Inverse optimal neural control for a class of discrete‐time nonlinear positive systems

Abstract

SUMMARY In this paper, a discrete‐time inverse optimal trajectory tracking for a class of nonlinear positive systems is proposed. The scheme is developed for MIMO affine discrete‐time positive nonlinear systems. This optimal controller is based on discrete time passivity and positive systems theory. The advantage of this scheme is that it avoids solving the associated Hamilton–Jacobi–Bellman equation and minimizes a meaningful cost function. The affine discrete‐time positive nonlinear system is obtained from an online neural identifier, which uses a recurrent neural network, trained with the extended Kalman filter. The applicability of the proposed approach is illustrated via simulation by trajectory tracking control of type 1 diabetes mellitus patients. Copyright © 2012 John Wiley & Sons, Ltd.