A new neural network model for the feedback stabilization of nonlinear systems

2008 ◽  
Vol 9 (8) ◽  
pp. 1015-1023 ◽  
Author(s):  
Mei-qin Liu ◽  
Sen-lin Zhang ◽  
Gang-feng Yan
Keyword(s):  
Neural Network ◽  
Nonlinear Systems ◽  
Network Model ◽  
Neural Network Model ◽  
Feedback Stabilization

DYNAMIC OUTPUT FEEDBACK STABILIZATION FOR NONLINEAR SYSTEMS BASED ON STANDARD NEURAL NETWORK MODELS

2006 ◽  
Vol 16 (04) ◽  
pp. 305-317 ◽  
Author(s):  
MEIQIN LIU
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Nonlinear Systems ◽  
Network Model ◽  
Neural Network Model ◽  
Output Feedback ◽  
Control Design ◽  
Feedback Stabilization ◽  
Dynamic Output Feedback ◽  
Dynamic Output

A neural-model-based control design for some nonlinear systems is addressed. The design approach is to approximate the nonlinear systems with neural networks of which the activation functions satisfy the sector conditions. A novel neural network model termed standard neural network model (SNNM) is advanced for describing this class of approximating neural networks. Full-order dynamic output feedback control laws are then designed for the SNNMs with inputs and outputs to stabilize the closed-loop systems. The control design equations are shown to be a set of linear matrix inequalities (LMIs) which can be easily solved by various convex optimization algorithms to determine the control signals. It is shown that most neural-network-based nonlinear systems can be transformed into input-output SNNMs to be stabilization synthesized in a unified way. Finally, some application examples are presented to illustrate the control design procedures.

scholarly journals A Multilayer Feed Forward Small-World Neural Network Controller and Its Application on Electrohydraulic Actuation System

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Xiaohu Li ◽  
Feng Xu ◽  
Jinhua Zhang ◽  
Sunan Wang
Keyword(s):  
Neural Network ◽  
Nonlinear Systems ◽  
Network Model ◽  
Neural Network Model ◽  
Small World ◽  
Random Disturbance ◽  
Proportional Integral ◽  
Neural Network Controller ◽  
Actuation System ◽  
Network Controller

Being difficult to attain the precise mathematical models, traditional control methods such as proportional integral (PI) and proportional integral differentiation (PID) cannot meet the demands for real time and robustness when applied in some nonlinear systems. The neural network controller is a good replacement to overcome these shortcomings. However, the performance of neural network controller is directly determined by neural network model. In this paper, a new neural network model is constructed with a structure topology between the regular and random connection modes based on complex network, which simulates the brain neural network as far as possible, to design a better neural network controller. Then, a new controller is designed under small-world neural network model and is investigated in both linear and nonlinear systems control. The simulation results show that the new controller basing on small-world network model can improve the control precision by 30% in the case of system with random disturbance. Besides the good performance of the new controller in tracking square wave signals, which is demonstrated by the experiment results of direct drive electro-hydraulic actuation position control system, it works well on anti-interference performance.

AN LMI APPROACH TO DESIGN H∞ CONTROLLERS FOR DISCRETE-TIME NONLINEAR SYSTEMS BASED ON UNIFIED MODELS

2008 ◽  
Vol 18 (05) ◽  
pp. 443-452 ◽  
Author(s):  
MEIQIN LIU ◽  
SENLIN ZHANG
Keyword(s):  
Neural Network ◽  
Nonlinear Systems ◽  
Network Model ◽  
Discrete Time ◽  
Neural Network Model ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Control Law ◽  
Closed Loop System ◽  
External Disturbances

A unified neural network model termed standard neural network model (SNNM) is advanced. Based on the robust L2 gain (i.e. robust H∞ performance) analysis of the SNNM with external disturbances, a state-feedback control law is designed for the SNNM to stabilize the closed-loop system and eliminate the effect of external disturbances. The control design constraints are shown to be a set of linear matrix inequalities (LMIs) which can be easily solved by various convex optimization algorithms (e.g. interior-point algorithms) to determine the control law. Most discrete-time recurrent neural network (RNNs) and discrete-time nonlinear systems modelled by neural networks or Takagi and Sugeno (T–S) fuzzy models can be transformed into the SNNMs to be robust H∞ performance analyzed or robust H∞ controller synthesized in a unified SNNM's framework. Finally, some examples are presented to illustrate the wide application of the SNNMs to the nonlinear systems, and the proposed approach is compared with related methods reported in the literature.

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