Adaptive Robust Stabilization of Rossler System With Time-Varying Mismatched Parameters Via Scalar Input

2016 ◽  
Vol 11 (4) ◽  
Author(s):  
Mohammad Mehdi Arefi
Keyword(s):  
A Priori ◽  
Robust Stabilization ◽  
Lyapunov Stability Theory ◽  
Time Varying ◽  
Robust Controller ◽  
Third Order ◽  
Rossler System ◽  
Scalar Input ◽  
Rössler System ◽  
Priori Information

This paper presents an adaptive robust controller for a class of uncertain chaotic Rossler system with time-varying mismatched parameters. The proposed controller is designed based on Lyapunov stability theory, and it is shown that using this controller all signals of the closed-loop system are uniformly ultimately bounded (UUB). In addition, the proposed scheme is such that it does not require a priori information about the bound of uncertainties. Furthermore, since all the signals are UUB, the control signal is smooth and feasible to implement. Simulation results on a third-order Rossler system with time-varying parameters confirm the effectiveness of the proposed controller.

Mathematical Modeling and Robust Control for Beam Reheating Furnace

2013 ◽  
Vol 380-384 ◽  
pp. 209-214
Author(s):  
Ling Yan Hu ◽  
Ling Yan Hu
Keyword(s):  
Robust Stabilization ◽  
Lyapunov Stability Theory ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Stabilization Problem ◽  
Robust Controller ◽  
Nonlinear Characteristics ◽  
Reheating Furnace ◽  
Simulation Results ◽  
The Mathematical Model

According to the large beam reheating furnace widely used in metallurgy area, the mathematical model was built basing on the heat transfer. Considering the uncertain and nonlinear characteristics existing in the system, the robust stabilization problem of the system is investigated basing on Lyapunov stability theory and linear matrix inequality (LMI) method. The robust controller is designed. A numerical example and its simulation results are given.

Local Bifurcations and Chaos in the Fractional Rössler System

2018 ◽  
Vol 28 (08) ◽  
pp. 1850098 ◽  
Author(s):  
Jan Čermák ◽  
Luděk Nechvátal
Keyword(s):  
Fractional Order ◽  
Control Method ◽  
Chaotic Behavior ◽  
A Priori ◽  
Hopf Bifurcations ◽  
Rossler System ◽  
Master System ◽  
Rössler System ◽  
Active Control Method

The paper discusses the fractional Rössler system and the dependence of its dynamics on some entry parameters. An explicit algorithm for a priori determination of fractional Hopf bifurcations is derived and scenarios documenting a route of the system from stability to chaos are performed with respect to a varying system’s fractional order as well as to a varying system’s coefficient. Contrary to the existing results, the searched values of the fractional Hopf bifurcations follow directly from a revealed analytical dependence between these two systems’ entries. Their various critical values are established and confirmed by numerical experiments demonstrating not only the loss of stability of an equilibrium point, but also other phenomena of transition to chaotic behavior. In addition, we suggest an active control method for synchronization of two chaotic fractional-order Rössler systems. Our theoretical analysis enables to synchronize them for any value of a free parameter under which the master system displays a chaotic behavior.

Innovative Approach to Information Search by Example of a Patent Analysis of an Important Substitution Plan

2020 ◽  
pp. 143-157
Author(s):  
Maria A. Milkova
Keyword(s):  
Information Search ◽  
Topic Modeling ◽  
Cognitive Biases ◽  
A Priori ◽  
Import Substitution ◽  
Innovative Approach ◽  
Iterative Search ◽  
Comprehensive Picture ◽  
Priori Information ◽  
Selection Of

Nowadays the process of information accumulation is so rapid that the concept of the usual iterative search requires revision. Being in the world of oversaturated information in order to comprehensively cover and analyze the problem under study, it is necessary to make high demands on the search methods. An innovative approach to search should flexibly take into account the large amount of already accumulated knowledge and a priori requirements for results. The results, in turn, should immediately provide a roadmap of the direction being studied with the possibility of as much detail as possible. The approach to search based on topic modeling, the so-called topic search, allows you to take into account all these requirements and thereby streamline the nature of working with information, increase the efficiency of knowledge production, avoid cognitive biases in the perception of information, which is important both on micro and macro level. In order to demonstrate an example of applying topic search, the article considers the task of analyzing an import substitution program based on patent data. The program includes plans for 22 industries and contains more than 1,500 products and technologies for the proposed import substitution. The use of patent search based on topic modeling allows to search immediately by the blocks of a priori information – terms of industrial plans for import substitution and at the output get a selection of relevant documents for each of the industries. This approach allows not only to provide a comprehensive picture of the effectiveness of the program as a whole, but also to visually obtain more detailed information about which groups of products and technologies have been patented.

scholarly journals Differential Transform Method as an Effective Tool for Investigating Fractional Dynamical Systems

2021 ◽  
Vol 11 (15) ◽  
pp. 6955
Author(s):  
Andrzej Rysak ◽  
Magdalena Gregorczyk
Keyword(s):  
Optimal Parameter ◽  
Differential Transform Method ◽  
Bifurcation Diagrams ◽  
Transform Method ◽  
Rossler System ◽  
Differential Transform ◽  
Rössler System ◽  
Fractional System ◽  
Parameter Values

This study investigates the use of the differential transform method (DTM) for integrating the Rössler system of the fractional order. Preliminary studies of the integer-order Rössler system, with reference to other well-established integration methods, made it possible to assess the quality of the method and to determine optimal parameter values that should be used when integrating a system with different dynamic characteristics. Bifurcation diagrams obtained for the Rössler fractional system show that, compared to the RK4 scheme-based integration, the DTM results are more resistant to changes in the fractionality of the system.

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