Coping with actuator dynamics using backstepping for boundary stabilization of Burgers' equation

Proceedings of the American Control Conference

Volumn 6, Issue , 2000, Pages 4264-4268

  Liu, Wei Jiu ^a   Krstic, Miroslav ^b  

^a DALHOUSIE UNIVERSITY   (Canada)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ACTUATOR DYNAMICS; BACK-STEPPING CONTROLS; BOUNDARY CONTROLS; BOUNDARY DYNAMICS; BOUNDARY STABILIZATION; BURGERS' EQUATIONS; CONTROL INPUTS; LYAPUNOV ANALYSIS;

ACTUATORS; BACKSTEPPING; CONTROL THEORY; BOUNDARY VALUE PROBLEMS; CLOSED LOOP CONTROL SYSTEMS; FUNCTIONS; LYAPUNOV METHODS; PARTIAL DIFFERENTIAL EQUATIONS; PROBLEM SOLVING; SYSTEM STABILITY;

DYNAMICS; FEEDBACK CONTROL;

ACTUATOR DYNAMICS; BACKSTEPPING; BOUNDARY STABILIZATION; BURGERS EQUATION;

EID: 0034546110     PISSN: 07431619     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ACC.2000.877025     Document Type: Conference Paper

References (14)

1. R. Adams, Soboleu Spaces. Academic Press, New York (1975).
2. A. Balogh and M. Krstid, Burgers' Equation with Nonlinear Boundary Feedback: H' Stability, Well-Posedness and Simulation. Mathematical Problems in Engineering (submitted).
3. J.A. Burns and S. Kang, A control problem for Burgers' equation with bounded input/output. Nonhear Dynamics 2 (1992) 235-262.
4. C.I. Byrnes, D.S. Gilliam and V.I. Shubov, Boundary control for a viscous Burgers' equation, in Identification Control for Systems Governed by Partzal Differential Equations, H.T. Banks, R.H. Fabiano and K. Ito Eds., SIAM (1993) 171-185.
5. H. Choi, R. Temam, P. Moin and J. Kim, Feedback control for unsteady flow and its application to the stochastic Burgers' equation. J. Fluid Mech. 253 (1993) 509-543.
6. J.-M. Coron and B. d'Andrea-Novel, Stabilization of a rotating body beam without damping. IEEE Trans. Automat. Control 43 (1998) 608-618.
7. K. Ito and S. Kang, A dissipative feedback control for systems arising in fluid dynamics. SIA M J. Control Optim. 32 (1994) 831-854.
8. K. Ito and Y. Yan, Viscous scalar conservation law with nonlinear flux feedback and global attractors. J. Math. Anal. Appl. 227 (1998) 271-299.
9. H. K. Khalil, Nonlinear Systems. Prentice-Hall, Inc., New Jersey (1996).
10. M. Krstic, On global stabilization of Burgers' equation by boundary control. Systems & Control Letters 37 (1999) 123-141.
11. M. KrstiC, I. Kanellakopoulos and P. Kokotovid, Nonlinear and Adaptive Control Design. John Wiley & Sons, Inc., New York (1995).
12. J.L. Lions and E. Magenes, Non-homogeneous Boundary value Problems and Applications, Vol. 1. Springer-Verlag, Berlin (1972).
13. W.J. Liu and M. Krstic, Adaptive control of Burgers' equation with unknown viscosity. ESA IM Contr. Optim. Calc. Var. (submitted).
14. H. V. Ly, K. D. Mease and E.S. Titi, Distributed and boundary control of the viscous Burgers' equation. Numer. Funct. Anal. Optim. 18 (1997) 143-188.