An abstract bang-bang principle and time-optimal boundary control of the heat equation

SIAM Journal on Control and Optimization

Volumn 35, Issue 4, 1997, Pages 1204-1216

  Mizel, Victor J ^a   Seidman, Thomas I ^b  

^a CARNEGIE MELLON UNIVERSITY   (United States)

^b UNIVERSITY OF MARYLAND BALTIMORE COUNTY   (United States)

Author keywords

Bang bang control; Nullcontrol; Partial differential equation; Reachability

Indexed keywords

BANG BANG CONTROL SYSTEMS; CONSTRAINT THEORY; OPTIMAL CONTROL SYSTEMS; PARTIAL DIFFERENTIAL EQUATIONS;

HEAT EQUATION; TIME OPTIMAL BOUNDARY CONTROL;

CONTROL THEORY;

EID: 0031186394     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012996265470     Document Type: Article

References (14)

1. P. BORWEIN AND T. ERDÉLYI, Müntz spaces and Remez inequalities, Bull. Amer. Math. Soc., 32 (1994), pp. 38-42.
2. P. BORWEIN AND T. ERDÉLYI, Generalizations of Müntz's Theorem via a Remez-type Inequality for Müntz Spaces, Simon Fraser University, Burnaby, BC, 1994, preprint.
3. P. BORWEIN and T. ERDÉLYI, Polynomials and Polynomial Inequalities, Springer-Verlag, New York, 1995.
4. H. O. FATTORINI AND D. L. RUSSELL, Exact controllability theorems for linear parabolic equa-tions in one space dimension, Arch. Rational Mech. Anal., 43 (1971), pp. 271-292.
5. G. HELLWIG, Partial Differential Equations, Blaisdell, New York, 1964.
6. J. HENRY, Un contre-exemple en théorie de la commande en temps minimal des systèmes paraboliques, C.R. Acad. Sci. Paris Sér. A 289 (1979), pp. 87-89.
7. I. KLUVANEK AND G. KNOWLES, Vector Measures and Control Systems, North-Holland Mathematics Studies 20, North-Holland, Amsterdam, 1975.
8. W. KRABS, On Moment Theory and Controllability of One-Dimensional Vibrating Systems and Heating Processes, Lecture Notes in Control and Information Sciences 173, Springer-Verlag, New York, 1992.
9. G. LEBEAU AND L. ROBBIANO, Contrôle exact de l'équation de la chaleur, Comm. Partial Differential Equations, 20 (1995), pp. 335-356.
10. J. L. LIONS AND E. MAGENES, Non-Homogeneous Boundary Value Problems and Applications, vol. II, Springer-Verlag, Berlin, 1972.
11. V. J. MIZEL AND T. I. SEIDMAN, Observation and prediction for the heat equation, I, J. Math. Anal. Appl., 28 (1969), pp. 303-312.
12. E. J. P. G. SCHMIDT, The 'bang-bang' principle for the time-optimal problem in boundary control of the heat equation, SIAM J. Control Optim., 18 (1980), pp. 101-107.
13. T. I. SEIDMAN, Observation and prediction for the heat equation, IV: Patch observability and controllability, SIAM J. Control Optim., 15 (1977), pp. 412-427.
14. T. I. SEIDMAN, Time-invariance of the reachable set for linear control problems, J. Math. Anal. Appl., 72 (1979), pp. 17-20.