Biblio

Resilience of urban infrastructure to sudden, system-wide, potentially catastrophic events is a critical need across domains. The growing connectivity of infrastructure, including its cyber-physical components which can be controlled in real time, offers an attractive path towards rapid adaptation to adverse events and adjustment of system objectives. However, existing work in the field often offers disjoint approaches that respond to particular scenarios. On the other hand, abstract work on control of complex systems focuses on attempting to adapt to the changes in the system dynamics or environment, but without understanding that the system may simply not be able to perform its original task after an adverse event. To address this challenge, this programmatic paper proposes a vision for a new paradigm of infrastructure resilience. Such a framework treats infrastructure across domains through a unified theory of controlled dynamical systems, but remains cognizant of the lack of knowledge about the system following a widespread adverse event and aims to identify the system's fundamental limits. As a result, it will enable the infrastructure operator to assess and assure system performance following an adverse event, even if the exact nature of the event is not yet known. Building off ongoing work on assured resilience of control systems, in this paper we identify promising early results, challenges that motivate the development of resilience theory for infrastructure system, and possible paths forward for the proposed effort.

Actuator malfunctions may have disastrous con-sequences for systems not designed to mitigate them. We focus on the loss of control authority over actuators, where some actuators are uncontrolled but remain fully capable. To counter-act the undesirable outputs of these malfunctioning actuators, we use real-time measurements and redundant actuators. In this setting, a system that can still reach its target is deemed resilient. To quantify the resilience of a system, we compare the shortest time for the undamaged system to reach the target with the worst-case shortest time for the malfunctioning system to reach the same target, i.e., when the malfunction makes that time the longest. Contrary to prior work on driftless linear systems, the absence of analytical expression for time-optimal controls of general linear systems prevents an exact calculation of quantitative resilience. Instead, relying on Lyapunov theory we derive analytical bounds on the nominal and malfunctioning reach times in order to bound quantitative resilience. We illustrate our work on a temperature control system.