Optimal fixed-structure control for linear non-negative dynamical systems

International Journal of Robust and Nonlinear Control

Volumn 14, Issue 5, 2004, Pages 487-511

  Nersesov, Sergey G ^a   Haddad, Wassim M ^a   Chellaboina, VijaySekhar ^b  

^a Georgia Institute of Technology   (United States)

^b UNIVERSITY OF MISSOURI   (United States)

Author keywords

Automated anesthesia; Compartmental systems; Domains of attraction; Non negative control; Non negative systems; Optimal control; Set point regulation

Indexed keywords

CLOSED LOOP CONTROL SYSTEMS; CONSTRAINT THEORY; CONTROL SYSTEM SYNTHESIS; FEEDBACK CONTROL; LYAPUNOV METHODS; OPTIMAL CONTROL SYSTEMS; STATE SPACE METHODS; SYSTEM STABILITY;

AUTOMATED ANESTHESIA; COMPARTMENTAL SYSTEMS; NON NEGATIVE CONTROL; NON NEGATIVE SYSTEMS; SETPOINT REGULATION;

LINEAR CONTROL SYSTEMS;

EID: 1642413440     PISSN: 10498923     EISSN: None     Source Type: Journal    
DOI: 10.1002/rnc.891     Document Type: Article

References (34)

1. Ohta Y, Maeda H, Kodama S. Reachability, observability and realizability of continuous-time positive systems. SIAM Journal of Control and Optimization 1984; 22: 171-180.
2. Berman A, Neumann M, Stern RJ. Non-negative Matrices in Dynamic Systems. Wiley: New York, 1989.
3. Haddad WM, Chellabonia V, August E. Stability and dissipativity theory for non-negative dynamical systems: A thermodynamic framework for biological and physiological systems. In Proceedings of the IEEE Conference on Decision and Cotnrol, Orlando, FL, 2001; 442-458.
4. Kaszkurewicz E, Bhaya A. Matrix Diagonal Stability in Systems and Computation. Birkhauser; Boston, NY, 2000.
5. Farina L, Rinaldi S. Positive Linear Systems: Theory and Applications. Wiley: New York, 2000.
6. Kaczorek T. Positive 1D and 2D Systems. Springer: London, UK, 2002.
7. Bernstein DS, Hyland DC. Compartmental modeling and second-moment analysis of state space systems. SIAM Journal on Matrix Analysis and Applications 1993; 14:880-901.
8. Mohler RR. Biological modeling with variable compartmental structure. IEEE Transactions on Automatic Control 1974; 1974:922-926.
9. Maeda H, Kodama S, Kajiya F. Compartmental system analysis: Realization of a class of linear systems with physical constraints. IEEE Transaction on Circuits and Systems 1977; 24:8-14.
10. Sandberg W. On the mathematical foundations of compartmental analysis in biology, medicine and ecology. IEEE Transactions on Circuits and Systems 1978; 25:273-279.
11. Maeda H, Kodama S, Ohta Y. Asymptotic behavior of nonlinear compartmental systems: Nonoscillation and stability. IEEE Transactions on Circuits and Systems 1978; 25:372-378.
12. Funderlic RE, Mankin JB. Solution of homogeneous systems of linear equations arising from compartmental models. SIAM Journal on Scientific Statistical Computing 1981; 2:375-383.
13. Anderson DH. Compartmental Modeling and Tracer Kinetics. Springer: Berlin, NY, 1983.
14. Godfrey K. Compartmental Models and their Applications. Academic Press; New York, 1983.
15. Jacquez JA. Compartmental Analysis in Biology and Medicine (2nd edn). University of Michigan Press: Ann Arbor, 1985.
16. Jacquez JA, Simon CP. Qualitative theory of compartmental systems. SIAM Review 1993; 35:43-79.
17. Bernstein DS, Hyland DC. Optimal projection approach to robust, fixed-structure control design. In: Mechanics and Control of Space Structures, Junkins J (ed). AIAA: Washington, DC, 1993.
18. ∞ optimal static output feedback. In Proceedings of the American Control Conference, Pittsburgh, PA, 1989; 2506-2511.
19. Levine WS, Athans M. On the determination of the optimal output feedback gains for linear multivariable systems. IEEE Transaction on Automatic Control 1970; 15:44-48.
20. Haddad WM, Kapila V, Chellaboina V. Guaranteed domains of attraction for multivariable Luré systems via open Lyapunov surfaces. International Journal of Robust and Nonlinear Control 1997; 7:935-949.
21. Berman A, Plemmons RJ. Non-negative Matrices in the Mathematical Sciences. Academic Press: New York, NY, 1979.
22. De Leenheer P, Aeyels D. Stabilization of positive linear systems. Systems Control Letters 2001; 44:259-271.
23. Brockett RW. Asymptotic stability and feedback stabilization. In Differential Geometric Control Theory, Brockett RW, Millman RS, Sussmann HJ (eds). Birkhauser: Boston, MA, 1983.
24. Dennis Jr. JE, Schnabel RB. Numerical Methods for Unconstrained Optimization and Nonlinear Equations. Prentice-Hall: Englewood Cliffs, NJ, 1983.
25. 2 optimal reduced-order control design. International Journal of Control 1998; 69:647-662.
26. Weinstock R. Calculus of Variations with Applications to Physics and Engineering. McGraw-Hill: New York, 1952.
27. Doze VA, Westphal LM, White PF. Comparison of propofol with methohexital for outpatient anesthesia. Anaesthesia Analogues 1986; 65: 1189-1195.
28. Linkens DA, Abbod MF, Peacock JE. Clinical implementation of advanced control in anesthesia. Transaction of the Institution of Measurement and Control 2000; 22:303-330.
29. White M, Kenny GNC. Intravenous propofol anesthesia using a computerised infusion system. Anaesthesia 1990; 45:204-209.
30. Sigl JC, Chamoun NG. An introduction to bispectral analysis for the electroencephalogram. Journal of Clinical Monitoring 1994; 10:392-404.
31. Mortier E, Struys M, De Smet T, Versichelen L, Rolly G. Closed-loop controlled administration of propofol using bispectral analysis. Anaesthesia 1998; 53:749-754.
32. Schnider TW, Minto CF, Stanski DR. The effect compartment concept in pharmacodynamic modelling. Anaesthesia Pharmacological Review 1994; 2:204-219.
33. Gentilini A, Rossoni-Gerosa M, Frei CW, Wymann R, Morari M, Zbinden AM, Schnider TW. Modeling and closed-loop control of hypnosis by means of bispectral index (BIS) with isoflurane. IEEE Transactions on Biomedical Engineering 2001; 48:874-889.
34. Glass PS, Goodman DK, Ginsberg B, Reves JG, Jacobs JR. Accuracy of pharmacokinetic model-driven infusion of propofol. Anesthesiology 1989; 71:A277.