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Adaptive neural control design for nonlinear distributed parameter systems with persistent bounded disturbances.

Huai-Ning Wu¹, Han-Xiong Li

¹School of Automation Science and Electrical Engineering, Beihang University (formerly Beijing University of Aeronautics and Astronautics), Beijing, China. whn@buaa.edu.cn

IEEE Transactions on Neural Networks

|September 12, 2009

Summary

This summary is machine-generated.

This study introduces an adaptive neural network control for parabolic partial differential equations (PDEs) with unknown nonlinearities and disturbances. The method ensures stability and performance, demonstrated in catalytic rod temperature control.

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Closed-loop Neuro-robotic Experiments to Test Computational Properties of Neuronal Networks

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Published on: March 2, 2015

Area of Science:

Control Systems Engineering
Applied Mathematics
Artificial Intelligence

Background:

Parabolic partial differential equation (PDE) systems often face challenges with unknown nonlinearities and persistent bounded disturbances.
Existing control methods may struggle to guarantee performance and stability in such complex systems.
Adaptive control strategies are crucial for handling uncertainties in dynamic systems.

Purpose of the Study:

To propose an adaptive neural network (NN) control strategy for parabolic PDE systems.
To guarantee a specific L(infinity)-gain performance for the closed-loop system.
To address systems with unknown nonlinearities and persistent bounded disturbances.

Main Methods:

Application of the Galerkin method to reduce the PDE system to a low-order ordinary differential equation (ODE) model.
Development of an adaptive modal feedback controller using Lyapunov techniques and radial basis function (RBF) neural networks.
Formulation of the control problem as a linear matrix inequality (LMI) for optimization and constraint handling.

Main Results:

The proposed controller ensures semiglobal input-to-state practical stability (ISpS) for the closed-loop slow system.
Guaranteed L(infinity)-gain performance is achieved, bounding the effect of disturbances.
A suboptimal controller is obtained using LMI optimization, respecting control constraints.

Conclusions:

The adaptive NN control scheme effectively manages unknown nonlinearities and disturbances in parabolic PDE systems.
The controller guarantees semiglobal ISpS and L(infinity)-gain performance for the closed-loop PDE system.
Simulations on catalytic rod temperature control validate the proposed method's effectiveness.