scholarly journals Entropy Analysis and Neural Network-Based Adaptive Control of a Non-Equilibrium Four-Dimensional Chaotic System with Hidden Attractors

Entropy ◽  
2019 ◽  
Vol 21 (2) ◽  
pp. 156 ◽  
Author(s):  
Hadi Jahanshahi ◽  
Maryam Shahriari-Kahkeshi ◽  
Raúl Alcaraz ◽  
Xiong Wang ◽  
Vijay Singh ◽  
...  
Keyword(s):  
Neural Network ◽  
Adaptive Control ◽  
Chaotic System ◽  
Adaptive Learning ◽  
Control Method ◽  
Direct Method ◽  
Dynamical Behavior ◽  
Hidden Attractors ◽  
Uncertain Dynamics ◽  
Non Equilibrium

Today, four-dimensional chaotic systems are attracting considerable attention because of their special characteristics. This paper presents a non-equilibrium four-dimensional chaotic system with hidden attractors and investigates its dynamical behavior using a bifurcation diagram, as well as three well-known entropy measures, such as approximate entropy, sample entropy, and Fuzzy entropy. In order to stabilize the proposed chaotic system, an adaptive radial-basis function neural network (RBF-NN)–based control method is proposed to represent the model of the uncertain nonlinear dynamics of the system. The Lyapunov direct method-based stability analysis of the proposed approach guarantees that all of the closed-loop signals are semi-globally uniformly ultimately bounded. Also, adaptive learning laws are proposed to tune the weight coefficients of the RBF-NN. The proposed adaptive control approach requires neither the prior information about the uncertain dynamics nor the parameters value of the considered system. Results of simulation validate the performance of the proposed control method.

scholarly journals Infinitely Many Coexisting Attractors in No-Equilibrium Chaotic System

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
Qiang Lai ◽  
Paul Didier Kamdem Kuate ◽  
Huiqin Pei ◽  
Hilaire Fotsin
Keyword(s):  
Adaptive Control ◽  
Chaotic System ◽  
Physical Meaning ◽  
Control Method ◽  
Initial Conditions ◽  
Periodic Motions ◽  
Hidden Attractors ◽  
Coexisting Attractors ◽  
Dynamic Behaviors

This paper proposes a new no-equilibrium chaotic system that has the ability to yield infinitely many coexisting hidden attractors. Dynamic behaviors of the system with respect to the parameters and initial conditions are numerically studied. It shows that the system has chaotic, quasiperiodic, and periodic motions for different parameters and coexists with a large number of hidden attractors for different initial conditions. The circuit and microcontroller implementations of the system are given for illustrating its physical meaning. Also, the synchronization conditions of the system are established based on the adaptive control method.

Multiscroll Hyperchaotic System with Hidden Attractors and Its Circuit Implementation

2019 ◽  
Vol 29 (09) ◽  
pp. 1950117 ◽  
Author(s):  
Xin Zhang ◽  
Chunhua Wang
Keyword(s):  
Numerical Simulation ◽  
Adaptive Control ◽  
Theoretical Analysis ◽  
Chaotic System ◽  
Control Method ◽  
Hyperchaotic System ◽  
Circuit Implementation ◽  
Hidden Attractors ◽  
System A ◽  
Simulation Results

Based on the study on Jerk chaotic system, a multiscroll hyperchaotic system with hidden attractors is proposed in this paper, which has infinite number of equilibriums. The chaotic system can generate [Formula: see text] scroll hyperchaotic hidden attractors. The dynamic characteristics of the multiscroll hyperchaotic system with hidden attractors are analyzed by means of dynamic analysis methods such as Lyapunov exponents and bifurcation diagram. In addition, we have studied the synchronization of the system by applying an adaptive control method. The hardware experiment of the proposed multiscroll hyperchaotic system with hidden attractors is carried out using discrete components. The hardware experimental results are consistent with the numerical simulation results of MATLAB and the theoretical analysis results.

scholarly journals Real-Time Stripe Width Computation Using Back Propagation Neural Network for Adaptive Control of Line Structured Light Sensors

Sensors ◽  
2020 ◽  
Vol 20 (9) ◽  
pp. 2618 ◽  
Author(s):  
Jingbo Zhou ◽  
Laisheng Pan ◽  
Yuehua Li ◽  
Peng Liu ◽  
Lijian Liu
Keyword(s):  
Neural Network ◽  
Adaptive Control ◽  
Real Time ◽  
Exposure Time ◽  
Control Method ◽  
Structured Light ◽  
Back Propagation ◽  
Back Propagation Neural Network ◽  
Stripe Width ◽  
Accuracy Result

A line structured light sensor (LSLS) is generally constituted of a laser line projector and a camera. With the advantages of simple construction, non-contact, and high measuring speed, it is of great perspective in 3D measurement. For traditional LSLSs, the camera exposure time is usually fixed while the surface properties can be varied for different measurement tasks. This would lead to under/over exposure of the stripe images or even failure of the measurement. To avoid these undesired situations, an adaptive control method was proposed to modulate the average stripe width (ASW) within a favorite range. The ASW is first computed based on the back propagation neural network (BPNN), which can reach a high accuracy result and reduce the runtime dramatically. Then, the approximate linear relationship between the ASW and the exposure time was demonstrated via a series of experiments. Thus, a linear iteration procedure was proposed to compute the optimal camera exposure time. When the optimized exposure time is real-time adjusted, stripe images with the favorite ASW can be obtained during the whole scanning process. The smoothness of the stripe center lines and the surface integrity can be improved. A small proportion of the invalid stripe images further proves the effectiveness of the control method.

scholarly journals Adaptive PD Control Based on RBF Neural Network for a Wire-Driven Parallel Robot and Prototype Experiments

2019 ◽  
Vol 2019 ◽  
pp. 1-15 ◽  
Author(s):  
Yuqi Wang ◽  
Qi Lin ◽  
Xiaoguang Wang ◽  
Fangui Zhou
Keyword(s):  
Neural Network ◽  
Adaptive Control ◽  
Control Method ◽  
Rbf Neural Network ◽  
Approximation Error ◽  
Wind Tunnel Test ◽  
Parallel Robot ◽  
Network Control ◽  
Pd Control ◽  
Control Scheme

An adaptive PD control scheme is proposed for the support system of a wire-driven parallel robot (WDPR) used in a wind tunnel test. The control scheme combines a PD control and an adaptive control based on a radial basis function (RBF) neural network. The PD control is used to track the trajectory of the end effector of the WDPR. The experimental environment, the external disturbances, and other factors result in uncertainties of some parameters for the WDPR; therefore, the RBF neural network control method is used to approximate the parameters. An adaptive control algorithm is developed to reduce the approximation error and improve the robustness and control precision of the WDPR. It is demonstrated that the closed-loop system is stable based on the Lyapunov stability theory. The simulation results show that the proposed control scheme results in a good performance of the WDPR. The experimental results of the prototype experiments show that the WDPR operates on the desired trajectory; the proposed control method is correct and effective, and the experimental error is small and meets the requirements.

The Adaptive Control of Grinding Force of CNC Cam Grinder Based on Neural Network

2012 ◽  
Vol 217-219 ◽  
pp. 2051-2055
Author(s):  
Ming Li Xie ◽  
Ling Lu
Keyword(s):  
Neural Network ◽  
Adaptive Control ◽  
Control Method ◽  
Metal Removal ◽  
Removal Rate ◽  
Grinding Force ◽  
Control Measures ◽  
Numerical Control ◽  
Grinding Wheel ◽  
Grinding Process

In the process of cam grinding, the fluctuation of grinding force can lead to the abnormal wear of the grinding wheel, the decrease of the grinding surface quality and even the damage of the grinding process system. The paper took the grinding process of numerical control cam grinding machine as research subject, the grinding force mathematical model was built, the indirect test and control measures were researched and an adaptive control method based on neural network was proposed and applied to the grinding force control of the cam grinding process. At last, the controller was designed and the grinding simulation was performed with MATLAB, which proved that the system could solve the fluctuation of grinding force during the process of cam grinding and the controller was equipped with good dynamic characteristic. The results indicate that the method can realize the purpose of optimal metal removal rate and enhance the grinding quality of cams.

On Complete Control and Synchronization of Zhang Chaotic System with Uncertain Parameters using Adaptive Control Method

2018 ◽  
Vol 7 (1) ◽  
pp. 45-50 ◽  
Author(s):  
Hamed Tirandaz
Keyword(s):  
Adaptive Control ◽  
Chaotic System ◽  
Control Method ◽  
Three Dimensional ◽  
Parameters Estimation ◽  
Control Law ◽  
Complete Control ◽  
Synchronization Problem ◽  
Control And Synchronization ◽  
Adaptive Control Law

Abstract Chaos control and synchronization of chaotic systems is seemingly a challenging problem and has got a lot of attention in recent years due to its numerous applications in science and industry. This paper concentrates on the control and synchronization problem of the three-dimensional (3D) Zhang chaotic system. At first, an adaptive control law and a parameter estimation law are achieved for controlling the behavior of the Zhang chaotic system. Then, non-identical synchronization of Zhang chaotic system is provided with considering the Lü chaotic system as the follower system. The synchronization problem and parameters identification are achieved by introducing an adaptive control law and a parameters estimation law. Stability analysis of the proposed method is proved by the Lyapanov stability theorem. In addition, the convergence of the estimated parameters to their truly unknown values are evaluated. Finally, some numerical simulations are carried out to illustrate and to validate the effectiveness of the suggested method.

scholarly journals A Novel Memductor-Based Chaotic System and Its Applications in Circuit Design and Experimental Validation

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-17 ◽  
Author(s):  
Li Xiong ◽  
Yanjun Lu ◽  
Yongfang Zhang ◽  
Xinguo Zhang
Keyword(s):  
Chaotic System ◽  
Secure Communication ◽  
Experimental Validation ◽  
Control Method ◽  
Dynamical Behavior ◽  
Chaotic Circuit ◽  
Initial State ◽  
Error System ◽  
The Stability ◽  
The Mathematical Model

This paper is expected to introduce a novel memductor-based chaotic system. The local dynamical entities, such as the basic dynamical behavior, the divergence, the stability of equilibrium set, and the Lyapunov exponent, are all investigated analytically and numerically to reveal the dynamic characteristics of the new memductor-based chaotic system as the system parameters and the initial state of memristor change. Subsequently, an active control method is derived to study the synchronous stability of the novel memductor-based chaotic system through making the synchronization error system asymptotically stable at the origin. Further to these, a memductor-based chaotic circuit is designed, realized, and applied to construct a new memductor-based secure communication circuit by employing the basic electronic components and memristor. Furthermore, the design principle of the memductor-based chaotic circuit is thoroughly analyzed and the concept of “the memductor-based chaotic circuit defect quantification index” is proposed for the first time to verify whether the chaotic output is consistent with the mathematical model. A good qualitative agreement is shown between the simulations and the experimental validation results.

Dynamical analysis, FPGA implementation and synchronization for secure communication of new chaotic system with hidden and coexisting attractors

2021 ◽  
Author(s):  
Qiang Lai ◽  
Ziling Wang ◽  
Paul Didier Kamdem Kuate
Keyword(s):  
Chaotic System ◽  
Secure Communication ◽  
Analog Circuit ◽  
Control Method ◽  
Simulation Analysis ◽  
Period Doubling ◽  
Fpga Implementation ◽  
Dynamical Analysis ◽  
Hidden Attractors ◽  
Coexisting Attractors

This paper proposes an interesting autonomous chaotic system with hidden attractors and coexisting attractors. The system has no equilibrium, one equilibrium, three equilibria and line equilibria for different parameter regions. The existence of hidden attractors and coexisting attractors of the system has been revealed by using simulation analysis. The bifurcation diagram shows the period-doubling bifurcation route to chaos with the variation of parameters. The analog circuit and FPGA implementation of the system are presented. The synchronization for secure communication of the system is investigated. The synchronization conditions are established by using the adaptive control method.

Sign in / Sign up

Export Citation Format

Share Document