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

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

Luis J. Ricalde (Universidad Autonoma de Yucatan, Mexico), Edgar N. Sanchez (CINVESTAV, Unidad Guadalajara, Mexico) and Alma Y. Alanis (CINVESTAV, Unidad Guadalajara, Mexico)
DOI: 10.4018/978-1-61520-711-4.ch013
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Abstract

This Chapter presents the design of an adaptive recurrent neural observer-controller scheme for nonlinear systems whose model is assumed to be unknown and with constrained inputs. The control scheme is composed of a neural observer based on Recurrent High Order Neural Networks which builds the state vector of the unknown plant dynamics and a learning adaptation law for the neural network weights for both the observer and identifier. These laws are obtained via control Lyapunov functions. Then, a control law, which stabilizes the tracking error dynamics is developed using the Lyapunov and the inverse optimal control methodologies . Tracking error boundedness is established as a function of design parameters.
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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.

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