  We introduce a novel data-driven method to mitigate the risk of cascading
failures in delayed discrete-time Linear Time-Invariant (LTI) systems. Our
approach involves formulating a distributionally robust finite-horizon optimal
control problem, where the objective is to minimize a given performance
function while satisfying a set of distributionally chances constraints on
cascading failures, which accounts for the impact of a known sequence of
failures that can be characterized using nested sets. The optimal control
problem becomes challenging as the risk of cascading failures and input
time-delay poses limitations on the set of feasible control inputs. However, by
solving the convex formulation of the distributionally robust model predictive
control (DRMPC) problem, the proposed approach is able to keep the system from
cascading failures while maintaining the system's performance with delayed
control input, which has important implications for designing and operating
complex engineering systems, where cascading failures can severely affect
system performance, safety, and reliability.
