Optimal Actuator/Sensor Placement for Nonlinear Control of the Kuramoto-Sivashinsky Equation

IEEE Transactions on Control Systems Technology

Volumn 11, Issue 5, 2003, Pages 737-745

  Lou, Yiming ^a   Christofides, Panagiotis D ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Galerkin's method; Highly dissipative partial differential equations; Nonlinear control; Optimal actuator sensor placement; Waves

Indexed keywords

BOUNDARY CONDITIONS; CLOSED LOOP CONTROL SYSTEMS; COMPUTER SIMULATION; CONTROL EQUIPMENT; FEEDBACK CONTROL; PARTIAL DIFFERENTIAL EQUATIONS;

INTERFACIAL INSTABILITY;

NONLINEAR CONTROL SYSTEMS;

EID: 0141638523     PISSN: 10636536     EISSN: None     Source Type: Journal    
DOI: 10.1109/TCST.2003.816405     Document Type: Article

References (20)

1. C. Antoniades and P. D. Christofides, "Integrating nonlinear output feedback control and optimal actuator/sensor placement for transport-reaction processes," Chem. Eng. Sci., vol. 56, pp. 4517-4535, 2001.
2. _, "Integrated robust control and optimal actuator/sensor placement for uncertain transport-reaction processes," Comp. Chem. Eng, vol. 26, pp. 187-203, 2002.
3. A. Arbel, "Controllability measures and actuator placement in oscillatory systems," Int. J. Contr., vol. 33, pp. 565-574, 1981.
4. A. Armaou and P. D. Christofides, "Feedback control of the Kuramoto-Sivashinsky equation," Phys. D, vol. 137, pp. 49-61, 2000.
5. _, "Wave suppression by nonlinear finite-dimensional control," Chem. Eng. Sci., vol. 55, pp. 2627-2640, 2000.
6. L. H. Chen and H. C. Chang, "Nonlinear waves on liquid film surfaces-II. Bifurcation analyzes of the long-wave equation," Chem. Eng. Sci., vol. 41, pp. 2477-2486, 1986.
7. K. Choe and H. Baruh, "Actuator placement in structural control," J. Guidance, vol. 15, pp. 40-48, 1992.
8. P. D. Christofides, Nonlinear and Robust Control of PDE Systems: Methods and Applications to Transport-Reaction Processes. Boston, MA: Birkhäuser, 2001.
9. P. D. Christofides and A. Armaou, "Global stabilization of the Kuramoto-Sivashinsky equation via distributed output feedback control," Syst. Contr. Lett, vol. 39, pp. 283-294, 2000.
10. P. D. Christofides and J. Baker, "Robust output feedback control of quasilinear parabolic PDE systems," Syst. Contr. Lett, vol. 36, pp. 307-316, 1999.
11. M. A. Demetriou, "Numerical investigation on optimal actuator/ sensor location of parabolic PDEs," in Proc. American Control Conf., San Diego, CA, 1999, pp. 1722-1726.
12. A. P. Hooper and R. Grimshaw, "Nonlinear instability at the interface between two viscous fluids," Phys. Fluids, vol. 28, pp. 37-45, 1985.
13. A. Isidori, Nonlinear Control Systems: An Introduction, 2nd ed. Berlin, Germany: Springer-Verlag, 1989.
14. C. S. Kubrusly and H. Malebranche, "Sensors and controllers location in distributed systems-a survey," Automatica, vol. 21, pp. 117-128, 1985.
15. S. Kumar and J. H. Seinfeld, "Optimal location of measurements for distributed parameter estimation," IEEE Trans. Automat. Contr., vol. AC-23, pp. 690-698, Oct. 1978.
16. W. S. Levine and M. Athans, "On the determination of the optimal constant output feedback gains for linear multivariable system," IEEE Trans. Automat. Contr., vol. AC-23, pp. 44-48, Jan. 1978.
17. W.-J. Liu and M. Kristic, "Stability enhancement by boundary control in the Kuramoto-Sivashinsky equation," Nonlinear Analysis: Theory. Methods, Applications, vol. 43, pp. 485-507, 2001.
18. M. Morari and J. O'Dowd, "Optimal sensor location in the presence of nonstationary noise," Automatica, vol. 16, pp. 463-480, 1980.
19. G. I. Sivashinsky, "Nonlinear analysis of hydrodynamic instability in laminar flames-I derivation of basic equations," Acta Astronautica, vol. 4, pp. 1177-1206, 1977.
20. R. Temam, Infnite-Dimensional Dynamical Systems in Mechanics and Physics. New York: Springer-Verlag, 1988.