Using Persistent Excitation with Fixed Energy to Stabilize Adaptive Controllers and Obtain Hard Bounds for the Parameter Estimation Error

1993 ◽  
Author(s):  
Miloje S. Radenkovic ◽  
B. Erik Ydstie
Keyword(s):  
Parameter Estimation ◽  
Estimation Error ◽  
Adaptive Controllers ◽  
Persistent Excitation ◽  
Fixed Energy

scholarly journals Online Adaptive Parameter Estimation for Quadrotors

Algorithms ◽  
2018 ◽  
Vol 11 (11) ◽  
pp. 167 ◽  
Author(s):  
Jun Zhao ◽  
Xian Wang ◽  
Guanbin Gao ◽  
Jing Na ◽  
Hongping Liu ◽  
...  
Keyword(s):  
Parameter Estimation ◽  
Exponential Convergence ◽  
Estimation Error ◽  
Persistent Excitation ◽  
System Parameters ◽  
Adaptive Parameter ◽  
Adaptive Laws ◽  
Accuracy Parameter ◽  
The Stability ◽  
Quadrotor System

The stability and robustness of quadrotors are always influenced by unknown or immeasurable system parameters. This paper proposes a novel adaptive parameter estimation technology to obtain high-accuracy parameter estimation for quadrotors. A typical mathematical model of quadrotors is first obtained, which can be used for parameter estimation. Then, an expression of the parameter estimation error is derived by introducing a set of auxiliary filtered variables. Moreover, an augmented matrix is constructed based on the obtained auxiliary filtered variables, which is then used to design new adaptive laws to achieve exponential convergence under the standard persistent excitation (PE) condition. Finally, a simulation and an experimental verification for a typical quadrotor system are shown to illustrate the effectiveness of the proposed method.

Robust adaptive control for vehicle active suspension systems with uncertain dynamics

2016 ◽  
Vol 40 (4) ◽  
pp. 1237-1249 ◽  
Author(s):  
Yingbo Huang ◽  
Jing Na ◽  
Xing Wu ◽  
Guan-Bin Gao ◽  
Yu Guo
Keyword(s):  
Parameter Estimation ◽  
Adaptive Control ◽  
Estimation Error ◽  
Simulation Software ◽  
Robust Adaptive Control ◽  
Vehicle Body ◽  
Uncertain Dynamics ◽  
Adaptive Law ◽  
Mass Moment ◽  
Robust Adaptive

This paper proposes a new robust adaptive law for adaptive control of vehicle active suspensions with unknown dynamics (e.g. non-linear springs and piece-wise dampers), where precise estimation of essential vehicle parameters (e.g. mass of vehicle body, mass moment of inertia for the pitch motions) may be achieved. This adaptive law is designed by introducing a novel leakage term with the parameter estimation error, such that exponential convergence of both the tracking error and parameter estimation error may be proved simultaneously. Appropriate comparisons with several traditional adaptive laws (e.g. gradient and σ-modification method) concerning the convergence and robustness are presented. The mitigation of the vertical and pitch displacements can be achieved with the proposed control to improve the ride comfort. The suspension space limitation and the tyre road holding are also studied. A dynamic simulator consisting of commercial vehicle simulation software Carsim® and Matlab® is built to validate the efficacy of the proposed control scheme and to illustrate the improved estimation performance with the new adaptive law.

Abstract: Option Valuation Models–Some Implications of Parameter Estimation

1977 ◽  
Vol 12 (4) ◽  
pp. 667-667
Author(s):  
P. P. Boyle ◽  
A. L. Ananthanarayan
Keyword(s):  
Parameter Estimation ◽  
Option Pricing ◽  
Stock Prices ◽  
Unbiased Estimate ◽  
Estimation Error ◽  
Option Price ◽  
Nonlinear Function ◽  
Option Valuation ◽  
Black Scholes ◽  
Parameter Values

The Black-Scholes option pricing formula assumes that the variance of the return on the underlying stock is known with certainty. In practice an estimate of the variance, based on a sample of historical stock prices, is used. The estimation error in the variance induces error in the option price. Since the option price is a nonlinear function of the variance, an unbiased estimate of the variance does not produce an unbiased estimate of the option price. For reasonable parameter values, it is shown that the magnitude of the bias is not large.

Parameter Estimation of Linear Sensorimotor Synchronization Models: Phase Correction, Period Correction, and Ensemble Synchronization

2015 ◽  
Vol 3 (1-2) ◽  
pp. 52-87 ◽  
Author(s):  
Nori Jacoby ◽  
Naftali Tishby ◽  
Bruno H. Repp ◽  
Merav Ahissar ◽  
Peter E. Keller
Keyword(s):  
Experimental Data ◽  
Parameter Estimation ◽  
Linear Models ◽  
Estimation Error ◽  
Phase Correction ◽  
Sensorimotor Synchronization ◽  
Estimation Methods ◽  
Single Subject ◽  
Novel Method ◽  
Parameter Estimation Methods

Linear models have been used in several contexts to study the mechanisms that underpin sensorimotor synchronization. Given that their parameters are often linked to psychological processes such as phase correction and period correction, the fit of the parameters to experimental data is an important practical question. We present a unified method for parameter estimation of linear sensorimotor synchronization models that extends available techniques and enhances their usability. This method enables reliable and efficient analysis of experimental data for single subject and multi-person synchronization. In a previous paper (Jacoby et al., 2015), we showed how to significantly reduce the estimation error and eliminate the bias of parameter estimation methods by adding a simple and empirically justified constraint on the parameter space. By applying this constraint in conjunction with the tools of matrix algebra, we here develop a novel method for estimating the parameters of most linear models described in the literature. Through extensive simulations, we demonstrate that our method reliably and efficiently recovers the parameters of two influential linear models: Vorberg and Wing (1996), and Schulze et al. (2005), together with their multi-person generalization to ensemble synchronization. We discuss how our method can be applied to include the study of individual differences in sensorimotor synchronization ability, for example, in clinical populations and ensemble musicians.

scholarly journals Least-Squares Parameter Estimation Algorithm for a Class of Input Nonlinear Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Weili Xiong ◽  
Wei Fan ◽  
Rui Ding
Keyword(s):  
Parameter Estimation ◽  
Nonlinear Systems ◽  
Least Squares ◽  
Moving Average ◽  
Estimation Algorithm ◽  
Autoregressive Moving Average ◽  
Parameter Estimates ◽  
Persistent Excitation ◽  
Estimation Algorithms ◽  
Parameter Estimation Algorithm

This paper studies least-squares parameter estimation algorithms for input nonlinear systems, including the input nonlinear controlled autoregressive (IN-CAR) model and the input nonlinear controlled autoregressive autoregressive moving average (IN-CARARMA) model. The basic idea is to obtain linear-in-parameters models by overparameterizing such nonlinear systems and to use the least-squares algorithm to estimate the unknown parameter vectors. It is proved that the parameter estimates consistently converge to their true values under the persistent excitation condition. A simulation example is provided.

Lower Bound on the Accuracy of Parameter Estimation Methods for Linear Sensorimotor Synchronization Models

2015 ◽  
Vol 3 (1-2) ◽  
pp. 32-51 ◽  
Author(s):  
Nori Jacoby ◽  
Peter E. Keller ◽  
Bruno H. Repp ◽  
Merav Ahissar ◽  
Naftali Tishby
Keyword(s):  
Parameter Estimation ◽  
Lower Bound ◽  
Computational Models ◽  
Linear Models ◽  
Estimation Error ◽  
Explanatory Power ◽  
Estimation Method ◽  
Sensorimotor Synchronization ◽  
Estimation Methods ◽  
Unbiased Estimation

The mechanisms that support sensorimotor synchronization — that is, the temporal coordination of movement with an external rhythm — are often investigated using linear computational models. The main method used for estimating the parameters of this type of model was established in the seminal work of Vorberg and Schulze (2002), and is based on fitting the model to the observed auto-covariance function of asynchronies between movements and pacing events. Vorberg and Schulze also identified the problem of parameter interdependence, namely, that different sets of parameters might yield almost identical fits, and therefore the estimation method cannot determine the parameters uniquely. This problem results in a large estimation error and bias, thereby limiting the explanatory power of existing linear models of sensorimotor synchronization. We present a mathematical analysis of the parameter interdependence problem. By applying the Cramér–Rao lower bound, a general lower bound limiting the accuracy of any parameter estimation procedure, we prove that the mathematical structure of the linear models used in the literature determines that this problem cannot be resolved by any unbiased estimation method without adopting further assumptions. We then show that adding a simple and empirically justified constraint on the parameter space — assuming a relationship between the variances of the noise terms in the model — resolves the problem. In a follow-up paper in this volume, we present a novel estimation technique that uses this constraint in conjunction with matrix algebra to reliably estimate the parameters of almost all linear models used in the literature.

scholarly journals SNP genotyping and parameter estimation in polyploids using low-coverage sequencing data

2017 ◽  
Author(s):  
Paul D. Blischak ◽  
Laura S. Kubatko ◽  
Andrea D. Wolfe
Keyword(s):  
Parameter Estimation ◽  
High Throughput Sequencing ◽  
Estimation Error ◽  
Parameter Estimates ◽  
Data Sets ◽  
Mixed Mating ◽  
Sequencing Data ◽  
Ploidy Levels ◽  
Sequencing Coverage ◽  
High Throughput Sequencing Data

AbstractMotivation:Genotyping and parameter estimation using high throughput sequencing data are everyday tasks for population geneticists, but methods developed for diploids are typically not applicable to polyploid taxa. This is due to their duplicated chromosomes, as well as the complex patterns of allelic exchange that often accompany whole genome duplication (WGD) events. For WGDs within a single lineage (auto polyploids), inbreeding can result from mixed mating and/or double reduction. For WGDs that involve hybridization (allopolyploids), alleles are typically inherited through independently segregating subgenomes.Results:We present two new models for estimating genotypes and population genetic parameters from genotype likelihoods for auto- and allopolyploids. We then use simulations to compare these models to existing approaches at varying depths of sequencing coverage and ploidy levels. These simulations show that our models typically have lower levels of estimation error for genotype and parameter estimates, especially when sequencing coverage is low. Finally, we also apply these models to two empirical data sets from the literature. Overall, we show that the use of genotype likelihoods to model non-standard inheritance patterns is a promising approach for conducting population genomic inferences in polyploids.Availability:A C++ program, EBG, is provided to perform inference using the models we describe. It is available under the GNU GPLv3 on GitHub:https://github.com/pblischak/polyploid-genotyping.Contact: [email protected].

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