Master-Slave Synchronization for Trajectory Tracking Error Using Fractional Order Time-Delay Recurrent Neural Networks via Krasovskii-Lur’e Functional for Chua’s Circuit

2021 ◽  
Vol 25 (3) ◽  
Author(s):  
J. Javier Perez D. ◽  
José Paz Pérez Padron ◽  
Atilano Martínez Huerta ◽  
Joel Pérez Padron
Keyword(s):  
Neural Networks ◽  
Time Delay ◽  
Fractional Order ◽  
Trajectory Tracking ◽  
Recurrent Neural Networks ◽  
Tracking Error ◽  
Chua’S Circuit ◽  
Chua's Circuit

scholarly journals Trajectory tracking error using fractional order time-delay recurrent neural networks using Krasovskii-Lur’e functional for Chua’s circuit via inverse optimal control

2019 ◽  
Vol 66 (1) ◽  
pp. 98
Author(s):  
J. Perez Padrón ◽  
J.P. Pérez Padrón ◽  
C.F. Mendez-Barrios ◽  
E.J. Gonzalez-Galvan
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Optimal Control ◽  
Time Delay ◽  
Fractional Order ◽  
Trajectory Tracking ◽  
Recurrent Neural Networks ◽  
Chaos Synchronization ◽  
Tracking Error ◽  
Inverse Optimal Control

This paper presents an application of a Fractional Order Time Delay Neural Networks to chaos synchronization. The two main methodologies, on which the approach is based, are fractional order time-delay recurrent neural networks and the fractional order  inverse optimal control for nonlinear systems. The problem of trajectory tracking is studied, based on the fractional order Lyapunov-Krasovskii and Lur’e theory, that achieves the global asymptotic stability of the tracking error between a delayed recurrent neural network and a reference function is obtained. The method is illustrated for the synchronization, the analytic results we present a trajectory tracking simulation of a fractional order time-delay dynamical network and the Fractional Order Chua’s circuits

Learning of Chua's circuit attractors by locally recurrent neural networks

2001 ◽  
Vol 12 (11) ◽  
pp. 2109-2115 ◽  
Author(s):  
Barbara Cannas ◽  
Silvano Cincotti ◽  
Michele Marchesi ◽  
Fabrizio Pilo
Keyword(s):  
Neural Networks ◽  
Recurrent Neural Networks ◽  
Chua’S Circuit ◽  
Chua's Circuit ◽  
Locally Recurrent

scholarly journals Adaptive fractional PID control of biped robots with time-delayed feedback

2019 ◽  
Vol 277 ◽  
pp. 01007 ◽  
Author(s):  
◽  
P Joel Perez ◽  
Jose P. Perez ◽  
Mayra Flores Guerrero ◽  
Ruben Perez P. ◽  
...  
Keyword(s):  
Neural Networks ◽  
Time Delay ◽  
Fractional Order ◽  
Degrees Of Freedom ◽  
Tracking Error ◽  
Reference Signal ◽  
Biped Robot ◽  
Control Laws ◽  
Adaptive Neural Networks ◽  
Fractional Order Pid

This paper presents the application of Fractional Order Time- Delay adaptive neural networks to the trajectory tracking for chaos synchronization between Fractional Order delayed plant, reference and Fractional Order Time-Delay adaptive neural networks. The proposed new control scheme is applied via simulations to control of a 4-DOF Biped Robot [1]. The main methodologies, on which the approach is based, are Fractional Order PID the Fractional Order Lyapunov-Krasovskii functions methodology. The structure of the biped robot is designed with two degrees of freedom per leg, corresponding to the knee and hip joints. Since torso and ankle are not considered, it is obtained a 4-DOF system, and each leg, we try to force this biped robot to track a reference signal given by undamped Duffing equation. The tracking error is globally asymptotically stabilized by two control laws derived based on a Lyapunov-Krasovski functional.

Bifurcation analysis of a fractional order time-delay Chua’s circuit based on coupled memristors

2019 ◽  
Vol 33 (30) ◽  
pp. 1950366
Author(s):  
Dawei Ding ◽  
Yecui Weng ◽  
Yongbing Hu ◽  
Zongli Yang
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Coupling Strength ◽  
Coupling Effect ◽  
Phase Portraits ◽  
Chua’S Circuit ◽  
Chua's Circuit ◽  
Integer Order ◽  
Dynamical Characteristics ◽  
Memristive System

In this paper, a fractional-order (and an integer-order) chaotic system, obtained from Chua’s circuit by substituting Chua’s diode with two active coupled memristors (MRs) characterized by quadratic nonlinearity, is introduced to probe the memristive coupling effect. Two MRs connected in parallel are coupled by the flux. For the integer-order memristive system, the dynamical characteristics depending on the coupling strength coefficient between MRs without changing the circuit parameters are illustrated theoretically and numerically by using phase portraits, time domain diagram, bifurcation diagram and the Lyapunov diagram. Then based on the Adams–Bashforth–Moulton algorithm, the study of dynamic behavior of the fractional-order memristive system containing the time-delay reveals that appropriately setting the coupling strength between MRs generates more interesting attractors that differ from its integer-order counterpart. Besides, the effects of the order and the time-delay on dynamics are discussed briefly. Finally, the simulation results verify the validity of the theoretical analysis.

Long-lead seasonal rainfall forecasting using time-delay recurrent neural networks: a case study

2007 ◽  
Vol 22 (2) ◽  
pp. 229-241 ◽  
Author(s):  
Mohammad Karamouz ◽  
Saman Razavi ◽  
Shahab Araghinejad
Keyword(s):  
Neural Networks ◽  
Time Delay ◽  
Recurrent Neural Networks ◽  
Seasonal Rainfall ◽  
Rainfall Forecasting

Dissipativity and stability analysis of fractional-order complex-valued neural networks with time delay

2017 ◽  
Vol 86 ◽  
pp. 42-53 ◽  
Author(s):  
G. Velmurugan ◽  
R. Rakkiyappan ◽  
V. Vembarasan ◽  
Jinde Cao ◽  
Ahmed Alsaedi
Keyword(s):  
Neural Networks ◽  
Stability Analysis ◽  
Time Delay ◽  
Fractional Order ◽  
Order Complex ◽  
Complex Valued
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