Neural Network Adaptive Control for Discrete-Time Nonlinear Nonnegative Dynamical Systems
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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 1
School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0150, USA Department of Mechanical and Aerospace Engineering, University of Tennessee, Knoxville, TN 37996-2210, USA 3 Department of Mechanical and Environmental Informatics (MEI), Tokyo Institute of Technology, O’okayama, Tokyo 152-8552, Japan 2
Correspondence should be addressed to W. M. Haddad, [email protected] Received 27 January 2008; Accepted 8 April 2008 Recommended by John Graef 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. Copyright q 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.
1. Introduction Neural networks have provided an ideal framework for online identification and control of many complex uncertain engineering systems because of their great flexibility in approximating a large class of continuous maps and their adaptability due to their inherently parallel architecture. Even though neuroadaptive control has been applied to numerous engineering problems, neuroadaptive methods have not been widely considered for problems involving systems with nonnegative state and control constraints 1, 2. Such systems are commonly referred to as nonnegative dynamical systems in the literature 3–8. A subclass of
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Advances in Difference Equations
nonnegative dynamical systems are compartmental systems 8–18. Compartmental systems involve dynamical models that are characterized by conservation laws e.g., mass and energy capturing the exchange of material between coupled macroscopic subsystems known as compartments. The range of applications of nonnegative systems and compartmental systems includes pharmacological systems, queuing systems, stochastic systems whose state variables represent probabilities, ecological systems, economic systems, demographic systems, teleco
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