Research Article

Adaptive control for non-negative and compartmental dynamical systems with applications to general anesthesia

  1. Wassim M. Haddad1,*,
  2. Tomohisa Hayakawa1,
  3. James M. Bailey2

Article first published online: 31 MAR 2003

DOI: 10.1002/acs.737

Issue

International Journal of Adaptive Control and Signal Processing

International Journal of Adaptive Control and Signal Processing

Volume 17, Issue 3, pages 209–235, April 2003

Additional Information

How to Cite

Haddad, W. M., Hayakawa, T. and Bailey, J. M. (2003), Adaptive control for non-negative and compartmental dynamical systems with applications to general anesthesia. International Journal of Adaptive Control and Signal Processing, 17: 209–235. doi: 10.1002/acs.737

Author Information

  1. 1

    School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0150, USA

  2. 2

    Department of Anesthesiology, Emory University School of Medicine, Atlanta, GA 30322, USA

*School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0150, USA

Publication History

  1. Issue published online: 31 MAR 2003
  2. Article first published online: 31 MAR 2003
  3. Manuscript Accepted: 11 NOV 2002
  4. Manuscript Received: 23 APR 2002

Funded by

  • National Science Foundation. Grant Number: ECS-9496249
  • Air Force Office of Scientific Research. Grant Number: F49620-00-1-0095

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Keywords:

  • adaptive control;
  • non-negative systems;
  • compartmental systems;
  • non-negative control;
  • set-point regulation;
  • automated anesthesia;
  • electroencephalography

Abstract

Non-negative and compartmental dynamical system models are composed of homogeneous interconnected subsystems or compartments which exchange variable non-negative quantities of material with conservation laws describing transfer, accumulation, and elimination between the compartments and the environment. These models are widespread in biological and physiological sciences and play a key role in understanding these processes. In this paper, we develop a direct adaptive control framework for linear uncertain non-negative and compartmental systems. The proposed framework is Lyapunov-based and guarantees partial asymptotic set-point regulation; that is, asymptotic set-point stability with respect to part of the closed-loop system states associated with the plant. In addition, the adaptive controller guarantees that the physical system states remain in the non-negative orthant of the state space. Finally, a numerical example involving the infusion of the anesthetic drug propofol for maintaining a desired constant level of depth of anesthesia for non-cardiac surgery is provided to demonstrate the efficacy of the proposed approach. Copyright © 2003 John Wiley & Sons, Ltd.

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