scholarly journals Synchronization of fractional-order Lü chaotic oscillators for voice encryption

2020 ◽  
Vol 66 (3 May-Jun) ◽  
pp. 364 ◽  
Author(s):  
O. García-Sepúlveda ◽  
C. Posadas-Castillo ◽  
A. D. Cortés-Preciado ◽  
M. A. Platas-Garza ◽  
E. Garza-González ◽  
...  
Keyword(s):  
Fractional Order ◽  
State Variables ◽  
Chaotic Oscillators ◽  
State Variable ◽  
Voice Message

In this paper, the encryption improvement via modulation of the fractional order chaotic oscillators state variables, is presented. A network of N-coupled fractional order Lü chaotic oscillators, is synchronized. A voice message is encrypted via additive encryption, by using a state variable of the synchronized network. The selected state variable is modulated and used to encrypt the message again. The results are compared.

scholarly journals A New No Equilibrium Fractional Order Chaotic System, Dynamical Investigation, Synchronization, and Its Digital Implementation

Inventions ◽  
2021 ◽  
Vol 6 (3) ◽  
pp. 49
Author(s):  
Zain-Aldeen S. A. Rahman ◽  
Basil H. Jasim ◽  
Yasir I. A. Al-Yasir ◽  
Raed A. Abd-Alhameed ◽  
Bilal Naji Alhasnawi
Keyword(s):  
Adaptive Control ◽  
Fractional Order ◽  
Chaotic System ◽  
Real World ◽  
Experimental Results ◽  
Chaotic Attractors ◽  
State Variables ◽  
Digital Implementation ◽  
Dynamical Behaviors ◽  
Real World Applications

In this paper, a new fractional order chaotic system without equilibrium is proposed, analytically and numerically investigated, and numerically and experimentally tested. The analytical and numerical investigations were used to describe the system’s dynamical behaviors including the system equilibria, the chaotic attractors, the bifurcation diagrams, and the Lyapunov exponents. Based on the obtained dynamical behaviors, the system can excite hidden chaotic attractors since it has no equilibrium. Then, a synchronization mechanism based on the adaptive control theory was developed between two identical new systems (master and slave). The adaptive control laws are derived based on synchronization error dynamics of the state variables for the master and slave. Consequently, the update laws of the slave parameters are obtained, where the slave parameters are assumed to be uncertain and are estimated corresponding to the master parameters by the synchronization process. Furthermore, Arduino Due boards were used to implement the proposed system in order to demonstrate its practicality in real-world applications. The simulation experimental results were obtained by MATLAB and the Arduino Due boards, respectively, with a good consistency between the simulation results and the experimental results, indicating that the new fractional order chaotic system is capable of being employed in real-world applications.

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.

Analysis, Design, and Optimization of High Speed Vehicle Suspensions Using State Variable Techniques

1974 ◽  
Vol 96 (2) ◽  
pp. 193-203 ◽  
Author(s):  
J. K. Hedrick ◽  
G. F. Billington ◽  
D. A. Dreesbach
Keyword(s):  
High Speed ◽  
Optimization Problems ◽  
Vertical Plane ◽  
Computer Application ◽  
Vehicle Suspension ◽  
State Variables ◽  
State Variable ◽  
Suspension Parameters ◽  
Suspension Model ◽  
High Speed Vehicle

This article applies state variable techniques to high speed vehicle suspension design. When a reasonably complex suspension model is treated, the greater adaptability of state variable techniques to digital computer application makes it more attractive than the commonly used integral transform method. A vehicle suspension model is developed, state variable techniques are applied, numerical methods are presented, and, finally, an optimization algorithm is chosen to select suspension parameters. A fairly complete bibliography is included in each of these areas. The state variable technique is illustrated in the solution of two suspension optimization problems. First, the vertical plane suspension of a high speed vehicle subject to guideway and aerodynamic inputs will be analyzed. The vehicle model, including primary and secondary suspension systems, and subject to both heave and pitch motions, has thirteen state variables. Second, the horizontal plane suspension of a high speed vehicle subject to guideway and lateral aerodynamic inputs is analyzed. This model also has thirteen state variables. The suspension parameters of both these models are optimized. Numerical results are presented for a representative vehicle, showing time response, mean square values, optimized suspension parameters, system eigenvalues, and acceleration spectral densities.

scholarly journals Robust Position Control of PMSM Using Fractional-Order Sliding Mode Controller

2012 ◽  
Vol 2012 ◽  
pp. 1-33 ◽  
Author(s):  
Jiacai Huang ◽  
Hongsheng Li ◽  
YangQuan Chen ◽  
Qinghong Xu
Keyword(s):  
Fractional Order ◽  
Position Control ◽  
Sliding Mode ◽  
Permanent Magnet Synchronous Motor ◽  
The State ◽  
Sliding Mode Controller ◽  
Sliding Surface ◽  
State Variables ◽  
Nonlinear Load ◽  
Special Case

A new robust fractional-order sliding mode controller (FOSMC) is proposed for the position control of a permanent magnet synchronous motor (PMSM). The sliding mode controller (SMC), which is insensitive to uncertainties and load disturbances, is studied widely in the application of PMSM drive. In the existing SMC method, the sliding surface is usually designed based on the integer-order integration or differentiation of the state variables, while in this proposed robust FOSMC algorithm, the sliding surface is designed based on the fractional-order calculus of the state variables. In fact, the conventional SMC method can be seen as a special case of the proposed FOSMC method. The performance and robustness of the proposed method are analyzed and tested for nonlinear load torque disturbances, and simulation results show that the proposed algorithm is more robust and effective than the conventional SMC method.

scholarly journals State Variable Effects in Graphical Event Models

2020 ◽  
Author(s):  
Debarun Bhattacharjya ◽  
Dharmashankar Subramanian ◽  
Tian Gao
Keyword(s):  
Real World ◽  
Continuous Time ◽  
Point Processes ◽  
Temporal Dynamics ◽  
Search Algorithm ◽  
State Variables ◽  
Discrete State ◽  
State Variable ◽  
Event Models ◽  
Real World Datasets

Many real-world domains involve co-evolving relationships between events, such as meals and exercise, and time-varying random variables, such as a patient's blood glucose levels. In this paper, we propose a general framework for modeling joint temporal dynamics involving continuous time transitions of discrete state variables and irregular arrivals of events over the timeline. We show how conditional Markov processes (as represented by continuous time Bayesian networks) and multivariate point processes (as represented by graphical event models) are among various processes that are covered by the framework. We introduce and compare two simple and interpretable yet practical joint models within the framework with relevant baselines on simulated and real-world datasets, using a graph search algorithm for learning. The experiments highlight the importance of jointly modeling event arrivals and state variable transitions to better fit joint temporal datasets, and the framework opens up possibilities for models involving even more complex dynamics whenever suitable.

scholarly journals Climatological Features of the Weakly and Very Stably Stratified Nocturnal Boundary Layers. Part I: State Variables Containing Information about Regime Occupation

2019 ◽  
Vol 76 (11) ◽  
pp. 3455-3484 ◽  
Author(s):  
Carsten Abraham ◽  
Adam H. Monahan
Keyword(s):  
Wind Speed ◽  
Turbulence Intensity ◽  
Three Dimensional ◽  
Static Stability ◽  
Wind Component ◽  
State Variables ◽  
Intermittent Turbulence ◽  
Additional Information ◽  
State Variable ◽  
Mean Wind Speed

Abstract The atmospheric nocturnal stable boundary layer (SBL) can be classified into two distinct regimes: the weakly SBL (wSBL) with sustained turbulence and the very SBL (vSBL) with weak and intermittent turbulence. A hidden Markov model (HMM) analysis of the three-dimensional state-variable space of Reynolds-averaged mean dry static stability, mean wind speed, and wind speed shear is used to classify the SBL into these two regimes at nine different tower sites, in order to study long-term regime occupation and transition statistics. Both Reynolds-averaged mean data and measures of turbulence intensity (eddy variances) are separated in a physically meaningful way. In particular, fluctuations of the vertical wind component are found to be much smaller in the vSBL than in the wSBL. HMM analyses of these data using more than two SBL regimes do not result in robust results across measurement locations. To identify which meteorological state variables carry the information about regime occupation, the HMM analyses are repeated using different state-variable subsets. Reynolds-averaged measures of turbulence intensity (such as turbulence kinetic energy) at any observed altitude hold almost the same information as the original set, without adding any additional information. In contrast, both stratification and shear depend on surface information to capture regime transitions accurately. Use of information only in the bottom 10 m of the atmosphere is sufficient for HMM analyses to capture important information about regime occupation and transition statistics. It follows that the commonly measured 10-m wind speed is potentially a good indicator of regime occupation.

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 Analysis of Resolution in Feedback Signals for Hardware-in-the-Loop Models of Power Converters

Electronics ◽  
2019 ◽  
Vol 8 (12) ◽  
pp. 1527
Author(s):  
María Sofía Martínez-García ◽  
Angel de Castro ◽  
Alberto Sanchez ◽  
Javier Garrido
Keyword(s):  
Power Converters ◽  
Design Criterion ◽  
Feedback Signal ◽  
Hardware In The Loop ◽  
State Variables ◽  
Gate Arrays ◽  
State Variable ◽  
Field Programmable ◽  
Programmable Gate Arrays ◽  
Optimum Width

One of the main techniques for debugging power converters is hardware-in-the-loop (HIL), which is used for real-time emulation. Field programmable gate arrays (FPGA) are the most common design platforms due to their acceleration capability. In this case, the widths of the signals have to be carefully chosen to optimize the area and speed. For this purpose, fixed-point arithmetic is one of the best options because although the design time is high, it allows the personalization of the number of bits in every signal. The representation of state variables in power converters has been previously studied, however other signals, such as feedback signals, can also have a big influence because they transmit the value of one state variable to the rest, and vice versa. This paper presents an analysis of the number of bits in the feedback signals of a boost converter, but the conclusions can be extended to other power converters. The purpose of this work is to study how many bits are necessary in order to avoid the loss of information, but also without wasting bits. Errors of the state variables are obtained with different sizes of feedback signals. These show that the errors in each state variable have similar patterns. When the number of bits increases, the error decreases down to a certain number of bits, where an almost constant error appears. However, when the bits decrease, the error increases linearly. Furthermore, the results show that there is a direct relation between the number of bits in feedback signals and the inputs of the converter in the global error. Finally, a design criterion is given to choose the optimum width for each feedback signal, without wasting bits.

scholarly journals A Fractional-Order Discrete Noninvertible Map of Cubic Type: Dynamics, Control, and Synchronization

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-21
Author(s):  
Xiaojun Liu ◽  
Ling Hong ◽  
Lixin Yang ◽  
Dafeng Tang
Keyword(s):  
Fractional Order ◽  
Initial Conditions ◽  
Dimensional Space ◽  
Equilibrium Points ◽  
Three Dimensional ◽  
State Variables ◽  
Discrete Maps ◽  
The Stability ◽  
Control And Synchronization ◽  
Simultaneous Variation

In this paper, a new fractional-order discrete noninvertible map of cubic type is presented. Firstly, the stability of the equilibrium points for the map is examined. Secondly, the dynamics of the map with two different initial conditions is studied by numerical simulation when a parameter or a derivative order is varied. A series of attractors are displayed in various forms of periodic and chaotic ones. Furthermore, bifurcations with the simultaneous variation of both a parameter and the order are also analyzed in the three-dimensional space. Interior crises are found in the map as a parameter or an order varies. Thirdly, based on the stability theory of fractional-order discrete maps, a stabilization controller is proposed to control the chaos of the map and the asymptotic convergence of the state variables is determined. Finally, the synchronization between the proposed map and a fractional-order discrete Loren map is investigated. Numerical simulations are used to verify the effectiveness of the designed synchronization controllers.

FPAA-based implementation of fractional-order multidirectional multiscroll chaotic oscillators

2022 ◽  
pp. 341-374
Author(s):  
Alejandro Silva-Juarez ◽  
Esteban Tlelo-Cuautle ◽  
Luis Gerardo de la Fraga
Keyword(s):  
Fractional Order ◽  
Chaotic Oscillators
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