Data-driven and Safe Networked Control with Applications to Microgrids

Today, automatic control is integrated into a wide spectrum of real-world systems such as electrical grids and transportation networks. Many of these systems comprise numerous interconnected agents, perform safety-critical operations, or generate large amounts of data. Their automation, therefore, must address the challenges pertinent to these three characteristics. Specifically, in multi-agent systems (MASs), one common objective is that agents reach consensus on state or output variables for achieving a desired collective behavior. For consensus in large MASs, distributed controllers employing a communication network are required. When distributed architectures are used, the security of the closed-loop system can be compromised due to the vulnerability of the communication network to adversarial interferences called cyber attacks. Timely detection of attacks is vital for ensuring security of safety-critical systems. Finally, it is relevant in data-rich systems to develop control and state-estimation methods that provide guarantees by using a finite amount of data and bypassing the need of knowing system models.Composed of three parts, this thesis contributes to address the abovementioned challenges of modern control systems. As an example, DC microgrids (DCmGs) are considered throughout the thesis for the development and validation of the proposed methods. The first part focuses on distributed consensus protocols. We first investigate the problem of state consensus in general linear interconnected MASs (LIMASs), for which we provide conditions based on the physical and communication graph properties as well as system matrices. Our results show that weak physical coupling and well-connected graphs are favorable features for consensus. We then focus on nonlinear DCmGs and propose a novel distributed controller to achieve voltage balancing and current sharing, which is a specific case of output consensus. By exploiting the structure of DCmG dynamics, we provide conditions on the attainment of these objectives and the stability of the closed-loop system. In the second part, a distributed cyber-attack detection scheme is developed for LIMASs controlled in a distributed fashion. The detection architecture comprises local monitoring units collocated with each agent and checking the presence of cyber attacks in variables communicated by neighboring agents. Each unit estimates the states of local and nearby agents, and detects an attack if a suitably defined error is sufficiently large. A thorough detectability analysis considering different types of attacks is also performed. The final part of the thesis provides direct data-driven methods for control and state estimation based on finite data. First, we look at the worst-case optimal tracking problem in presence of measurement noises satisfying a quadratic bound. Control design is formulated as a semidefinite program (SDP), whose computational complexity is independent of the amount of data. Then, we turn our attention to state estimation in presence of unknown inputs, for which we present data-driven necessary and sufficient conditions. Under these conditions, a novel data-driven state estimation method with stability guarantees is provided.