A sliding mode strategy for adaptive learning in Adalines

A dynamical sliding mode control approach is proposed for robust adaptive learning in analog Adaptive Linear Elements (Adalines), constituting basic building blocks for perceptron-based feedforward neural networks. The zero level set of the learning error variable is regarded as a sliding surface in the space of learning parameters. A sliding mode trajectory can then be induced, in finite time, on such a desired sliding manifold. Neuron weights adaptation trajectories are shown to be of continuous nature, thus avoiding bang-bang weight adaptation procedures. Sliding mode invariance conditions determine a least squares characterization of the adaptive weights average dynamics whose stability features may be studied using standard time-varying linear systems results. Robustness of the adaptative learning algorithm, with respect to bounded external perturbation signals, and measurement noises, is also demonstrated. The article presents some simulation examples dealing with applications of the proposed algorithm to forward and inverse plant dynamics identification.