 ◽  
Vol 2 (1) ◽  
pp. 99-125
Author(s):  
Edward W. Kamen
Keyword(s):  
Discrete Time ◽  
Initial Conditions ◽  
Linear Time ◽  
Order Term ◽  
Initial Time ◽  
Time Varying ◽  
Varying Coefficients ◽  
Time Signals ◽  
Time Varying Systems ◽  
Time Varying Coefficients

A transform approach based on a variable initial time (VIT) formulation is developed for discrete-time signals and linear time-varying discrete-time systems or digital filters. The VIT transform is a formal power series in z−1, which converts functions given by linear time-varying difference equations into left polynomial fractions with variable coefficients, and with initial conditions incorporated into the framework. It is shown that the transform satisfies a number of properties that are analogous to those of the ordinary z-transform, and that it is possible to do scaling of z−i by time functions, which results in left-fraction forms for the transform of a large class of functions including sinusoids with general time-varying amplitudes and frequencies. Using the extended right Euclidean algorithm in a skew polynomial ring with time-varying coefficients, it is shown that a sum of left polynomial fractions can be written as a single fraction, which results in linear time-varying recursions for the inverse transform of the combined fraction. The extraction of a first-order term from a given polynomial fraction is carried out in terms of the evaluation of zi at time functions. In the application to linear time-varying systems, it is proved that the VIT transform of the system output is equal to the product of the VIT transform of the input and the VIT transform of the unit-pulse response function. For systems given by a time-varying moving average or an autoregressive model, the transform framework is used to determine the steady-state output response resulting from various signal inputs such as the step and cosine functions.

scholarly journals Estimating latent group structure in time-varying coefficient panel data models

2019 ◽  
Author(s):  
Jia Chen
Keyword(s):  
Panel Data ◽  
Data Models ◽  
Panel Data Models ◽  
Time Varying ◽  
Clustering Method ◽  
Varying Coefficient ◽  
Varying Coefficients ◽  
Time Varying Coefficients ◽  
Latent Group ◽  
Group Structures

Summary This paper studies the estimation of latent group structures in heterogeneous time-varying coefficient panel data models. While allowing the coefficient functions to vary over cross-sections provides a good way to model cross-sectional heterogeneity, it reduces the degree of freedom and leads to poor estimation accuracy when the time-series length is short. On the other hand, in a lot of empirical studies, it is not uncommon to find that heterogeneous coefficients exhibit group structures where coefficients belonging to the same group are similar or identical. This paper aims to provide an easy and straightforward approach for estimating the underlying latent groups. This approach is based on the hierarchical agglomerative clustering (HAC) of kernel estimates of the heterogeneous time-varying coefficients when the number of groups is known. We establish the consistency of this clustering method and also propose a generalised information criterion for estimating the number of groups when it is unknown. Simulation studies are carried out to examine the finite-sample properties of the proposed clustering method as well as the post-clustering estimation of the group-specific time-varying coefficients. The simulation results show that our methods give comparable performance to the penalised-sieve-estimation-based classifier-LASSO approach by Su et al. (2018), but are computationally easier. An application to a panel study of economic growth is also provided.

Modeling and Dynamic Analysis of a Slider-Crank Mechanism With Flexible Coupler and Joint

1991 ◽  
Author(s):  
Junghsen Lieh ◽  
Imtiaz Haque
Keyword(s):  
Dynamic Analysis ◽  
Virtual Work ◽  
Equations Of Motion ◽  
Joint Stiffness ◽  
Mechanism Model ◽  
Double Frequency ◽  
Varying Coefficients ◽  
Matrix Expansion ◽  
Time Varying Coefficients ◽  
Crank Mechanism

Abstract Modeling and dynamic analysis of a slider-crank mechanism with flexible joint and coupler is presented. The equations of motion of the mechanism model are formulated using a virtual work multibody formalism and cast in terms of a minimum set of generalized coordinates through a Jacobian matrix expansion. Numerical results show the influence of time-varying coefficients on the mechanism dynamic behavior due to a repeated task. The results illustrate that the joint motion and coupler deformation are highly coupled. The joint response is dominated by double frequency of input, however, the coupler deformation is influenced by the same frequency as that of excitation. Increase in joint stiffness tends to decrease the variations in coupler deformation.

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