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A new method of exact controllability in short time and applications. (English) Zbl 0702.93010
Summary: We introduce a new general and constructive method which allows us to obtain the best or almost the best estimates of the time of exact controllability of linear evolution systems. The method is based on the Hilbert uniqueness method of J.-L. Lions [see C. R. Acad. Sci., Paris, Sér. I 302, 471-475 (1986; Zbl 0589.49022)] and on an estimation method introduced by A. Haraux [“Quelques propriétés des séries lacunaires utiles dans l’étude des vibrations élastiques”, Nonlinear partial differential equations and their applications, Coll. de France semin., Paris/Fr. 1987-1988, Pitman Res. Notes Math. Ser. (to appear)]. Our method is applied to several concrete problems related to the wave equation and to various plate models.

MSC:
93B05 Controllability
93C20 Control/observation systems governed by partial differential equations
74M05 Control, switches and devices (“smart materials”) in solid mechanics
35B37 PDE in connection with control problems (MSC2000)
Citations:
Zbl 0589.49022
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References:
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