On the cost of fast control for heat-like semigroups: spectral inequalities and transmutation

Luc Miller (1)

1 MODAL'X - Modélisation aléatoire de Paris X

The Lebeau-Robbiano strategy deduces the null-controllability of parabolic systems of linear PDEs from some spectral inequalities: we implement it so simply that it yields valuable estimates on the cost of the distributed control as the time available to perform it tends to zero. The solutions and controls of some parabolic equations can be expressed in terms of those of the hyperbolic equation obtained by changing the time derivative into a second oder derivative: such transmutation formulas yield geometric bounds on both the spectral and cost rates.

Mots clés: Observability; null-controllability; fast control cost; heat semigroup

Domaines: Equations aux dérivées partielles [math.AP]; Optimisation et contrôle [math.OC]

Luc Miller. On the cost of fast control for heat-like semigroups: spectral inequalities and transmutation. V International Conference on Inverse Problems, Control and Shape Optimization, Apr 2010, Cartagena, Spain. ⟨hal-00459601⟩