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• W2791036616 abstract "We consider linear control systems of the form y ′ ( t ) = Ay ( t ) + Bu ( t ) on a Hilbert space Y . We suppose that the control operator B is bounded from the control space U to a larger extrapolation space containing Y . The aim is to study the null controllability in the case where the control u is constrained to lie in a bounded subset Γ ⊂ U . We obtain local constrained controllability properties. When ( e tA ) t ∈ℝ is a group of isometries, we establish necessary conditions and sufficient ones for global constrained controllability. Moreover, when the constraint set Γ contains the origin in its interior, the local constrained property turns out to be equivalent to a dual observability inequality of L 1 type with respect to the time variable. In this setting, the study is focused on hyperbolic-like systems which can be reduced to a second order evolution equation. Furthermore, we treat the problem of determining a steering control for general constraint set Γ in nonsmooth convex analysis context. In the case where Γ contains the origin in its interior, a steering control can be obtained by minimizing a convenient smooth convex functional. Applications to the wave equation and Euler-Bernoulli beams are presented." @default.
• W2791036616 created "2018-03-29" @default.
• W2791036616 creator A5041294831 @default.
• W2791036616 date "2019-01-01" @default.
• W2791036616 modified "2023-10-18" @default.
• W2791036616 title "Constrained null controllability for distributed systems and applications to hyperbolic-like equations" @default.
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• W2791036616 doi "https://doi.org/10.1051/cocv/2018018" @default.
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