Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology
Constructive Approximation of Discontinuous Functions by Neural Networks
Neural Processing Letters
Adaptive growing-and-pruning neural network control for a linear piezoelectric ceramic motor
Engineering Applications of Artificial Intelligence
Adaptive stick-slip friction and backlash compensation using dynamic fuzzy logic system
Applied Soft Computing
IEEE Transactions on Neural Networks
A performance driven methodology for cancelable face templates generation
Pattern Recognition
A simple nonlinear proportional-derivative controller for friction compensation
ROBIO'09 Proceedings of the 2009 international conference on Robotics and biomimetics
Adaptive wavelet neural network friction compensation of mechanical systems
ISNN'06 Proceedings of the Third international conference on Advnaces in Neural Networks - Volume Part II
On the approximation capabilities of hard limiter feedforward neural networks
SETN'10 Proceedings of the 6th Hellenic conference on Artificial Intelligence: theories, models and applications
Compensating modeling and control for friction using RBF adaptive neural networks
ISNN'05 Proceedings of the Second international conference on Advances in Neural Networks - Volume Part III
Active control of friction self-excited vibration using neuro-fuzzy and data mining techniques
Expert Systems with Applications: An International Journal
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One of the most important properties of neural nets (NNs) for control purposes is the universal approximation property. Unfortunately,, this property is generally proven for continuous functions. In most real industrial control systems there are nonsmooth functions (e.g., piecewise continuous) for which approximation results in the literature are sparse. Examples include friction, deadzone, backlash, and so on. It is found that attempts to approximate piecewise continuous functions using smooth activation functions require many NN nodes and many training iterations, and still do not yield very good results. Therefore, a novel neural-network structure is given for approximation of piecewise continuous functions of the sort that appear in friction, deadzone, backlash, and other motion control actuator nonlinearities. The novel NN consists of neurons having standard sigmoid activation functions, plus some additional neurons having a special class of nonsmooth activation functions termed "jump approximation basis function." Two types of nonsmooth jump approximation basis functions are determined- a polynomial-like basis and a sigmoid-like basis. This modified NN with additional neurons having "jump approximation" activation functions can approximate any piecewise continuous function with discontinuities at a finite number of known points. Applications of the new NN structure are made to rigid-link robotic systems with friction nonlinearities. Friction is a nonlinear effect that can limit the performance of industrial control systems; it occurs in all mechanical systems and therefore is unavoidable in control systems. It can cause tracking errors, limit cycles, and other undesirable effects. Often, inexact friction compensation is used with standard adaptive techniques that require models that are linear in the unknown parameters. It is shown here how a certain class of augmented NN, capable of approximating piecewise continuous functions, can be used for friction compensation