Advances in Difference Equations
Volume 2008 (2008), Article ID 868425, 29 pages
Research Article

Neural Network Adaptive Control for Discrete-Time Nonlinear Nonnegative Dynamical Systems

Wassim M. Haddad,1 VijaySekhar Chellaboina,2 Qing Hui,1 and Tomohisa Hayakawa3

1School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0150, USA
2Department of Mechanical and Aerospace Engineering, University of Tennessee, Knoxville, TN 37996-2210, USA
3Department of Mechanical and Environmental Informatics (MEI), Tokyo Institute of Technology, O'okayama, Tokyo 152-8552, Japan

Received 27 January 2008; Accepted 8 April 2008

Academic Editor: John Graef

Copyright © 2008 Wassim M. Haddad et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Nonnegative and compartmental dynamical system models are derived from mass and energy balance considerations that involve dynamic states whose values are nonnegative. These models are widespread in engineering and life sciences, and they typically involve the exchange of nonnegative quantities between subsystems or compartments, wherein each compartment is assumed to be kinetically homogeneous. In this paper, we develop a neuroadaptive control framework for adaptive set-point regulation of discrete-time nonlinear uncertain nonnegative and compartmental systems. The proposed framework is Lyapunov-based and guarantees ultimate boundedness of the error signals corresponding to the physical system states and the neural network weighting gains. In addition, the neuroadaptive controller guarantees that the physical system states remain in the nonnegative orthant of the state space for nonnegative initial conditions.