scholarly journals Complex Dynamical Network Control for Trajectory Tracking Using Delayed Recurrent Neural Networks

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Jose P. Perez ◽  
Joel Perez Padron ◽  
Angel Flores Hemandez ◽  
Santiago Arroyo
Keyword(s):  
Neural Network ◽  
Dynamical System ◽  
Trajectory Tracking ◽  
Recurrent Neural Networks ◽  
Tracking Error ◽  
Network Control ◽  
Lyapunov Theory ◽  
Control Law ◽  
Complex Dynamical Network ◽  
Dynamical Network

In this paper, the problem of trajectory tracking is studied. Based on the V-stability and Lyapunov theory, a control law that achieves the global asymptotic stability of the tracking error between a delayed recurrent neural network and a complex dynamical network is obtained. To illustrate the analytic results, we present a tracking simulation of a dynamical network with each node being just one Lorenz’s dynamical system and three identical Chen’s dynamical systems.

Direct Adaptive Control of Underwater Vehicles using Neural Networks

2003 ◽  
Vol 9 (5) ◽  
pp. 605-619 ◽  
Author(s):  
Myung-Hyun Kim ◽  
Daniel J. Inman
Keyword(s):  
Neural Network ◽  
Adaptive Control ◽  
Network Architecture ◽  
Explicit Knowledge ◽  
Tracking Error ◽  
Network Control ◽  
Lyapunov Theory ◽  
Direct Adaptive Control ◽  
Neural Network Controller ◽  
Comparison Of The Results

A direct adaptive neural network controller is developed for a model of an underwater vehicle. A radial basis neural network and a multilayer neural network are used in the closed-loop to approximate the nonlinear vehicle dynamics. No prior off-line training phase and no explicit knowledge of the structure of the plant are required, and this scheme exploits the advantages of both neural network control and adaptive control. A control law and a stable on-line adaptive law are derived using the Lyapunov theory, and the convergence of the tracking error to zero and the boundedness of signals are guaranteed. A comparison of the results with different neural network architecture is made, and the performance of the controller is demonstrated by computer simulations.

Trajectory Tracking of a Spherical Robot Based on an RBF Neural Network

2011 ◽  
Vol 383-390 ◽  
pp. 631-637 ◽  
Author(s):  
Ming Hui Zheng ◽  
Qiang Zhan ◽  
Jin Kun Liu ◽  
Yao Cai
Keyword(s):  
Neural Network ◽  
Trajectory Tracking ◽  
Rbf Neural Network ◽  
Tracking Error ◽  
Lyapunov Theory ◽  
Pd Controller ◽  
Spherical Robot ◽  
Rule Based ◽  
Rbf Network ◽  
Spherical Mobile Robot

This paper deals with trajectory tracking problem of a spherical mobile robot, BHQ-1. First, a desired velocity is obtained by proposing a PD controller based on the kinematics. Then a PD controller with an RBF (Radial Basis Function) neural network is proposed based on the desired velocity and the inexact dynamics. The weights of the RBF network are designed with an adaptive rule based on the tracking error, and hence the network can compensate the uncertainties of the dynamics more effectively. Stability is presented via Lyapunov Theory and simulation results are provided to illustrate the tracking performance.

Adaptive Tracking in Mobile Robots With Input-Output Linearization

2014 ◽  
Vol 136 (5) ◽  
Author(s):  
Cesáreo Raimúndez ◽  
Alejandro F. Villaverde ◽  
Antonio Barreiro
Keyword(s):  
Neural Network ◽  
Mobile Robots ◽  
Trajectory Tracking ◽  
Tracking Error ◽  
Adaptive Controller ◽  
Lyapunov Theory ◽  
Input Output ◽  
External Perturbations ◽  
Neural Network Controller ◽  
Input Output Linearization

This paper presents a neural network adaptive controller for trajectory tracking of nonholonomic mobile robots. By defining a point to follow (look-ahead control), the path-following problem is solved with input-output linearization. A computed torque plus derivative (PD) controller and a dynamic inversion neural network controller are responsible for reducing tracking error and adapting to unmodeled external perturbations. The adaptive controller is implemented through a hidden layer feed-forward neural network, with weights updated in real time. The stability of the whole system is analyzed using Lyapunov theory, and control errors are proven to be bounded. Simulation results demonstrate the good performance of the proposed controller for trajectory tracking under external perturbations.

scholarly journals Research on Adaptive Trajectory Tracking Algorithm for a Quadrotor Based on Backstepping and the Sigma-Pi Neural Network

2019 ◽  
Vol 2019 ◽  
pp. 1-9
Author(s):  
Zhiming Chen ◽  
Kang Niu ◽  
Lei Li
Keyword(s):  
Neural Network ◽  
Trajectory Tracking ◽  
Tracking Control ◽  
Position Control ◽  
Tracking Error ◽  
Tracking Algorithm ◽  
Control Law ◽  
Matlab Simulation ◽  
Adaptive Tracking Control ◽  
Tracking Time

In this paper, adaptive tracking control is applied to improve performances of an underactuated quadrotor helicopter with respect to attitude and position control. Firstly, the dynamic model is presented. Then a new trajectory tracking algorithm is designed by using the sigma-pi neural network and backstepping. The paper designs the sigma-pi neural network compensation control law and gives the Lyapunov-type stability analysis. Then the corresponding numerical simulations are performed by using MATLAB. Simulation results are shown to demonstrate the effectiveness of the proposed control strategy, which could reduce tracking error, decrease tracking time, and improve the anti-interference ability of the system.

PD Control Law for Trajectory Tracking of Chaotic Pendulum

2013 ◽  
Vol 646 ◽  
pp. 208-215
Author(s):  
Joel P. Perez ◽  
Jose P. Perez ◽  
Francisco Rdz ◽  
Angel H. Flores
Keyword(s):  
Neural Network ◽  
Nonlinear System ◽  
Trajectory Tracking ◽  
Experimental Results ◽  
Control Law ◽  
Adaptive Neural Network ◽  
Pd Control ◽  
Dynamical Network ◽  
Analytical Results

This paper presents the application of trajectory tracking using the adaptive neural network to the double chaotic pendulum. The proposed controller structute is composed of a neural identifier and a PD Control. Experimental results with the chaotic pendulun shown the usefulness of the proposed approach. To verify the analytical results, an example of dynamical network is simulated and a theorem is proposed to ensure the tracking of the nonlinear system.

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

Recurrent Higher Order Neural Network Control for Output Trajectory Tracking with Neural Observers and Constrained Inputs

2010 ◽  
pp. 286-311 ◽  
Author(s):  
Luis J. Ricalde ◽  
Edgar N. Sanchez ◽  
Alma Y. Alanis
Keyword(s):  
Neural Network ◽  
Tracking Error ◽  
Network Control ◽  
Design Parameters ◽  
The Neural Network ◽  
Control Scheme ◽  
Output Trajectory ◽  
Error Dynamics ◽  
Adaptation Law ◽  
Constrained Inputs

This Chapter presents the design of an adaptive recurrent neural observer-controller scheme for nonlinear systems whose model is assumed to be unknown and with constrained inputs. The control scheme is composed of a neural observer based on Recurrent High Order Neural Networks which builds the state vector of the unknown plant dynamics and a learning adaptation law for the neural network weights for both the observer and identifier. These laws are obtained via control Lyapunov functions. Then, a control law, which stabilizes the tracking error dynamics is developed using the Lyapunov and the inverse optimal control methodologies . Tracking error boundedness is established as a function of design parameters.

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