Recurrent Higher Order Neural Network Control for Output Trajectory Tracking with Neural Observers and Constrained Inputs

1. Introduction

Over the past decade, adaptive neural control schemes have received an increasing attention for applications on nonlinear systems control. Mainly due to the seminal paper (Narendra & Parthasarathy, 1990), there has been continuously increasing interest in applying neural networks to identification and control of nonlinear systems. Lately, the use of recurrent neural networks is being developed, which allows more efficient modeling of the underlying dynamical systems (Poznyak et al.). Three representative books (Suykens et al., 1996), (Rovitahkis & Christodoulou, 2000) and (Poznyak et al., 2000) have reviewed the application of recurrent neural networks for nonlinear system identification and control. In particular, (Suykens et al., 1996) uses off-line learning, while (Rovitahkis & Christodoulou, 2000) analyzes adaptive identification and control by means of on-line learning, where stability of the closed-loop system is established based on the Lyapunov function method. In (Rovitahkis & Christodoulou, 2000), the trajectory tracking problem is reduced to a linear model following problem, with application to DC electric motors. In (Poznyak et al., 2000), analysis of Recurrent Neural Networks for identification, estimation and control are developed, with applications on chaos control, robotics and chemical processes. One recent publication (Sanchez et al., 2008), explores the application of Recurrent Higher Order Neural Networks (RHONN) for trajectory tracking control schemes using the Kalman filtering training with real time applications to electrical machines.