Lyapunov adaptive boundary control for parabolic PDEs with spatially varying coefficients

Proceedings of the American Control Conference

Volumn 2006, Issue , 2006, Pages 41-48

  Smyshlyaev, Andrey ^a   Krstic, Miroslav ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ADAPTIVE CONTROL SYSTEMS; APPROXIMATION THEORY; LYAPUNOV FUNCTIONS; LYAPUNOV METHODS; PARAMETER ESTIMATION; PARTIAL DIFFERENTIAL EQUATIONS;

BOUNDARY ACTUATION; LYAPUNOV ADAPTIVE BOUNDARY CONTROL; PARABOLIC PDE; SPATIALLY VARYING COEFFICIENTS;

CONTROL SYSTEM ANALYSIS;

EID: 34047200945     PISSN: 07431619     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/acc.2006.1655328     Document Type: Conference Paper

References (20)

1. J. Bentsman and Y. Orlov, "Reduced spatial order model reference adaptive control of spatially varying distributed parameter systems of parabolic and hyperbolic types," Int. J. Adapt. Control Signal Process. vol. 15, pp. 679-696, 2001.
2. M. Bohm, M. A. Demetriou, S. Reich, and I. G. Rosen, "Model reference adaptive control of distributed parameter systems," SIAM J. Control Optim., Vol. 36, No. 1, pp. 33-81, 1998.
3. M. S. de Queiroz, D. M. Dawson, M. Agarwal, and F. Zhang, "Adaptive nonlinear boundary control of a flexible link robot arm," IEEE Trans. Robotics and Automation, vol. 15, pp. 779-787, 1999.
4. T. E. Duncan, B. Maslowski, and B. Pasik-Duncan, "Adaptive boundary and point control of linear stochastic distributed parameter systems," SIAM J. Control Optim., vol. 32, no. 3, pp. 648-672, 1994.
5. K. S. Hong and J. Bentsman, "Direct adaptive control of parabolic systems: Algorithm synthesis, and convergence, and stability analysis," IEEE Trans. Automatic Control, vol. 39, pp. 2018-2033, 1994.
6. P. Ioannou and J. Sun, Robust Adaptive Control, Prentice Hall, 1996.
7. M. Jovanovic and B. Bamieh, "Lyapunov-based distributed control of systems on lattices," IEEE Trans. Automatic Control, Vol. 50, No. 4, pp. 422 - 433, 2005.
8. T. Kobayashi, "Adaptive regulator design of a viscous Burgers' system by boundary control," IMA Journal of Mathematical Control and Information, vol. 18, pp. 427-437, 2001.
9. M. Krstic, "Lyapunov adaptive stabilization of parabolic PDEs - Part I: A benchmark for boundary control," CDC-ECC 2005.
10. M. Krstic, "Lyapunov adaptive stabilization of parabolic PDEs - Part II: Output feedback and other benchmark problems," CDC-ECC 2005.
11. M. Krstic, I. Kanellakopoulos, and P. Kokotovic, Nonlinear and Adaptive Control Design, Wiley, New York, 1995.
12. W. Liu and M. Krstic, "Adaptive control of Burgers' equation with unknown viscosity," Int. J. Adapt. Contr. Sig. Proc., vol. 15, pp. 745-766, 2001.
13. H. Logemann and S. Townley, "Adaptive stabilization without identification for distributed parameter systems: An overview," IMA J. Math. Control and Information, vol. 14, pp. 175-206, 1997.
14. Y. Orlov, "Sliding mode observer-based synthesis of state derivative-free model reference adaptive control of distributed parameter systems," J. of Dynamic Syst. Meas. Contr., vol. 122, pp. 726-731, 2000.
15. A. Smyshlyaev and M. Krstic, "Closed form boundary state feedbacks for a class of ID partial integro-differential equations," IEEE Trans. on Automatic Control, Vol. 49, No. 12, pp. 2185-2202, 2004.
16. A. Smyshlyaev and M. Krstic, "On control design for PDEs with space-dependent diffusivity or time-dependent reactivity," Automatica, vol. 41, pp. 1601-1608, 2005.
17. A. Smyshlyaev and M. Krstic, "Passive Identifiers for Boundary Adaptive Control of 3D Reaction-Advection-Diffusion PDEs," CDC-ECC'05, Seville, Spain, 2005.
18. A. Smyshlyaev and M. Krstic, "Output Feedback Adaptive Controllers with Swapping Identifiers for Two Unstable PDEs with Infinite Relative Degree," CDC-ECC'05, Seville, Spain, 2005.
19. V. Solo and B. Bamieh, "Adaptive distributed control of a parabolic system with spatially varying parameters," Proc. 38th IEEE Conf. Decision and Control, pp. 2892-2895, 1999.
20. J. T.-Y. Wen and M. J. Balas, "Robust adaptive control in Hilbert space," J. Math. Analysis and Appl., vol. 143, pp. 1-26, 1989.