  Our goal is to achieve a high degree of fault tolerance through the control
of a safety critical systems. This reduces to solving a game between a
malicious environment that injects failures and a controller who tries to
establish a correct behavior. We suggest a new control objective for such
systems that offers a better balance between complexity and precision: we seek
systems that are k-resilient. In order to be k-resilient, a system needs to be
able to rapidly recover from a small number, up to k, of local faults
infinitely many times, provided that blocks of up to k faults are separated by
short recovery periods in which no fault occurs. k-resilience is a simple but
powerful abstraction from the precise distribution of local faults, but much
more refined than the traditional objective to maximize the number of local
faults. We argue why we believe this to be the right level of abstraction for
safety critical systems when local faults are few and far between. We show that
the computational complexity of constructing optimal control with respect to
resilience is low and demonstrate the feasibility through an implementation and
experimental results.

Systems and Control