Boundary feedback stabilization of an unstable heat equation

SIAM Journal on Control and Optimization

Volumn 42, Issue 3, 2003, Pages 1033-1043

  Liu, Weijiu ^a  

^a Massachusetts Institute of Technology Cambridge   (United States)

Author keywords

Boundary control; Heat equation; Stabilization

Indexed keywords

BOUNDARY CONTROL; BOUNDARY FEEDBACK STABILIZATION; CONTROL LAW; HEAT EQUATIONS;

BOUNDARY CONDITIONS; BOUNDARY VALUE PROBLEMS; FEEDBACK CONTROL; MATHEMATICAL TECHNIQUES; PROBLEM SOLVING; STABILIZATION;

HEAT CONDUCTION;

EID: 2942514669     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012902402414     Document Type: Article

References (15)

1. R. ADAMS, Sobolev Spaces, Academic Press, New York, 1975.
2. H. AMAMM, Feedback stabilization of linear and semilinear parabolic systems, in Semigroup Theory and Applications, P. Clement, S. Invernizzi, E. Mitidieri, and I. I. Vrabie, eds., Lecture Notes in Pure and Appl. Math. 116, Marcel Dekker, New York, 1989, pp. 21-57.
3. A. BALOGH AND M. KRSTIC, Infinite-step backstepping for a heat equation-like PDE with arbitrarily many unstable eigenvalues, in Proceedings of the 2001 American Control Conference, Vol. 3, IEEE Press, Piscataway, NJ, 2001, pp. 2480-2485.
4. A. BALOGH AND M. KRSTIC, Infinite dimensional backstepping - style feedback transformations for a heat equation with an arbitrary level of instability, European J. Control, 8 (2002), pp. 165-176.
5. D. M. BOSKOVIC, M. KRSTIC, AND W. J. LIU, Boundary control of an unstable heat equation via measurement of domain-averaged temperature, IEEE Trans. Automat. Control, 46 (2001), pp. 2022-2028.
6. J. A. BURNS AND D. RUBIO, A distributed parameter control approach to sensor location for optimal feedback control of thermal processes, in Proceedings of the 36th IEEE Conference on Decision and Control, Vol. 3, IEEE Press, Piscataway, NJ, 1998, pp. 2243-2247.
7. J. A. BURNS, D. RUBIO, AND B. B. KING, Regularity of feedback operators for boundary control of thermal processes, in Proceedings of the First International Conference on Nonlinear Problems in Aviation and Aerospace, Daytona Beach, FL, 1996.
8. W. A. DAY, A decreasing property of solutions of parabolic equations with applications to thermoelasticity, Quart. Appl. Math., 40 (1982/83), pp. 468-475.
9. O. A. LADYZHENSKAYA, V. A. SOLONNIKOV, AND N. N. URAL'CEVA, Linear and Quasi-linear Equations of Parabolic Type, Transl. Math. Monogr. 23, AMS, Providence, RI, 1968.
10. I. LASIECKA AND R. TRIGGIANI, Stabilization of Neumann boundary feedback of parabolic equations: The case of trace in the feedback loop, Appl. Math. Optim., 10 (1983), pp. 307-350.
11. I. LASIECKA AND R. TRIGGIANI, Stabilization and structural assignment of Dirichlet boundary feedback parabolic equations, SIAM J. Control Optim., 21 (1983), pp. 766-803.
12. I. LASIECKA AND R. TRIGGIANI, The regulator problem for parabolic equations with Dirichlet boundary control. I. Riccati's feedback synthesis and regularity of optimal solution, Appl. Math. Optim., 16 (1987), pp. 147-168.
13. I. LASIECKA AND R. TRIGGIANI, The regulator problem for parabolic equations with Dirichlet boundary control, II. Galerkin approximation, Appl. Math. Optim., 16 (1987), pp. 187-216.
14. J. L. LIONS AND E. MAGENES, Non-Homogeneous Boundary Value Problems and Applications, Vol. I, Springer-Verlag, Berlin, Heidelberg, New York, 1972.
15. R. TRIGGIANI, Boundary feedback stabilization of parabolic equations, Appl. Math. Optim., 6 (1980), pp. 201-220.