Adaptive Neural Boundary Control Design for Nonlinear Flexible Distributed Parameter Systems

This paper proposes an adaptive neural boundary feedback control design for a nonlinear flexible distributed parameter system described by a nonuniform wave equation containing an unknown nonlinear function in the boundary conditions. In the proposed design method, a radial-basis-function neural net...

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Bibliographic Details
Published in:IEEE transactions on control systems technology 2019-09, Vol.27 (5), p.2085-2099
Main Authors: Wang, Jun-Wei, Liu, Ya-Qiang, Sun, Chang-Yin
Format: Article
Language:English
Subjects:
Adaptive control
Adaptive systems
Artificial neural networks
Boundary conditions
Boundary control
Computer simulation
Control design
Distributed parameter systems
Euler-Bernoulli beams
Euler–Bernoulli beam equation
Feedback control
Liapunov direct method
Mathematical model
Mathematical models
Neural networks
neural networks (NNs)
Nonlinear control
Nonlinear systems
Propagation
Radial basis function
Stability analysis
wave equation
Wave equations
Weight
Well posed problems
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Summary:This paper proposes an adaptive neural boundary feedback control design for a nonlinear flexible distributed parameter system described by a nonuniform wave equation containing an unknown nonlinear function in the boundary conditions. In the proposed design method, a radial-basis-function neural network (NN) with an adaptive weight update law is used to approximate the unknown nonlinear term. By using this adaptive NN, an adaptive boundary feedback controller is constructed to ensure that the resulting closed-loop system is practically exponentially stable. The closed-loop stability of the system is analyzed by the Lyapunov direct method and technique of integration by parts, and the update law of an NN weight vector is determined simultaneously. The closed-loop well-posedness analysis is also provided by applying the C_{0} -semigroup approach. Moreover, the proposed design method is extended for a nonlinear flexible distributed parameter system modeled by a nonuniform Euler-Bernoulli beam equation containing an unknown nonlinear function in the boundary conditions. Finally, extensive numerical simulation results are given to demonstrate the performance of the proposed adaptive neural boundary control design method.
ISSN:1063-6536
1558-0865
DOI:10.1109/TCST.2018.2849072