Controlling Nonlinear Dynamic Systems with Projection Pursuit Learning

Projection pursuit learning (PPL) refers to a well-known constructive learning algorithm characterized by a very efficient and accurate computational procedure oriented to nonparametric regression. It has been employed as a means to counteract some problems related to the design of artificial neural network (ANN) models, namely, the estimation of a (usually large) number of free parameters, the proper definition of the model´s dimension, and the choice of the sources of nonlinearities (activation functions). In this work, the potentials of PPL are exploited through a different perspective, namely, in designing one-hidden-layer feedforward ANNs for the adaptive control of nonlinear dynamic systems. For such purpose, the proposed methodology is divided into three stages. In the first, the model identification process is undertaken. In the second, the ANN structure is defined according to an offline control setting. In these two stages, the PPL algorithm estimates not only the optimal number of hidden neurons but also the best activation function for each node. The final stage is performed online and promotes a fine-tuning in the parameters of the identification model and the controller. Simulation results indicate that it is possible to design effective neural models based on PPL for the control of nonlinear multivariate systems, with superior performance when compared to benchmarks