scholarly journals Analytic Programming – a Novel Tool for Synthesis of Controller for Chaotic Lozi Map

2021 ◽  
Vol 15 ◽  
pp. 50-55
Author(s):  
Roman Senkerik ◽  
Zuzana Kominkova Oplatkova ◽  
Michal Pluhacek
Keyword(s):  
Feedback Control ◽  
Differential Evolution ◽  
Cost Function ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Symbolic Regression ◽  
Control Law ◽  
Two Dimensional ◽  
Function Design ◽  
Analytic Programming

In this paper, it is presented a utilization of a novel tool for symbolic regression, which is analytic programming, for the purpose of the synthesis of a new feedback control law. This new synthesized chaotic controller secures the fully stabilization of selected discrete chaotic systems, which is the two-dimensional Lozi map. The paper consists of the descriptions of analytic programming as well as selected chaotic system, used heuristic and cost function design. For experimentation, Self-Organizing Migrating Algorithm (SOMA) and Differential evolution (DE) were used. Two selected experiments are detailed described.

CHAOS SYNTHESIS BY MEANS OF EVOLUTIONARY ALGORITHMS

2008 ◽  
Vol 18 (04) ◽  
pp. 911-942 ◽  
Author(s):  
IVAN ZELINKA ◽  
GUANRONG CHEN ◽  
SERGEJ CELIKOVSKY
Keyword(s):  
Genetic Algorithm ◽  
Evolutionary Algorithms ◽  
Genetic Programming ◽  
Differential Evolution ◽  
Cost Function ◽  
Case Studies ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Reliability And Robustness ◽  
Eleven Case

This paper introduces the notion of chaos synthesis by means of evolutionary algorithms and develops a new method for chaotic systems synthesis. This method is similar to genetic programming and grammatical evolution and is being applied along with three evolutionary algorithms: differential evolution, self-organizing migration and genetic algorithm. The aim of this investigation is to synthesize new and "simple" chaotic systems based on some elements contained in a prechosen existing chaotic system and a properly defined cost function. The investigation consists of eleven case studies: the aforementioned three evolutionary algorithms in eleven versions. For all algorithms, 100 simulations of chaos synthesis were repeated and then averaged to guarantee the reliability and robustness of the proposed method. The most significant results were carefully selected, visualized and commented in this report.

scholarly journals Hybrid Passivity Based and Fuzzy Type-2 Controller for Chaotic and Hyper-Chaotic Systems

2017 ◽  
Vol 11 (2) ◽  
pp. 96-103 ◽  
Author(s):  
Fernando Serrano ◽  
Josep M. Rossell
Keyword(s):  
Lyapunov Exponents ◽  
Chaotic System ◽  
Control Strategy ◽  
Chaotic Systems ◽  
Control Law ◽  
Four Dimensions ◽  
Design Requirements ◽  
The Stability ◽  
Theoretical Results

AbstractIn this paper a hybrid passivity based and fuzzy type-2 controller for chaotic and hyper-chaotic systems is presented. The proposed control strategy is an appropriate choice to be implemented for the stabilization of chaotic and hyper-chaotic systems due to the energy considerations of the passivity based controller and the flexibility and capability of the fuzzy type-2 controller to deal with uncertainties. As it is known, chaotic systems are those kinds of systems in which one of their Lyapunov exponents is real positive, and hyper-chaotic systems are those kinds of systems in which more than one Lyapunov exponents are real positive. In this article one chaotic Lorentz attractor and one four dimensions hyper-chaotic system are considered to be stabilized with the proposed control strategy. It is proved that both systems are stabilized by the passivity based and fuzzy type-2 controller, in which a control law is designed according to the energy considerations selecting an appropriate storage function to meet the passivity conditions. The fuzzy type-2 controller part is designed in order to behave as a state feedback controller, exploiting the flexibility and the capability to deal with uncertainties. This work begins with the stability analysis of the chaotic Lorentz attractor and a four dimensions hyper-chaotic system. The rest of the paper deals with the design of the proposed control strategy for both systems in order to design an appropriate controller that meets the design requirements. Finally, numerical simulations are done to corroborate the obtained theoretical results.

scholarly journals Control of Chaos Using Sampled-Data Feedback Control

1998 ◽  
Vol 08 (12) ◽  
pp. 2433-2438 ◽  
Author(s):  
Tao Yang
Keyword(s):  
Feedback Control ◽  
Asymptotic Stability ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Sampling Rate ◽  
Control Input ◽  
Sampled Data ◽  
Control Of Chaos ◽  
Data Feedback ◽  
Theoretical Results

In this paper we present a theory for control of chaotic systems using sampled data. The output of the chaotic system is sampled at a given sampling rate and the sampled output is used by a feedback subsystem to construct a control signal, which is held constant by a holding subsystem. Hence, during each control iteration, the control input remains unchanged. Theoretical results on the asymptotic stability of the resulting controlled chaotic systems are presented. Numerical experimental results via Chua's circuit are used to verify the theoretical results.

scholarly journals Chaos Enhanced Differential Evolution in the Task of Evolutionary Control of Selected Set of Discrete Chaotic Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Roman Senkerik ◽  
Ivan Zelinka ◽  
Michal Pluhacek ◽  
Donald Davendra ◽  
Zuzana Oplatková Kominkova
Keyword(s):  
Differential Evolution ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Chaotic Map ◽  
Differential Evolution Algorithm ◽  
Pseudorandom Number Generator ◽  
Pseudorandom Sequences ◽  
Evolutionary Technique ◽  
Evolutionary Tuning ◽  
Different Chaotic Systems

Evolutionary technique differential evolution (DE) is used for the evolutionary tuning of controller parameters for the stabilization of set of different chaotic systems. The novelty of the approach is that the selected controlled discrete dissipative chaotic system is used also as the chaotic pseudorandom number generator to drive the mutation and crossover process in the DE. The idea was to utilize the hidden chaotic dynamics in pseudorandom sequences given by chaotic map to help differential evolution algorithm search for the best controller settings for the very same chaotic system. The optimizations were performed for three different chaotic systems, two types of case studies and developed cost functions.

Anti-Synchronization for a Modified Chen-Qi-Like Chaotic System

2012 ◽  
Vol 220-223 ◽  
pp. 2113-2116
Author(s):  
Su Hai Huang
Keyword(s):  
Numerical Simulation ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Stability Theorem ◽  
Control Law ◽  
Lyapunov Stability Theorem ◽  
Unknown Parameters ◽  
Dynamical Characteristics ◽  
Control Scheme ◽  
Adaptive Control Scheme

A modified Chen-Qi-like chaotic system is presented. Some basic dynamical characteristics of this system are studied by calculating the Lyapunov exponent and phase figure. Based on the Lyapunov stability theorem, adaptive control scheme and parameters update law are presented for the anti-synchronization of new chaotic systems with fully unknown parameters. Finally, the numerical simulation verify that the control law and parameter changing are correct.

scholarly journals FPGA Realization and Lyapunov–Krasovskii Analysis for a Master-Slave Synchronization Scheme Involving Chaotic Systems and Time-Delay Neural Networks

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
J. Perez-Padron ◽  
C. Posadas-Castillo ◽  
J. Paz-Perez ◽  
E. Zambrano-Serrano ◽  
M. A. Platas-Garza
Keyword(s):  
Time Delay ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Tracking Error ◽  
Control Law ◽  
Trajectory Tracking Control ◽  
Field Programmable ◽  
Different Chaotic Systems ◽  
Synchronization Scheme ◽  
Theoretical Results

In this paper, the trajectory tracking control and the field programmable gate array (FPGA) implementation between a recurrent neural network with time delay and a chaotic system are presented. The tracking error is globally asymptotically stabilized by means of a control law generated from the Lyapunov–Krasovskii and Lur’e theory. The applicability of the approach is illustrated by considering two different chaotic systems: Liu chaotic system and Genesio–Tesi chaotic system. The numerical results have shown the effectiveness of obtained theoretical results. Finally, the theoretical results are implemented on an FPGA, confirming the feasibility of the synchronization scheme and showing that it is hardware realizable.

scholarly journals Adaptive Control Synchronization of a Novel Memristive Chaotic System for Secure Communication Applications

Inventions ◽  
2019 ◽  
Vol 4 (2) ◽  
pp. 30 ◽  
Author(s):  
Zain-Aldeen S. A. Rahman ◽  
Hayder A. A. Al-Kashoash ◽  
Saif Muneam Ramadhan ◽  
Yasir I. A. Al-Yasir
Keyword(s):  
Adaptive Control ◽  
Chaotic System ◽  
Data Transmission ◽  
Secure Communication ◽  
Chaotic Systems ◽  
Lyapunov Theory ◽  
Control Law ◽  
Slave System ◽  
Synchronization Mechanism ◽  
Adaptive Control Law

In this paper, a new memristive chaotic system is designed, analyzed, tested, and proposed. An adaptive control synchronization mechanism for both master and slave chaotic systems is also designed. The adaptive control law of this mechanism is derived based on the Lyapunov theory. A single parameter in the slave system has been assumed to be unknown. As the parameters of the master and slave are asymptotically matched, the unknown slave parameters will be identified according to the master’s parameters. The proposed system is used in a secure communication system. The achieved results prove a simple system implementation with a high security of data transmission.

ANTICIPATED FUNCTION SYNCHRONIZATION WITH UNKNOWN PARAMETERS OF DISCRETE-TIME CHAOTIC SYSTEMS

2009 ◽  
Vol 20 (04) ◽  
pp. 597-608 ◽  
Author(s):  
YIN LI ◽  
BIAO LI ◽  
YONG CHEN
Keyword(s):  
Chaotic System ◽  
Discrete Time ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Control Law ◽  
Unknown Parameters ◽  
Synchronization Problem ◽  
Synchronization Scheme ◽  
Hyperchaotic Systems ◽  
Function Synchronization

In this paper, firstly, the control problem for the chaos synchronization of discrete-time chaotic (hyperchaotic) systems with unknown parameters are considered. Next, backstepping control law is derived to make the error signals between drive 2D discrete-time chaotic system and response 2D discrete-time chaotic system with two uncertain parameters asymptotically synchronized. Finally, the approach is extended to the synchronization problem for 3D discrete-time chaotic system with two unknown parameters. Numerical simulations are presented to show the effectiveness of the proposed chaos synchronization scheme.

scholarly journals An Error Compensation Method for Improving the Properties of a Digital Henon Map Based on the Generalized Mean Value Theorem of Differentiation

Entropy ◽  
2021 ◽  
Vol 23 (12) ◽  
pp. 1628
Author(s):  
Yashuang Deng ◽  
Yuhui Shi
Keyword(s):  
Chaotic System ◽  
Error Compensation ◽  
Chaotic Systems ◽  
Mean Value ◽  
Mean Value Theorem ◽  
Two Dimensional ◽  
High Complexity ◽  
Digital World ◽  
Higher Dimensional ◽  
Generalized Mean

Continuous chaos may collapse in the digital world. This study proposes a method of error compensation for a two-dimensional digital system based on the generalized mean value theorem of differentiation that can restore the fundamental performance of chaotic systems. Different from other methods, the compensation sequence of our method comes from the chaotic system itself and can be applied to higher-dimensional digital chaotic systems. The experimental results show that the improved system is highly consistent with the real chaotic system, and it has excellent chaotic characteristics such as high complexity, randomness, and ergodicity.

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