Optimal boundary control of cardiac alternans

International Journal of Robust and Nonlinear Control

Volumn 19, Issue 2, 2009, Pages 135-150

  Dubljevic, Stevan ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Action potential propagation; Cardiac alternans; Dissipative parabolic PDEs; LQR; Optimal boundary control

Indexed keywords

AIRCRAFT ENGINES; FEEDBACK; FEEDBACK CONTROL; STATE FEEDBACK;

ACTION POTENTIAL PROPAGATION; CARDIAC ALTERNANS; DISSIPATIVE PARABOLIC PDES; LQR; OPTIMAL BOUNDARY CONTROL;

OPTIMIZATION;

EID: 59149096975     PISSN: 10498923     EISSN: 10991239     Source Type: Journal    
DOI: 10.1002/rnc.1298     Document Type: Article

References (30)

1. Zipes DP, Wellens HJJ. Sudden cardiac death. Circulation 1998; 98:2334-2351.
2. Hall K, Christini DJ, Tremblay M, Collins JJ, Glass L, Billette J. Dynamic control of cardiac alternans. Physical Review Letters 1997; 78:4518-4521.
3. Hall G, Gauthier D. Experimental control of cardiac muscle alternans. Physical Review Letters 2002; 88:198102.
4. Christini DJ, Riccio ML, Culianu CA, Fox JJ, Karma A, Gilmour RF. Control of electric alternans in canine cardiac purkinje fibers. Physical Review Letters 2006; 96:104101.
5. Echebarria B, Karma A. Spatiotemporal control of cardiac alternans. Chaos 2002; 12:923-930.
6. Lin SF, Dubljevic S. Pacing real-time spatiotemporal control of cardiac alternans. Proceedings of the American Control Conference, New York City, New York, 2007; 600-606.
7. Ray WH. Advanced Process Control. McGraw-Hill: New York, NY, 1981.
8. Cross MC, Hohenberg PC. Pattern formation outside of equilibrium. Reviews of Modem Physics 1993; 65:851.
9. Friedman A. Partial Differential Equations. Holt, Rinehart & Winston: New York, 1976.
10. Fattorini HO. Boundary control systems. SIAM Journal on Control 1986; 6:349-385.
11. Triggiani R. Boundary feedback stabilization of parabolic equations. Applied Mathematics and Optimization 1980; 6:201-220.
12. Curtain RF, Zwart H. An Introduction to Infinite-dimensional Linear Systems Theory. Springer: New York, 1995.
13. Emirsjlow Z, Townley S. From PDEs with boundary control to the abstract state equation with an unbounded input operator: a tutorial. European Journal of Control 2000; 6:27-49.
14. Chakravarti S, Ray WH. Boundary indentification and control of distributed parameter systems using singular functions. Chemical Engineering Science 1999; 54:1189-1204.
15. Byrnes CI, Gilliam DS, Isidori A, Shubov VI. Static and dynamic controllers for boundary controlled distributed parameter systems. Proceedings of the 43rd IEEE Conference on Decision and Control, 2004; 3324-3325.
16. Boskovic DM, Krstic M, Liu W. Boundary control of an unstable heat equation via measurement of domainaveraged temperature. IEEE Transactions on Automatic Control 2001; 46:2022-2028.
17. Dubljevic S, Christofides PD. Predictive control of parabolic PDEs with boundary control actuation. Chemical Engineering Science 2006; 61:6239-6248.
18. Noble D. A modification of the Hodgkin-Huxley equations applicable to purkinje fibre action and pace-maker potentials. Journal of Physiology 1962; 160:317-352.
19. Echebarria B, Karma A. Instability and spatiotemporal dynamics of alternans in paced cardiac tissue. Physical Review Letters 2002; 88:208101.
20. Oh JK, Seward JB, Tajik AJ. The Echo Manual. Lippincott Williams & Wilkins: 1999.
21. Curtain RF. On stabilizability of linear spectral systems via state boundary feedback. SIAM Journal on Control and Optimization 1985; 23:144-152.
22. Winkin J. Dochain D, Ligarius P. Dynamical analysis of distributed parameter tubular reactors. Automatica 2000; 36:349-361.
23. Willems JC. Least squares stationary optimal control and the algebraic Riccati equation. IEEE Transactions on Automatic Control 1071; 6:621-634.
24. Dochain D. State observation and adaptive linearizing control for distributed parameter (bio)chemical reactors. International Journal of Adaptive Control and Signal Processing 2001; 15:633-653.
25. Christofides PD. Nonlinear and Robust Control of PDE Systems: Methods and Applications to Transport-Reaction Processes. Birkhäuser: Boston, MA, 2001.
26. Temam R. Infinite-dimensional Dynamical Systems in Mechanics and Physics. Springer: New York, 1988.
27. Balas MJ. Active control of flexible systems. Journal of Optimization Theory and Applications 1978; 25:415-436.
28. Hagen G, Mezic I. Spillover stabilization in finite-dimensional control and observer design for dissipative evolution equation. SIAM Journal on Control and Optimization 2003; 42:746-768.
29. Herve H, Rappel WJ. Dynamics of conduction block in a model of a paced cardiac tissue. Physical Review E 2005; 71:051911.
30. Pastore JM, Girouard SD, Laurita KR, Akar FG, Rosenbaum DS. Mechanism linking T-wave alternans to the genesis of cardiac fibrillation. Circulation 1999; 99:1385-1394.