Quantitative Resilience Analysis through Control Design

 

Critical infrastructure resilience has become a national priority for the U. S. Department of Homeland Security. System resilience has been studied for several decades in many different disciplines, but no standards or unifying methods exist for critical infrastructure resilience analysis. Few quantitative resilience methods exist, and those existing approaches tend to be rather simplistic and, hence, not capable of sufficiently assessing all aspects of critical infrastructure resilience. In particular, most current methods used in resilience analysis provide predictions of systemic impacts due to disruption, but are unable to provide an estimate of costs required to bring a system back online. Recent work has resulted in a quantitative resilience technique that leverages the advantages of control design methods. Many control design methods provide estimations of system impacts due to disruption as well as estimations of costs required to bring the system back to its nominal operating condition. Moreover, modern control design techniques are robust, compensating automatically to system disturbances to keep operation at target conditions. Specifically, feedback control methods continually monitor system performance as compared to target conditions, quickly providing needed additional input to the system when operating conditions deviate too far from nominal. System dimension is often a limiting factor when using control design methods to analyze system resilience. An exceedingly large system dimension can result in control formulations that are computationally intractable. Reduced-order modeling is often used to reduce the dimension of the system in order to lessen the burden of computation. For example, proper orthogonal decomposition is a popular order reduction technique that extricates a small set of basis functions from large sets of observed system data. This small set of basis functions can then used to develop a low-dimensional dynamical system model which can be used for control design and subsequent resilience analysis. In order to utilize these control design and order reduction tools, a general framework is proposed for assessing the resilience of infrastructure and economic systems. The framework consists of three primary components: (1) a definition of resilience that is specific to infrastructure systems; (2) a quantitative model for measuring the resilience of systems to disruptive events through the evaluation of both impacts to system performance and the cost of recovery; and (3) a qualitative method for assessing the system properties that inherently determine system resilience, providing insight and direction for potential improvements in these systems. With the framework in hand, its advantages are illustrated by application to a disrupted chemical supply chain network and other examples.