  Resilience is a rehashed concept in natural hazard management - resilience of
cities to earthquakes, to floods, to fire, etc. In a word, a system is said to
be resilient if there exists a strategy that can drive the system state back to
"normal" (acceptable states) after a shock. What formal flesh can we put on
such malleable notion? We propose to frame the concept of resilience in the
mathematical garbs of control theory under uncertainty. Our setting covers
dynamical systems both in discrete or continuous time, deterministic or subject
to uncertainties. Our definition of resilience extends others, be they "a la
Holling" or rooted in viability theory. Indeed, we require that, after a shock,
the system returns to an acceptable "regime" , that is, that the state-control
path as a whole must return to a set of acceptable paths (and not only the
state values must belong to an acceptable subset of the state set). More
generally, as state and control paths are contingent on uncertainties, we
require that their tails processes must lay within acceptable domains of
stochastic processes. We end by pointing out how such domains can be delineated
thanks to so called risk measures.
