Difference Synchronization of Identical and Nonidentical Chaotic and Hyperchaotic Systems of Different Orders Using Active Backstepping Design

2018 ◽  
Vol 13 (5) ◽  
Author(s):  
Eric Donald Dongmo ◽  
Kayode Stephen Ojo ◽  
Paul Woafo ◽  
Abdulahi Ndzi Njah
Keyword(s):  
Chaotic System ◽  
Initial Conditions ◽  
Lyapunov Stability Theory ◽  
The State ◽  
State Variables ◽  
State Variable ◽  
New Type ◽  
The Difference ◽  
Synchronization Scheme ◽  
Hyperchaotic Systems

This paper introduces a new type of synchronization scheme, referred to as difference synchronization scheme, wherein the difference between the state variables of two master [slave] systems synchronizes with the state variable of a single slave [master] system. Using the Lyapunov stability theory and the active backstepping technique, controllers are derived to achieve the difference synchronization of three identical hyperchaotic Liu systems evolving from different initial conditions, as well as the difference synchronization of three nonidentical systems of different orders, comprising the 3D Lorenz chaotic system, 3D Chen chaotic system, and the 4D hyperchaotic Liu system. Numerical simulations are presented to demonstrate the validity and feasibility of the theoretical analysis. The development of difference synchronization scheme has increases the number of existing chaos synchronization scheme.

scholarly journals Exploring the Limits of Floating-Point Resolution for Hardware-In-the-Loop Implemented with FPGAs

Electronics ◽  
2018 ◽  
Vol 7 (10) ◽  
pp. 219 ◽  
Author(s):  
Alberto Sanchez ◽  
Elías Todorovich ◽  
Angel de Castro
Keyword(s):  
The State ◽  
Floating Point ◽  
Hardware In The Loop ◽  
State Variables ◽  
Numerical Resolution ◽  
Digital Devices ◽  
State Variable ◽  
Simulation Step ◽  
Field Programmable ◽  
The Difference

As the performance of digital devices is improving, Hardware-In-the-Loop (HIL) techniques are being increasingly used. HIL systems are frequently implemented using FPGAs (Field Programmable Gate Array) as they allow faster calculations and therefore smaller simulation steps. As the simulation step is reduced, the incremental values for the state variables are reduced proportionally, increasing the difference between the current value of the state variable and its increments. This difference can lead to numerical resolution issues when both magnitudes cannot be stored simultaneously in the state variable. FPGA-based HIL systems generally use 32-bit floating-point due to hardware and timing restrictions but they may suffer from these resolution problems. This paper explores the limits of 32-bit floating-point arithmetics in the context of hardware-in-the-loop systems, and how a larger format can be used to avoid resolution problems. The consequences in terms of hardware resources and running frequency are also explored. Although the conclusions reached in this work can be applied to any digital device, they can be directly used in the field of FPGAs, where the designer can easily use custom floating-point arithmetics.

A SIMPLE SYNCHRONIZATION SCHEME OF GENESIO–TESI SYSTEM BASED ON THE BACK-STEPPING DESIGN

2014 ◽  
Vol 28 (05) ◽  
pp. 1450012 ◽  
Author(s):  
ZUOLEI WANG ◽  
YAOLIN JIANG
Keyword(s):  
Numerical Simulations ◽  
Chaotic System ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Lyapunov Stability Theory ◽  
Convergence Speed ◽  
Control Coefficient ◽  
State Variable ◽  
Synchronization Scheme

Synchronization of the Genesio–Tesi chaotic system is investigated via back-stepping method. Based on the Lyapunov stability theory, a novel scheme is designed. A global asymptotical synchronization can be realized via two simpler controllers, each controller involving only one state variable. Furthermore, the convergence speed can be adjusted by control coefficient. Finally, some numerical simulations are employed to verify the effectiveness of the proposed methods.

ADAPTIVE SYNCHRONIZATION OF A NOVEL HYPERCHAOTIC SYSTEM WITH FULLY UNKNOWN PARAMETERS

2013 ◽  
Vol 27 (32) ◽  
pp. 1350197
Author(s):  
XING-YUAN WANG ◽  
SI-HUI JIANG ◽  
CHAO LUO
Keyword(s):  
Lyapunov Stability ◽  
Lyapunov Stability Theory ◽  
Adaptive Controller ◽  
Chaotic Synchronization ◽  
Adaptive Synchronization ◽  
Hyperchaotic System ◽  
Unknown Parameters ◽  
Chen System ◽  
Synchronization Scheme ◽  
Hyperchaotic Systems

In this paper, a chaotic synchronization scheme is proposed to achieve adaptive synchronization between a novel hyperchaotic system and the hyperchaotic Chen system with fully unknown parameters. Based on the Lyapunov stability theory, an adaptive controller and parameter updating law are presented to synchronize the above two hyperchaotic systems. The corresponding theoretical proof is given and numerical simulations are presented to verify the effectiveness of the proposed scheme.

Output Control by Linear Time-Varying Systems using Parametric Identification Methods

2020 ◽  
Vol 21 (7) ◽  
pp. 387-393
Author(s):  
V. Q. Dat ◽  
A. A. Bobtsov
Keyword(s):  
Differential Equation ◽  
Initial Conditions ◽  
Control Object ◽  
The State ◽  
Time Varying ◽  
State Variables ◽  
Matrix Differential Equation ◽  
Matrix Differential ◽  
Uniform Observability ◽  
Riccati Matrix

In this paper the problem of control for time-varying linear systems by the output (i.e. without measuring the vector of state variables or derivatives of the output signal) was considered. For the control design, the well-known online procedure for solving the Riccati matrix differential equation is chosen. This procedure involves the synthesis of linear static feedbacks on state variables in the case of known parameters of the plant. If state variables are not measured, then for the observer design using the matrix Riccati differential equation, using the dual scheme, which provides for the transposition of the state matrix and the replacement of the input matrix by the output matrix. It is well known that an observer of state variables built on the basis of a solution of the Riccati matrix differential equation ensures the exponential stability of a closed loop system in the case of uniform observability. Despite the fact that this type of observer can be classified as universal, its have a number of significant drawbacks. The main problem of such observers is the need for accurate knowledge of the parameters and the requirement for uniform observability, which in practice cannot always be realized. Thus, the problem of the new methods design for constructing observers of state variables of linear non-stationary systems is still relevant. Some time ago, a number of methods for the adaptive observers design of state variables for nonlinear systems were proposed. The main idea of the synthesis of observers was based on the transformation of the original dynamic system to a linear regression model containing unknown parameters, which in turn were functions of the initial conditions of the state variables of the control object. This approach in the English language literature is called PEBO. This paper, based on the PEBO method, proposes a new approach for the observers design of state for non-stationary systems. This approach provides the possibility of obtaining monotonic convergence estimates with transient time tuning.

Evaluation of state variable interface between the Activated Sludge Models and Anaerobic Digestion Model no 1

2008 ◽  
Vol 57 (6) ◽  
pp. 901-907 ◽  
Author(s):  
H. Yasui ◽  
K. Komatsu ◽  
R. Goel ◽  
Y. Y. Li ◽  
T. Noike
Keyword(s):  
Activated Sludge ◽  
State Of The Art ◽  
Degradation Kinetics ◽  
The State ◽  
State Variables ◽  
Anaerobic Conditions ◽  
State Variable ◽  
Kinetics Of ◽  
Aerobic And Anaerobic ◽  
Aerobic And Anaerobic Conditions

For plant wide modelling of wastewater treatment, it is necessary to develop a suitable state variables interface for integrating state of the art models of ASM and ADM1. ADM1 currently describes such an interface, however, its suitability needs to be experimentally evaluated. In this study, we characterised activated sludge under aerobic and anaerobic conditions to obtain representative state variables for both models. ASM state variables of XS, XH and XI (as obtained from aerobic tests) and ADM1 state variables of XC and XI (as obtained from anaerobic tests) were then correlated to assess the suitability of current interface. Based on the seven datasets of this study and seven datasets from literatures, it was found that in general ASM state variables were well correlated to the state variables of ADM1. The ADM1 state variable of XC could be correlated to the sum of state variables of XS and XH, while XI in both the models showed direct correspondence. It was also observed that the degradation kinetics of XC under anaerobic condition could be better described by individual degradation kinetics of XS and XH. Therefore, to establish a one to one correspondence between ASM and ADM1 state variables and better description of degradation kinetics in ADM1, replacing the composite variable of XC by the state variables of XS and XH is recommended.

scholarly journals Specific Mathematical Aspects of Dynamics Generated by Coherence Functions

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
Ezzat G. Bakhoum ◽  
Cristian Toma
Keyword(s):  
Differential Equations ◽  
Complex Systems ◽  
Integral Equations ◽  
Quantum Physics ◽  
Initial Conditions ◽  
Coherence Function ◽  
Multiple Integral ◽  
The State ◽  
Integrodifferential Equations ◽  
State Variables

This study presents specific aspects of dynamics generated by the coherence function (acting in an integral manner). It is considered that an oscillating system starting to work from initial nonzero conditions is commanded by the coherence function between the output of the system and an alternating function of a certain frequency. For different initial conditions, the evolution of the system is analyzed. The equivalence between integrodifferential equations and integral equations implying the same number of state variables is investigated; it is shown that integro-differential equations of second order are far more restrictive regarding the initial conditions for the state variables. Then, the analysis is extended to equations of evolution where the coherence function is acting under the form of a multiple integral. It is shown that for the coherence function represented under the form of annth integral, some specific aspects as multiscale behaviour suitable for modelling transitions in complex systems (e.g., quantum physics) could be noticed whennequals 4, 5, or 6.

scholarly journals Adaptive Terminal Synergetic Synchronization of Hyperchaotic Systems

2021 ◽  
Vol 54 (5) ◽  
pp. 789-795
Author(s):  
Yamina Haddadji ◽  
Mohamed Naguib Harmas ◽  
Abdlouahab Bouafia ◽  
Ziyad Bouchama
Keyword(s):  
Nonlinear Control ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Initial Conditions ◽  
Lyapunov Stability Theory ◽  
Slave System ◽  
Unknown Parameters ◽  
Master System ◽  
Simulation Results ◽  
Hyperchaotic Systems

This research paper introduces an adaptive terminal synergetic nonlinear control. This control aims at synchronizing two hyperchaotic Zhou systems. Thus, the adaptive terminal synergetic control’s synthesis is applied to synchronize a hyperchaotic i.e., slave system with unknown parameters with another hyperchaotic i.e., master system. Accordingly, simulation results of each system in different initial conditions reveal significant convergence. Moreover, the findings proved stability and robustness of the suggested scheme using Lyapunov stability theory.

scholarly journals STACK with state

2017 ◽  
Vol 15 (2) ◽  
pp. 60 ◽  
Author(s):  
Matti Harjula ◽  
Jarmo Malinen ◽  
Antti Rasila
Keyword(s):  
Finite State Machine ◽  
State Machine ◽  
The State ◽  
Point Of View ◽  
State Variables ◽  
State Variable ◽  
Finite State ◽  
Input Event ◽  
Single Input ◽  
The Right

The question model of STACK provides an easy way for building automatically assessable questions with mathematical content, but it requires that the questions and their assessment logic depend only on the current input, given by the student at a single instant. However, the present STACK question model already has just the right form to be extended with state variables that would remove this limitation. In this article, we report our recent work on the state-variable extension for STACK, and we also discuss combining the use of state variables with our previous work on conditional output processing. As an outcome, we propose an expansion to the STACK question model, allowing the questions to act as state machines instead of pure functions of a single input event from the studentWe present a model question using the state variable extension of STACK that demonstrates some of the new possibilities that open up for the question author. This question is based on a finite state machine in its assessment logic, and it demonstrates aspects of strategic planning to solve problems of recursive nature. The model question also demonstrates how the state machine can interpret the solution path taken by the student, so as to dynamically modify the question behaviour and progress by, e.g., asking additional questions relevant to the path. We further explore the future possibilities from the point of view of learning strategic competencies in mathematics (Kilpatrick et al., 2001; Rasila et al., 2015).

A New Type of Function Projective Synchronization of Nonautonomous Chaotic System

2013 ◽  
Vol 705 ◽  
pp. 590-595
Author(s):  
Xiao Shan Zhao ◽  
Zhen Bo Li ◽  
Fang Fang Liu
Keyword(s):  
Numerical Simulation ◽  
Chaotic System ◽  
Scaling Function ◽  
Projective Synchronization ◽  
Function Projective Synchronization ◽  
State Variable ◽  
Gyroscope System ◽  
New Type ◽  
The Scaling Function ◽  
General Method

The function projective synchronization of nonautonomous chaotic system with a new type of scaling function is investigated. The scaling function factor discussed in this paper is a new kind of function which contains the state variable. Obviously, this kind of scaling function is complicated than former ones. Based on modified active control, the general method of this synchronization is proposed. In numerical simulation, the heavy symmetric gyroscope system is taken as the instance to demonstrate the validity of the controller and the feasibility of the proposed synchronization.

Sensor Synthesis for Control of Manufacturing Processes

1992 ◽  
Vol 114 (2) ◽  
pp. 158-174 ◽  
Author(s):  
G. Chryssolouris ◽  
M. Domroese ◽  
P. Beaulieu
Keyword(s):  
The State ◽  
Process Models ◽  
State Variables ◽  
Test Bed ◽  
Control Approach ◽  
State Variable ◽  
Sensor Signals ◽  
Multiple Sensor ◽  
Sensor Information ◽  
Basic Approaches

When a human controls a manufacturing process he or she uses multiple senses to monitor the process. Similarly, one can consider a control approach where measurements of process variables are performed by several sensing devices which in turn feed their signals into process models. Each of these models contains mathematical expressions based on the physics of the process which relate the sensor signals to process state variables. The information provided by the process models should be synthesized in order to determine the best estimates for the state variables. In this paper two basic approaches to the synthesis of multiple sensor information are considered and compared. The first approach is to synthesize the state variable estimates determined by the different sensors and corresponding process models through a mechanism based on training such as a neural network. The second approach utilizes statistical criteria to estimate the best synthesized state variable estimate from the state variable estimates provided by the process models. As a “test bed” for studying the effectiveness of the above sensor synthesis approaches turning has been considered. The approaches are evaluated and compared for providing estimates of the state variable tool wear based on multiple sensor information. The robustness of each scheme with respect to noisy and inaccurate sensor information is investigated.

Sign in / Sign up

Export Citation Format

Share Document