Approximations of the NARMA model of non-affine plants

When the NARMA model is used in adaptive control using neural networks, it often requires heavy computation due to its nonlinear dependence on the control input. To overcome this, two classes of approximate models to the NARMA model, which are linear in the control input were introduced. They are known as NARMA-L1 and NARMA-L2. Though these approximations are useful in practical implementation of the controllers, their use is restricted to systems with small input magnitude. In this paper, we introduce two new classes of approximated models, referred as NARMA-L1B and NARMA-L2B that relax the small input magnitude restriction. The proposed models are also linear in the control input and therefore suitable for control design. A simulation example is provided for illustration.