Discrete-time tuning of neural network controllers for nonlinear

Abstract

A family of novel multi-layer discrete-time neural net controllers is presented for the control of an multi-input multi-output (MIMO) dynamical system. No learning phase is needed. The structure of the neural net (NN) controller is derived using a filtered error/passivity approach. For guaranteed stability, the upper bound on the constant learning rate parameter for the delta rule employed in standard back propagation is shown to decrease with the number of hidden-layer neurons so that learning must slow down. This major drawback is shown to be easily overcome by using a projection algorithm in each layer. The notion of persistency of excitation for multilayer NN is defined and explored. New on-line improved tuning algorithms for discrete-time systems are derived, which are similar to e-modification for the case of continuous-time systems, that include a modification to the learning rate parameter plus a correction term. These algorithms guarantee tracking as well as bounded NN weights. An extension of these novel weight tuning updates to NN with an arbitrary number of hidden layers is discussed. The notions of discrete-time passive NN, dissipative NN, and robust NN are introduced.