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2006•SIAM Journal on Control and OptimizationOpen access

Insensitizing Controls for the 1‐D Wave Equation

René Dáger

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Abstract

We study the insensitizing controllability property of the one‐dimensional wave equation observed in some open set in two cases: when the control acts in an interior region and when it acts on the boundary. In both cases, when the control time is sufficiently large the ε‐insensitizing controllability holds. Moreover, for the boundary controlled equation the (exact) insensitizing controllability also holds.

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What this paper is about

We study the insensitizing controllability property of the one‐dimensional wave equation observed in some open set in two cases: when the control acts in an interior region and when it acts on the boundary. In both cases, when the control time is sufficiently large the ε‐insensitizing controllability holds. Moreover, for the boundary controlled equation the (exact) insensitizing controllability also holds.

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Available abstract

We study the insensitizing controllability property of the one‐dimensional wave equation observed in some open set in two cases: when the control acts in an interior region and when it acts on the boundary. In both cases, when the control time is sufficiently large the ε‐insensitizing controllability holds. Moreover, for the boundary controlled equation the (exact) insensitizing controllability also holds.

Key concepts: Controllability, Mathematics, Wave equation, Boundary (topology), Property (philosophy), Mathematical analysis, Set (abstract data type), Control (management)

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