Diagonal recurrent neural network with modified backlash operators for modeling of rate-dependent hysteresis in piezoelectric actuators

Abstract A novel neural network based method for modeling of rate-dependent hysteresis in piezoelectric actuators is proposed. In order to approximate the behavior of rate-dependent hysteresis which is a kind of nonsmooth dynamic nonlinearity with multi-valued mapping, a diagonal recurrent neural network (DRNN) with modified backlash operators (MBOs) is developed. In the proposed neural architecture, the MBOs are used as the activation functions of the hidden layer. Then, the corresponding Levenberg–Marquardt (L-M) algorithm for the DRNN with MBOs is proposed. Taking into account the nonsmooth characteristic of the MBO, the proximal bundle (PB) method is applied to search the appropriate subgradients at the nonsmooth vertexes of the MBOs. Finally, the experimental result on rate-dependent hysteresis in piezoelectric actuators is presented.