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 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.

Learning Control of Time-Delay Chaotic Systems and its Applications

1998 ◽  
Vol 08 (12) ◽  
pp. 2457-2465 ◽  
Author(s):  
Keiji Konishi ◽  
Hideki Kokame
Keyword(s):  
Control System ◽  
Time Delay ◽  
Chaotic System ◽  
Numerical Experiments ◽  
Chaotic Systems ◽  
Learning Control ◽  
Uncertain Information ◽  
Stable Orbit ◽  
One Dimensional ◽  
Theoretical Results

The present paper proposes a learning control system that automatically stabilizes one-dimensional time-delayed chaotic systems. We give a systematic procedure to design the control system using a few pieces of uncertain information on the chaotic system. Furthermore, this control system can be applied to a technique that moves a stable orbit of nonchaotic systems to coexistent unstable points and stabilizes the moving orbit onto these unstable points. To check the theoretical results, we demonstrate some numerical experiments.

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.

Synchronization of Continuous Scalar Chaotic Signal from Uncertain Chaotic System

2013 ◽  
Vol 816-817 ◽  
pp. 843-846
Author(s):  
Jing Wang ◽  
Hui Zhong
Keyword(s):  
Canonical Form ◽  
Chaotic System ◽  
Chaotic Systems ◽  
System Simulation ◽  
Chaotic Signal ◽  
Response System ◽  
Synchronization Scheme

This paper presents the synchronizing problem of scalar chaotic signal. A class of nonlinear chaotic systems is discussed which has unknown part in model. The proposed approach is based on canonical form of the response system. Simulation result shows the effectiveness of our synchronization scheme.

Rapid iterative learning algorithm of nonlinear time-delay system with initial deviation

2020 ◽  
pp. 002072092094057
Author(s):  
Xiaoyan Cheng ◽  
Hongbin Wang ◽  
Qinzhao Wang ◽  
Shaochan Feng
Keyword(s):  
Time Delay ◽  
Trajectory Tracking ◽  
Learning Algorithm ◽  
Tracking Error ◽  
Iterative Learning ◽  
Forgetting Factor ◽  
Initial State ◽  
Trajectory Tracking Control ◽  
Joint Rotation ◽  
Variable Forgetting Factor

A rapid iterative learning control algorithm with variable forgetting factor is applied for a class of nonlinear system with initial error and time-delay. This algorithm eliminats the limitation that the initial state should be reset to the expected one or fixed value at the start of iteration in the learning process of conventional algorithms. The error and the differences between two adjacent error is adopted to correct the controller avoiding the unstable influence of the derivative for PD type algorithm and the available information is fully used to increase convergence rate. Furthermore variable forgetting factor introduced guaranteed a fast convergence of trajectory tracking error Then, with applying the rapid algorithm to the trajectory tracking control of manipulator, the learning speed and tracking performance are both greatly improved. Meanwhile, the control strategy is proposed for the limitation of each joint rotation. The convergence of the method is also proved theoretically. Finally, simulation results illustrates the effectiveness and the real-time ability of the proposed way.

scholarly journals Synthetic Jet Actuator-Based Aircraft Tracking Using a Continuous Robust Nonlinear Control Strategy

2017 ◽  
Vol 2017 ◽  
pp. 1-13
Author(s):  
N. Ramos-Pedroza ◽  
W. MacKunis ◽  
M. Reyhanoglu
Keyword(s):  
Nonlinear Control ◽  
Trajectory Tracking ◽  
Parameter Uncertainty ◽  
Tracking Error ◽  
Synthetic Jet ◽  
Parameter Estimates ◽  
Control Law ◽  
Robust Nonlinear Control ◽  
Trajectory Tracking Control ◽  
Nonlinear Control Law

A robust nonlinear control law that achieves trajectory tracking control for unmanned aerial vehicles (UAVs) equipped with synthetic jet actuators (SJAs) is presented in this paper. A key challenge in the control design is that the dynamic characteristics of SJAs are nonlinear and contain parametric uncertainty. The challenge resulting from the uncertain SJA actuator parameters is mitigated via innovative algebraic manipulation in the tracking error system derivation along with a robust nonlinear control law employing constant SJA parameter estimates. A key contribution of the paper is a rigorous analysis of the range of SJA actuator parameter uncertainty within which asymptotic UAV trajectory tracking can be achieved. A rigorous stability analysis is carried out to prove semiglobal asymptotic trajectory tracking. Detailed simulation results are included to illustrate the effectiveness of the proposed control law in the presence of wind gusts and varying levels of SJA actuator parameter uncertainty.

PROJECTIVE SYNCHRONIZATION OF DIFFERENT CHAOTIC SYSTEMS WITH NONLINEARITY INPUTS

2012 ◽  
Vol 26 (11) ◽  
pp. 1250059 ◽  
Author(s):  
YUJUN NIU ◽  
XINGYUAN WANG
Keyword(s):  
Chaotic Systems ◽  
Control Method ◽  
Sliding Mode ◽  
External Noise ◽  
Projective Synchronization ◽  
Adaptive Technique ◽  
Noise Disturbances ◽  
Different Chaotic Systems ◽  
Synchronization Scheme ◽  
The Given

In this paper, projective synchronization of different chaotic systems is studied, in the presence of uncertainties of system parameter variation, external noise disturbance and nonlinearity inputs. Using adaptive technique, sliding mode control method and pole assignment technique, an adaptive projective synchronization scheme is proposed to ensure the drive system and the response system with nonlinearity inputs can be rapidly synchronized up to the given scaling factor, without requiring the bounds of the system uncertainties and external noise disturbances be known in advance. The results of numerical simulation further verify the effectiveness and feasibility of the proposed scheme.

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.

Dynamics and Trajectory Tracking Control of a Two-Link Robot Manipulator

2004 ◽  
Vol 10 (10) ◽  
pp. 1415-1440 ◽  
Author(s):  
Anthony Green ◽  
Jurek Z. Sasiadek
Keyword(s):  
Fuzzy Logic ◽  
Time Delay ◽  
Inverse Dynamics ◽  
Position Control ◽  
Robot Manipulator ◽  
Phase Response ◽  
Control Law ◽  
Minimum Phase ◽  
Linear Quadratic ◽  
Trajectory Tracking Control

Operational problems with robot manipulators in space relate to several factors, most importantly, structural flexibility and subsequent difficulties with their position control. In this paper we present control methods for endpoint tracking of a 12.6 × 12.6m2 trajectory by a two-link robot manipulator. Initially, a manipulator with rigid links is modeled using inverse dynamics, a linear quadratic regulator and fuzzy logic schemes actuated by a Jacobian transpose control law computed using dominant cantilever and pinned-pinned assumed mode frequencies. The inverse dynamics model is pursued further to study a manipulator with flexible links where nonlinear rigid-link dynamics are coupled with dominant assumed modes for cantilever and pinned-pinned beams. A time delay in the feedback control loop represents elastic wave travel time along the links to generate non-minimum phase response. A time delay acting on control commands ameliorates non-minimum phase response. Finally, a fuzzy logic system outputs a variable to adapt the control law in response to elastic deformation inputs. Results show greater endpoint position control accuracy using a flexible inverse dynamics robot model combined with a fuzzy logic adapted control law and time delays than could be obtained for the rigid dynamics models.

scholarly journals Adaptive - Synchronization of Fractional-Order Chaotic Systems with Nonidentical Structures

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Li-xin Yang ◽  
Wan-sheng He
Keyword(s):  
Adaptive Control ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Chaotic Systems ◽  
Control Technique ◽  
Adaptive Synchronization ◽  
Fractional Order Systems ◽  
The Stability ◽  
Different Chaotic Systems ◽  
Theoretical Results

This paper investigates the adaptive - synchronization of the fractional-order chaotic systems with nonidentical structures. Based on the stability of fractional-order systems and adaptive control technique, a general formula for designing the controller and parameters update law is proposed to achieve adaptive - synchronization between two different chaotic systems with different structures. The effective scheme parameters identification and - synchronization of chaotic systems can be realized simultaneously. Furthermore, two typical illustrative numerical simulations are given to demonstrate the effectiveness of the proposed scheme, for each case, we design the controller and parameter update laws in detail. The numerical simulations are performed to verify the effectiveness of the theoretical results.

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