Abstract
The increasingly recognized vulnerability of industrial control systems to cyber-attacks has inspired a considerable amount of research into techniques for cyber-resilient control systems. The majority of this effort involves the application of well known information security (IT) techniques to control system networks. While these efforts are important to protect the control systems that operate critical infrastructure, they are never perfectly effective. Little research has focused on the design of closed-loop dynamics that are resilient to cyber-attack. The majority of control system protection measures are concerned with how to prevent unauthorized access and protect data integrity. We believe that the ability to analyze how an attacker can effect the closed loop dynamics of a control system configuration once they have access is just as important to the overall security of a control system. To begin to analyze this problem, consistent mathematical definitions of concepts within resilient control need to be established so that a mathematical analysis of the vulnerabilities and resiliencies of a particular control system design methodology and configuration can be made. In this paper, we propose rigorous definitions for state awareness, operational normalcy, and resiliency as they relate to control systems. We will also discuss some mathematical consequences that arise from the proposed definitions. The goal is to begin to develop a mathematical framework and testable conditions for resiliency that can be used to build a sound theoretical foundation for resilient control research.
