Detection and Optimization Algorithms for Cyber-Physical Systems

Cyber-Physical Systems (CPS) play an ubiquitous role in operation and control in many different domains: power systems, finance, robotics, and automation. The complex interplay between cyber components such as software, communication protocols, computer servers and physical components, such as sensors and pieces of dedicated hardware, requires advanced and sophisticated methods and algorithms that ensure safe and efficient operation. In this thesis we tackle both safety and efficiency: We develop novel detection algorithms that are able to identify malicious attacks, sensor corruption and faulty measurements. Our detection mechanisms have provable guarantees based on rigorous asymptotic and non-asymptotic statistical analysis and can be readily implemented in CPS, such as robotic systems and autonomous vehicles. In addition, we developed collusion detection mechanisms that can be used to identify whether two or more CPS are colluding or not. We also design a mechanism that is able to induce selfish systems/agents to behave cooperatively. We showcase the performance of our algorithms with several different case studies. In our analyses, we place emphasis on algorithms that can be implemented in real-time, that is can be used while the system is under operation in the real-world. On the efficiency side, we developed real-time non-linear Model Predictive Control (MPC) Methods that can provide optimal solutions to the Optimal Control problem faced by the CPS during operation. Our algorithm exploits the control structure and is tailored for implementation in embedded hardware and can operate both with memory and computation time constraints. We showcase the performance of our algorithm with a C/C++ implementation and we compare to several current state-of-the-art Optimal Control solvers. We also extend our methodology to be used together with Pseudo-spectral Methods and Hybrid Systems, developing an integrated Mixed-Integer MPC algorithm that can handle complex non-linear dynamics and both continuous and discrete variables. With this thesis, our goal is to provide real-time practical algorithms that have provable guarantees in performance both in the detection task and in the optimal control task. Our algorithms are based on rigorous theoretical analysis and display very good performance and can be readily implemented in practical Cyber-Physical Systems.