Mathematical Models for Cyber-Physical System Security: Securing Critical Infrastructure Through Control-Theoretic Approaches

Abstract

Cyber-Physical Systems (CPS) is now an important part of modern vital infrastructure. They combine physical and digital parts to make things more efficient and automated. But as they get more connected and complicated, they become more vulnerable to different online risks, which make security much harder. In this situation, control-theoretic methods look like they could help protect CPS by using ideas from control theory to create strong and flexible defenses. The main focus of this work is on control-theoretic methods to mathematical models for CPS security. We talk about the special problems that come up with CPS security, like making sure that the system is reliable, private, honest, and accessible even when working conditions change and online risks change. We talk about how control theory can help solve these problems by giving us a way to model, analyze, and lower the security risks in CPS. First, we look at how feedback control theory can be used to improve CPS security. In this case, control methods are used to change system settings and reactions on the fly to protect against cyber attacks and keep the system working. We look at several types of control-based defenses, such as breach detection and reaction systems, anomaly detection, and adaptable access control, to show how they can improve CPS's security while keeping vital processes running as smoothly as possible. Next, we talk about how to use cryptography and control theory together to make sure that communication is safe and data is kept safe in CPS. By using cryptographic primitives in control algorithms, CPS can make sure that components can safely share information with each other and protect against threats like listening in, changing data, and playing back information. We look at the problems that uncertainty and system dynamics can cause in CPS security models and suggest probabilistic and robust control methods that can effectively deal with uncertain settings and bad behavior. Lastly, we show case studies and real-world uses of control-theoretic security methods in key infrastructure areas like healthcare, transportation, and energy. This shows how well they work in the real world. This paper talks about how control theory helps keep key infrastructure systems safe and points out areas where more study is needed to make these systems even safer and more reliable.