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Event-Triggered Adaptive Neural Network Control of Manipulators with Model-Based Weights Initialization Method

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Abstract

In the paper, a novel controller is proposed to reach better control performance for manipulator system with unknown dynamics. We notice the initial weights of neural network may have influence to control performance in neural network controller. A casual selection of the initial weights may cause poorer production quality and result in consumption of more energy. A natural way is to give neural network values close to the ideal values, which is developed through estimating system parameters by common adaptive controller. In the proposed controller, precautions are considered in case of large tracking error, neural network approximating capability is ensured, input dimension is reduced and a novel weights decay term is given. Simulation and experiment results show that these techniques result in improvement in accuracy and saving of energy.

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Abbreviations

\({\mathbb{R}}\) :

Set of real numbers

0n :

n-Dimensional null vector

1 m×n :

m × n-Dimensional ones matrix

I n :

n-Dimensional identity matrix

σ(·):

Sigmoid function

tanh (·):

Hyperbolic function

H(·):

Right-continuous Heaviside function

δ(·):

Dirac delta function

\(\bar{\sigma }\left( x \right)\) :

[1, σ(x)T]T

\(\bar{\sigma }^{\prime}\left( x \right)\) :

[0n, diag(σ′(x))]

⊗ :

Kronecher product

⊙ :

Hadmard product

Tr(A):

Trace of matrix A

‖A‖:

Frobenius norm of matrix A

min (A):

Minimum value of matrix A

max (A):

Maximum value of matrix A

λmin(A):

Minimum eigenvalue of matrix A

λmax(A):

Maximum eigenvalue of matrix A

A > ( ≥ )0:

Matrix A is positive (semi-)definite

\({\text{Proj}}\left( {A,b,c} \right)\) :

cH( - c)H(‖A‖ - b)A/‖A‖2

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Nos. 91748205, 11772229, 11872277) and the Fundamental Research Funds for the Central Universities. The authors thank the reviewers for their valuable suggestions to improve the quality of the paper.

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Authors and Affiliations

  1. School of Aerospace Engineering and Applied Mechanics, Tongji University, 1239 Siping Road, Shanghai, China

    Naijing Jiang, Jian Xu & Shu Zhang

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  1. Naijing Jiang
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  2. Jian Xu
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Correspondence to Shu Zhang.

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Jiang, N., Xu, J. & Zhang, S. Event-Triggered Adaptive Neural Network Control of Manipulators with Model-Based Weights Initialization Method. Int. J. of Precis. Eng. and Manuf.-Green Tech. 7, 443–454 (2020). https://doi.org/10.1007/s40684-019-00095-4

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