Neural network approximation of piecewise continuous functions: application to friction compensation

A new neural network (NN) structure is given for approximation of piecewise continuous (PC) functions of the sort that appear in friction, deadzone, backlash and other motion control actuator nonlinearities. The NN consists of neurons having a special class of nonsmooth activation functions termed 'jump approximation basis functions'. This 'jump approximation' NN plus a NN based on standard smooth sigmoidal activation functions can approximate any piecewise continuous function with discontinuities at a finite number of known points. Industrial motion device actuator nonlinearities are in this class of functions, therefore, the new NN structure is ideal for motion control applications in robotics and other industrial systems.