OPTIMAL CONTROL OF CHAOTIC SYSTEMS

2001 ◽  
Vol 11 (07) ◽  
pp. 2007-2018 ◽  
Author(s):  
PAWEŁ GÓRA ◽  
ABRAHAM BOYARSKY
Keyword(s):  
Optimal Control ◽  
Probability Density Function ◽  
Probability Measure ◽  
Probability Density ◽  
Density Function ◽  
Chaotic Systems ◽  
Invariant Probability Measure ◽  
Optimization Methods ◽  
Point Transformation

The problem of controlling a chaotic system is treated from a long term statistical basis. Unlike the OGY targeting method that exploits individual unstable orbits, this approach is concerned with targeting the density function of an invariant probability measure. Given a point transformation T, possessing a density function f, we choose [Formula: see text], a different probability density function, to be the target. Using optimization methods, we construct a point transformation [Formula: see text], close to T, whose invariant probability density function is [Formula: see text], or close to [Formula: see text].

scholarly journals An Application of New Method to Obtain Probability Density Function of Solution of Stochastic Differential Equations

2020 ◽  
Vol 5 (1) ◽  
pp. 337-348 ◽  
Author(s):  
Nihal İnce ◽  
Aladdin Shamilov
Keyword(s):  
Probability Density Function ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Probability Density ◽  
Density Function ◽  
Model Fitting ◽  
Random Variable ◽  
Optimization Methods ◽  
Fixed Time ◽  
New Method

AbstractIn this study, a new method to obtain approximate probability density function (pdf) of random variable of solution of stochastic differential equations (SDEs) by using generalized entropy optimization methods (GEOM) is developed. By starting given statistical data and Euler–Maruyama (EM) method approximating SDE are constructed several trajectories of SDEs. The constructed trajectories allow to obtain random variable according to the fixed time. An application of the newly developed method includes SDE model fitting on weekly closing prices of Honda Motor Company stock data between 02 July 2018 and 25 March 2019.

Methods of Computing the Probability of Failure Under Extreme Values of Bending Moment

1972 ◽  
Vol 16 (02) ◽  
pp. 113-123
Author(s):  
Alaa Mansour
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Extreme Values ◽  
Bending Moment ◽  
Random Variable ◽  
Probability Of Failure ◽  
Short Term ◽  
Term Analysis

Methods for predicting the probability of failure under extreme values of bending moment (primary loading only) are developed. In order to obtain an accurate estimate of the extreme values of the bending moment, order statistics are used. The wave bending moment amplitude treated as a random variable is considered to follow, in general, Weibull distribution so that the results could be used for short-term as well as long-term analysis. The probability density function of the extreme values of the wave bending moment is obtained and an estimate is made of the most probable value (that is, the mode) and other relevant statistics. The probability of exceeding a given value of wave bending moment in "n" records and during the operational lifetime of the ship is derived. Using this information, the probability of failure is obtained on the basis of an assumed normal probability density function of the resistive strength and deterministic still-water bending moment. Charts showing the relation of the parameters in a nondimensional form are presented. Examples of the use of the charts for long-term and short-term analysis for predicting extreme values of wave bending moment and the corresponding probability of failure are given.

scholarly journals INVESTIGATING THE BEACH PREDICTIONS OF A NEW LONG-TERM NUMERICAL MORPHOLOGICAL MODEL – A CARIBBEAN CONTEXT

2012 ◽  
Vol 1 (33) ◽  
pp. 127 ◽  
Author(s):  
Deborah Ann Villarroel-Lamb
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Model Performance ◽  
Shoreline Change ◽  
Change Model ◽  
Morphological Model ◽  
Commercial Package ◽  
Formed Part

A recently developed beach change model was investigated to assess its predictive capability with respect to shoreline change. This investigation formed part of a number of analyses being conducted to assess the capability of the numerical model. The model was firstly compared to a commonly used commercial model to assess its output on wave and sediment responses. Secondly, the beach changes were investigated to determine a likely probability density function for the shoreline responses. A number of probability density functions were compared with the results and critical deductions were made. Lastly, the new beach change model has a distinctive feature which attempts to reduce the model run-time to promote greater use. This wave-averaging feature was investigated to determine model performance as parameters were changed. It was shown that the model compares favorably to the commercial package in some aspects, but not all. The shoreline response may be best described by a single probability density function, which makes it quite suitable for quantitative risk analyses. Lastly, the wave-averaging feature can be used to reduce runtime although this requires the user to apply sound judgment in the analyses.

scholarly journals First-Order Statistical Characteristics of Macrodiversity System with Three Microdiversity MRC Receivers in the Presence of k-µ Short-Term Fading and Gamma Long-Term Fading

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Branimir Jaksic ◽  
Mihajlo Stefanovic ◽  
Danijela Aleksic ◽  
Dragan Radenkovic ◽  
Sinisa Minic
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Output Signal ◽  
Multipath Fading ◽  
Statistical Characteristics ◽  
Cumulative Density Function ◽  
Short Term ◽  
Maximum Ratio Combining

Macrodiversity system with macrodiversity SC receiver and three microdiversity MRC (maximum ratio combining) receivers is considered. Independent k-μ short-term fading and correlated Gamma long-term fading are present at the inputs of microdiversity MRC receivers. For this model, the probability density function and the cumulative density function of microdiversity MRC receivers and macrodiversity SC receiver output signal envelopes are calculated. Influences of Gamma shadowing severity, k-μ multipath fading severity, Rician factor and correlation coefficient at probability density function, and cumulative density function of macrodiversity SC receiver output signal envelopes are graphically presented.

scholarly journals The Long Term Behaviour of Classical Old Novae

1990 ◽  
Vol 122 ◽  
pp. 13-23
Author(s):  
A. Bianchini
Keyword(s):  
Mass Transfer ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Time Scales ◽  
Transfer Rate ◽  
Mass Transfer Rate ◽  
Solar Type ◽  
Definition Of

AbstractQuiescent novae are more stable against mass transfer rate than dwarf novae. They may however show cyclical variations of their quiescent magnitudes on time scales of years, probably caused by solar–type cycles of activity of the secondary. The probability density function of the periods of the cycles observed in CVs is similar to that for single stars. Sometimes, periodic or quasi periodic light variations on time scales of tens to hundreds of days are also observed. Although the magnitudes of prenovae and postnovae are essentially the same, the definition of the magnitude of a quiescent nova is still uncertain. At present, the hibernation theory for old novae seems to be supported only by the observations of two very old novae.

Hausdorff moment problem: Recovery of an unknown support for a probability density function

2017 ◽  
Vol 25 (6) ◽  
Author(s):  
Amir Kazemi ◽  
Hamid Reza Shahdoosti ◽  
Robert M. Mnatsakanov
Keyword(s):  
Probability Density Function ◽  
Probability Measure ◽  
Probability Density ◽  
Density Function ◽  
Moment Problem ◽  
Hausdorff Moment Problem

AbstractIn this work the following problem is discussed: Unknown are two objects, a probability density (corresponding to a distribution, or to a probability measure)

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