  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" after any perturbation. What formal flesh can we put on such a
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. We will say that a system state is resilient if there exists
an adaptive strategy such that the generated state and control paths,
contingent on uncertainties, lay within an acceptable domain of random
processes, called recovery regimes. We point out how such recovery regimes can
be delineated thanks to so called risk measures, making the connection with
resilience indicators. Our definition of resilience extends others, be they "`
a la Holling" or rooted in viability theory. Indeed, our definition of
resilience is a form of controlability for whole random processes (regimes),
whereas others require that the state values must belong to an acceptable
subset of the state set.
