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Neural-network approximation of piecewise continuous functions: application to friction compensation
1Signalogic Inc., Dallas, TX.
IEEE Transactions on Neural Networks
|February 5, 2008
Summary
This study introduces a novel neural network (NN) structure designed to approximate nonsmooth functions common in industrial control systems. The enhanced NN effectively compensates for nonlinearities like friction in robotic systems.
Area of Science:
- Control Systems Engineering
- Artificial Intelligence
- Robotics
Background:
- The universal approximation property of neural networks (NNs) is crucial for control but typically proven for continuous functions.
- Real-world industrial control systems often involve nonsmooth functions (e.g., friction, deadzone, backlash), where approximation results are limited.
- Existing methods using smooth activation functions struggle to accurately approximate piecewise continuous functions, requiring excessive resources and yielding suboptimal results.
Purpose of the Study:
- To develop a novel neural network structure capable of approximating piecewise continuous functions prevalent in motion control actuator nonlinearities.
- To address the limitations of current NN approaches in handling nonsmooth functions like friction, deadzone, and backlash.
- To demonstrate the application of this enhanced NN for friction compensation in robotic systems.
Main Methods:
- Introduced a modified NN architecture incorporating standard sigmoid activation neurons alongside new neurons with nonsmooth 'jump approximation basis functions'.
- Defined two types of nonsmooth jump approximation basis functions: polynomial-like and sigmoid-like.
- Applied the novel NN structure to rigid-link robotic systems exhibiting friction nonlinearities.
Main Results:
- The proposed NN structure effectively approximates any piecewise continuous function with a finite number of known discontinuities.
- Demonstrated successful application of the augmented NN for friction compensation in robotic systems.
- The enhanced NN overcomes the limitations of smooth activation functions in approximating nonsmooth nonlinearities.
Conclusions:
- The novel NN with jump approximation basis functions provides a powerful tool for modeling and controlling systems with nonsmooth nonlinearities.
- This approach offers improved performance for friction compensation in industrial control and robotics.
- The study advances the capability of neural networks in handling complex, real-world control challenges.
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