scholarly journals A Study on the Bayesian Estimation of Unknown Parameters of a Nonlinear Controlled System

1967 ◽  
Vol 3 (3) ◽  
pp. 197-202
Author(s):  
Yoshikazu SAWARAGI ◽  
Toshio YOSHIMURA
Keyword(s):  
Bayesian Estimation ◽  
Unknown Parameters ◽  
Controlled System ◽  
Nonlinear Controlled System

scholarly journals Bayesian estimation of the parameters of the bivariate generalized exponential distribution using accelerated life testing under censoring data

2015 ◽  
Vol 3 (2) ◽  
pp. 215
Author(s):  
Abd El-Maseh, M. P
Keyword(s):  
Bayesian Estimation ◽  
Accelerated Life Testing ◽  
Constant Stress ◽  
Type I ◽  
Life Testing ◽  
Unknown Parameters ◽  
Numerical Studies ◽  
Inverse Power Law ◽  
Accelerated Life ◽  
Power Law Function

<p>In this paper, the Bayesian estimation for the unknown parameters for the bivariate generalized exponential (BVGE) distribution under Bivariate censoring type-I samples with constant stress accelerated life testing (CSALT) are discussed. The scale parameter of the lifetime distribution at constant stress levels is assumed to be an inverse power law function of the stress level. The parameters are estimated by Bayesian approach using Markov Chain Monte Carlo (MCMC) method based on Gibbs sampling. Then, the numerical studies are introduced to illustrate the approach study using samples which have been generated from the BVGE distribution.</p>

scholarly journals Adaptive Control Design with Assigned Tracking Accuracy for a Class of Nonlinearly Parameterized Input-Delayed Systems

2019 ◽  
Vol 2019 ◽  
pp. 1-9
Author(s):  
Dajie Yao ◽  
Jing Li ◽  
Jian Wu
Keyword(s):  
Adaptive Control ◽  
Closed Loop ◽  
A Priori ◽  
Tracking Error ◽  
Input Delay ◽  
Tracking Accuracy ◽  
Unknown Parameters ◽  
Controlled System ◽  
Delayed Systems ◽  
Nonlinearly Parameterized

This paper addresses the adaptive control problem of a class of nonlinear systems with unknown parameters and input delay, and the tracking accuracy of the controlled system is assigned a priori. The Pade approximation method is introduced to deal with the problem from the input delay. By creating a group of nonnegative functions, an appropriate controller is designed with the backstepping technology. It is shown that under the obtained controller, the boundedness of all the closed-loop signals is guaranteed, and the tracking error especially can converge to the accuracy assigned a priori. Finally, a simulation example is given to verify the effectiveness of the proposed scheme.

scholarly journals An Optimal Control Problem Governed by Nonlinear First Order Dynamic Equation on Time Scales

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Jian-Ping Sun ◽  
Qiu-Yan Ren ◽  
Ya-Hong Zhao
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Time Scales ◽  
Dynamic Equation ◽  
Optimal Solution ◽  
Control Policy ◽  
Controlled System ◽  
First Order ◽  
Nonlinear Controlled System

In this paper, we are concerned with a class of optimal control problem governed by nonlinear first order dynamic equation on time scales. By imposing some suitable conditions on the related functions, for any given control policy, we first obtain the existence of a unique solution for the nonlinear controlled system. Then, we study the existence of an optimal solution for the optimal control problem.

Reservoir History Matching by Bayesian Estimation

1976 ◽  
Vol 16 (06) ◽  
pp. 337-350 ◽  
Author(s):  
G.R. Gavalas ◽  
P.C. Shah ◽  
J.H. Seinfeld
Keyword(s):  
Bayesian Estimation ◽  
History Matching ◽  
Statistical Uncertainty ◽  
Modeling Error ◽  
Unknown Parameters ◽  
Reservoir Properties ◽  
One Dimensional ◽  
Additional Information ◽  
Geological Information ◽  
Porosity And Permeability

Abstract The estimation of reservoir properties is inherently an underdetermined problem (one having a nonunique solution) because of the large number of unknown parameters relative to the available data. parameters relative to the available data. The common zonation approach to reducing the number of parameters introduces considerable modeling error by insisting that reservoir properties are uniform within each zone and by assigning the boundaries of these zones more or less arbitrarily. In this paper, Bayesian estimation theory is applied to history matching as an alternative to zonation. By using a priori statistical information on the unknown parameters, the problem becomes statistically better determined. Bayesian estimation and zonation are applied to the problem of porosity and permeability estimation in a one-dimensional, permeability estimation in a one-dimensional, one-phase reservoir. Introduction The estimation of parameters such as porosity and permeability in a reservoir model using well production and pressure data is commonly referred production and pressure data is commonly referred to as history matching. Although an inhomogeneous reservoir is in principle specified by an infinite number of parameters, a computational reservoir model can only contain a finite number. The most detailed description is obtained by allowing porosity and permeability to vary independently at each block of the spatial grid used in the finite-difference solution. While minimizing the modeling error, this approach entails a great deal of uncertainty because of the large number of unknowns compared with the limited data available. Thus, in a given problem, many different sets of property estimates problem, many different sets of property estimates may provide satisfactory and essentially indistinquishable data fits. Some of these parameter estimates can be grossly in error with respect to the actual properties, and as a result can lead to erroneous prediction of future reservoir behavior. To reduce the statistical uncertainty one must either decrease the number of unknowns or utilize additional information. A commonly used procedure for reducing the number of unknown parameters is zonation; the reservoir is divided into a small number of zones, in each of which the properties are treated as uniform. A modeling error is thus introduced through the assumption of uniform properties within each zone and through the more or less arbitrary assignment of the zone boundaries. As the number of zones is decreased, the error due to statistical uncertainty decreases while the modeling error increases. The total error passes through a minimum at some intermediate number of zones. The specification of this optimum level of description, which has been briefly considered in past work, will be treated in detail in a future report. An alternative to decreasing the statistical uncertainty by reducing the number of unknown parameters is the utilization of additional parameters is the utilization of additional information. This information need not be limited to measurements on the reservoir under study, but can be based on prior geological information about property variability in reservoirs of the same type. property variability in reservoirs of the same type. This paper examines this alternative method of reducing statistical uncertainty. The prior geological information is utilized by a formulation akin to classical Bayesian estimation. The Bayesian estimation is illustrated and is compared with the zonation approach for the case of a hypothetical, one-dimensional reservoir with variable porosity and permeability. The numerical simulations are used to investigate questions such as the optimum number of parameters in zonation and the effect of erroneous prior statistics in Bayesian estimation, and to compare the two methods. Considerable attention is also given to computational aspects such as convergence rate and computer time required by two of the most commonly used minimization algorithms, Marquardt's and the conjugate gradient. NATURE OF PRIOR GEOLOGICAL INFORMATION The application of probabilistic models in geology is the subject of a recent review. SPEJ P. 337

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