Robust adaptive control of nonaffine nonlinear plants with small input signal changes

Assuming small input signal magnitudes, ARMA models can approximate the NARMA model of nonaffine plants. Recently, NARMA-L1 and NARMA-L2 approximate models were introduced to relax such input magnitude restrictions. However, some applications require larger input signals than allowed by ARMA, NARMA-L1 and NARMA-L2 models. Under certain assumptions, we recently developed an affine approximate model that eliminates the small input magnitude restriction and replaces it with a requirement of small input changes. Such a model complements existing models. Using this model, we present an adaptive controller for discrete nonaffine plants with unknown system equations, accessible input-output signals, but inaccessible states. Our approximate model is realized by a neural network that learns the unknown input-output map online. A deadzone is used to make the weight update algorithm robust against modeling errors. A control law is developed for asymptotic tracking of slowly varying reference trajectories.