Adaptive Neural Control Design for Nonlinear Distributed Parameter Systems With Persistent Bounded Disturbances

In this paper, an adaptive neural network (NN) control with a guaranteed L infin -gain performance is proposed for a class of parabolic partial differential equation (PDE) systems with unknown nonlinearities and persistent bounded disturbances. Initially, Galerkin method is applied to the PDE system...

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Bibliographic Details
Published in:IEEE transactions on neural networks Vol. 20; no. 10; pp. 1630 - 1644
Main Authors: WU, Huai-Ning, LI, Han-Xiong
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.10.2009
Institute of Electrical and Electronics Engineers
Subjects:
Adaptative systems
Adaptive control
Adaptive systems
Algorithms
Applied sciences
Artificial intelligence
Computer science; control theory; systems
Computer Simulation
Connectionism. Neural networks
Control design
Control nonlinearities
Control system analysis
Control system synthesis
Control systems
Control theory. Systems
Distributed parameter systems
Exact sciences and technology
Feedback
input-to-state stability (ISS)
linear matrix inequality (LMI)
Models, Theoretical
neural network (NN)
Neural networks
Neural Networks (Computer)
Nonlinear control systems
Nonlinear Dynamics
Programmable control
Temperature control
{\cal L}_{\infty} -gain control
Differential equation
Non linear control
Lyapunov method
Feedback regulation
Control synthesis
L
Adaptive control
Modeling
Partial differential equation
Optimization
Control constraint
Parabolic equation
Linear matrix inequality
neural network (NN)
distributed parameter systems
Distributed parameter system
linear matrix inequality (LMI)
Neural network
Non linear system
Closed feedback
Radial basis function
Galerkin-Petrov method
Neurocontrollers
Upper bound
Input to state stability
input-to-state stability (ISS)
Distributed control
Derivative
gain control
Galerkin method
Temperature control
Lyapunov function
ISSN:1045-9227, 1941-0093, 1941-0093
Online Access:Get full text
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Summary:In this paper, an adaptive neural network (NN) control with a guaranteed L infin -gain performance is proposed for a class of parabolic partial differential equation (PDE) systems with unknown nonlinearities and persistent bounded disturbances. Initially, Galerkin method is applied to the PDE system to derive a low-order ordinary differential equation (ODE) system that accurately describes the dynamics of the dominant (slow) modes of the PDE system. Subsequently, based on the low-order slow model and the Lyapunov technique, an adaptive modal feedback controller is developed such that the closed-loop slow system is semiglobally input-to-state practically stable (ISpS) with an L infin -gain performance. In the proposed control scheme, a radial basis function (RBF) NN is employed to approximate the unknown term in the derivative of the Lyapunov function due to the unknown system nonlinearities. The outcome of the adaptive L infin -gain control problem is formulated as a linear matrix inequality (LMI) problem. Moreover, by using the existing LMI optimization technique, a suboptimal controller is obtained in the sense of minimizing an upper bound of the L infin -gain, while control constraints are respected. Furthermore, it is shown that the proposed controller can ensure the semiglobal input-to-state practical stability and L infin -gain performance of the closed-loop PDE system. Finally, by applying the developed design method to the temperature profile control of a catalytic rod, the achieved simulation results show the effectiveness of the proposed controller.
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ISSN:1045-9227
1941-0093
1941-0093
DOI:10.1109/TNN.2009.2028887