Approximation of control
problems involving ordinary  and impulsive controls

Fabio Camilli; Maurizio Falcone

Control Norms for Large Control Times

Sergei Ivanov (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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A control system of the second order in time with control $u = u (t) \in L^{2} ([0, T]; U)$ is considered. If the system is controllable in a strong sense and is the control steering the system to the rest at time , then the –norm of decreases as $1 / \sqrt{T}$ while the $L^{1} ([0, T]; U)$ –norm of is approximately constant. The proof is based on the moment approach and properties of the relevant exponential family. Results are applied to the wave equation with boundary or distributed controls.

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Control Norms for Large Control Times