scholarly journals Parameters Identification of Nonlinear Lorenz Chaotic System and its Application to High Precision Model Reference Synchronization

2021 ◽  
Author(s):  
Chao-Chung Peng ◽  
Yang-Rui Li
Keyword(s):  
Parameter Identification ◽  
Chaotic System ◽  
Initial Guess ◽  
Parameters Estimation ◽  
Identification Algorithm ◽  
Model Reference ◽  
System Parameters ◽  
Identification Schemes ◽  
True Value ◽  
Lorenz Chaotic System

Abstract The Lorenz chaotic system synchronization has been a popular research topic in the last two decades. Most of the studies focus on the design of model reference adaptive control (MRAC) synchronization schemes. In the existing MRAC schemes, adaptive laws are designed to estimate the system parameters online. However, due to the system parameters being unknown, arbitrary selection results in a longer estimation period. Although applying large values of adaptive gains can increase the estimation convergence speed, it usually induces obvious estimation oscillations and large control efforts. On the contrary, small adaptive gains result in smooth but sluggish transient estimations. None of the studies addressed on the parameters estimation and its contribution to precise synchronization. To address this issue, two system identification schemes are presented. The first applied scheme is called observer/Kalman filter identification (OKID). The second one is called bilinear transform discretization (BTD). The related detail derivations for the Lorenz chaotic system parameter identification will be presented in this paper. Results show that the proposed BTD identification algorithm is relatively simple and computationally efficient. Moreover, highly precise parameter estimations can be achieved as well. Nevertheless, due to the complex nonlinearity of the chaotic system, it will be illustrated that even extremely small parameter deviations could lead to dramatic mismatch for the chaotic system model output prediction. To further solve this issue, a MRAC is further designed in which the initial guess of the system parameters is obtained through the proposed BTD identification algorithm. Since the identified parameters are already very close to the true value, smaller values of adaptive gains can be used. With the aid of the precise parameter identification, the transient dynamics and the convergence performance of the MARC are both improved significantly. Simulations demonstrate the effectiveness of the proposed scheme.

The Parameters Identification of Time - Delay Models of Heat Transfer Systems From Input-Output Measurements

2009 ◽  
Author(s):  
Goran Simeunovic´ ◽  
Pavel Zitek ◽  
Jan Chysky´
Keyword(s):  
Heat Transfer ◽  
Time Delay ◽  
Time Delays ◽  
Parameters Estimation ◽  
Parameters Identification ◽  
Delay Systems ◽  
Parameter Estimates ◽  
Identification Algorithm ◽  
System Parameters ◽  
Variable Projection

The paper presents the identification issues and proposes a parameter identification algorithm that separates the system parameters from the time-delays for a class of single input single output (SISO) linear time delay systems (LTDS). The presence of the unknown time delay greatly complicates the parameters estimation problem, because the parameters of the model are not linear with respect to the time-delay. However, once the time delay is determined, the model becomes linear for the other parameters and hence the common least square method can be utilized directly. Motivated by the nonlinear least squares problem developed in the paper Golub and Pereyra (1973), a novel modification of the so-called variable projection functional is worked out for identification of time delays. In this way, the parameters estimation is separated from the estimation of time delays and the large errors in the parameter estimates, in the case of presence of errors in the time-delay identified values, are avoided. Namely, the small error in the time-delay identified values may often cause a large error in the system parameters identification. A hybrid optimalization method combining a Genetic Algorithm and Nelder-Mead technique is used for minimization of variable projection functional for the identification of time delays. This approach is illustrated by a particular application in the field of heat transfer, concretely on the time-delay model of the recuperative heat exchanger.

An improved nonlinear innovation-based parameter identification algorithm for ship models

2021 ◽  
pp. 1-9
Author(s):  
Baigang Zhao ◽  
Xianku Zhang
Keyword(s):  
Parameter Identification ◽  
Test Data ◽  
Stochastic Gradient ◽  
Least Square ◽  
Gradient Algorithm ◽  
Model Parameters ◽  
Identification Algorithm ◽  
Process Innovations ◽  
Stochastic Gradient Algorithm ◽  
Tangent Function

Abstract To solve the problem of identifying ship model parameters quickly and accurately with the least test data, this paper proposes a nonlinear innovation parameter identification algorithm for ship models. This is based on a nonlinear arc tangent function that can process innovations on the basis of an original stochastic gradient algorithm. A simulation was carried out on the ship Yu Peng using 26 sets of test data to compare the parameter identification capability of a least square algorithm, the original stochastic gradient algorithm and the improved stochastic gradient algorithm. The results indicate that the improved algorithm enhances the accuracy of the parameter identification by about 12% when compared with the least squares algorithm. The effectiveness of the algorithm was further verified by a simulation of the ship Yu Kun. The results confirm the algorithm's capacity to rapidly produce highly accurate parameter identification on the basis of relatively small datasets. The approach can be extended to other parameter identification systems where only a small amount of test data is available.

scholarly journals Hybrid Image Encryption Technique Using Genetic Algorithm and Lorenz Chaotic System

2020 ◽  
Vol 32 ◽  
pp. 03009
Author(s):  
Vishwanath Chikkareddi ◽  
Anurag Ghosh ◽  
Preksha Jagtap ◽  
Sahil Joshi ◽  
Jeel Kanzaria
Keyword(s):  
Genetic Algorithm ◽  
Image Encryption ◽  
Chaotic System ◽  
Random Number ◽  
Current Image ◽  
Space Efficiency ◽  
Highly Sensitive ◽  
Key Sensitivity ◽  
Lorenz Chaotic System ◽  
Time And Space Complexity

One of the important application of image encryption is storing confidential and important images on a local device or a database in such a way that only the authorized party can view or perceive it. The current image encryption technique employs the genetic algorithm to increase confusion in the image, but compromises in time and space complexity. The other method employs chaos or pseudo random number generating systems which have fast and highly sensitive keys but fails to make the image sufficiently noisy and is risky due to its deterministic nature. We propose a technique which employs the non-deterministic, optimizing power of genetic algorithm and the space efficiency and key sensitivity of chaotic systems into a unified, efficient algorithm which will retain the merits of both the methods whereas tries to minimize their demerits in a software system. The encryption process proceeds in two steps, generating two keys. First, an encryption sequence is generated using Lorenz Chaotic system of differential equation. The seed values used are the user’s actual key having key sensitivity of 10-14. Second, the encrypted image’s genetic encryption sequence is generated which will result in an encrypted image with entropy value greater than 7.999 thus ensuring the image is very noisy. Proposed technique uses variations of Lorenz system seed sets to generate all random mutations and candidate solutions in Genetic encryption. Since only the seed sets leading to desired solution is stored, space efficiency is higher compared to storing the entire sequences. Using this image encryption technique we will ensure that the images are hidden securely under two layers of security, one chaotic and other non-deterministic.

scholarly journals Physical Parameter Identification Algorithm Modeling for Complex Microsystem via Triangulation Functions

2018 ◽  
Vol 7 (4.36) ◽  
pp. 962
Author(s):  
Elena N. Meshcheryakova ◽  
. .
Keyword(s):  
Parameter Identification ◽  
Physical Parameter ◽  
Delaunay Triangulation ◽  
Model Development ◽  
Physical Object ◽  
Identification Algorithm ◽  
Classification Analysis ◽  
Advantages And Disadvantages ◽  
Object Parameters ◽  
D Model

This article describes the possibility of triangulation function use for the classification, analysis and identification of complex microsystem physical object parameters. They analyzed the existing methods and identification algorithms, their advantages and disadvantages are highlighted. The existing methods of triangulation are considered, the possibility of Delaunay triangulation is described for surfactant signal 3-D model development and analysis. They developed the algorithm to identify the state of an object using the triangulation function that takes into account the change of node coordinates and the length of the triangulation grid edges. They presented the visual UML model. The conclusions are drawn about the possibility of triangulation function use for the analysis of complex microsystem state.  

Causation Entropy Identifies Sparsity Structure for Parameter Estimation of Dynamic Systems

2016 ◽  
Vol 12 (1) ◽  
Author(s):  
Pileun Kim ◽  
Jonathan Rogers ◽  
Jie Sun ◽  
Erik Bollt
Keyword(s):  
Parameter Estimation ◽  
Time Series Data ◽  
Multivariate Time Series ◽  
Measurement Data ◽  
Relative Magnitude ◽  
Initial Guess ◽  
Series Data ◽  
System Parameters ◽  
Estimation Problems ◽  
System States

Parameter estimation is an important topic in the field of system identification. This paper explores the role of a new information theory measure of data dependency in parameter estimation problems. Causation entropy is a recently proposed information-theoretic measure of influence between components of multivariate time series data. Because causation entropy measures the influence of one dataset upon another, it is naturally related to the parameters of a dynamical system. In this paper, it is shown that by numerically estimating causation entropy from the outputs of a dynamic system, it is possible to uncover the internal parametric structure of the system and thus establish the relative magnitude of system parameters. In the simple case of linear systems subject to Gaussian uncertainty, it is first shown that causation entropy can be represented in closed form as the logarithm of a rational function of system parameters. For more general systems, a causation entropy estimator is proposed, which allows causation entropy to be numerically estimated from measurement data. Results are provided for discrete linear and nonlinear systems, thus showing that numerical estimates of causation entropy can be used to identify the dependencies between system states directly from output data. Causation entropy estimates can therefore be used to inform parameter estimation by reducing the size of the parameter set or to generate a more accurate initial guess for subsequent parameter optimization.

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