Modified Elman neural network based neural adaptive inverse control of rate-dependent hysteresis

A modified Elman neural network (MENN) based neural adaptive inverse control scheme is proposed for trajectory tracking of rate-dependent hysteresis. To attenuate the influence of the rate-dependent hysteresis, a modified inverse backlash operator (MIBO) is developed to act as the hidden layer neuron of the MENN to describe the dynamic behavior of the inverse rate-dependent hysteresis. The diagonal recurrent weights of context layer and the recurrent weights from hidden layer to context layer are designed to enhance the dynamic learning capability of the MENN. To determine an appropriate structure and the parameters of the MENN for adaptive inverse control, a MENN is trained first based on the data of inverse rate-dependent hysteresis. In view of the nonsmooth characteristics of the MIBOs, a restricted step proximal bundle (RSPB) method is employed to search the appropriate subgradients at the nonsmooth vertexes of the MIBOs. The relevant Levenberg-Marquardt (L-M) algorithm is developed to acquire an appropriate MENN that is used as the initial controller to implement adaptive inverse control for rate-dependent hysteresis via gradient descent learning algorithm. Numerical control results on a Duhem model of piezoelectric actuators have validated the effectiveness of the proposed method.

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