Robust Hybrid Systems for Control, Learning, and Optimization in Networked Dynamical Systems

The deployment of advanced real-time control and optimization strategies in socially-integratedengineering systems could significantly improve our quality of life whilecreating jobs and economic opportunity. However, in cyber-physical systems such assmart grids, transportation networks, healthcare, and robotic systems, there still existseveral challenges that prevent the implementation of intelligent control strategies.These challenges include the existence of limited communication networks, dynamicand stochastic environments, multiple decision makers interacting with the system,and complex hybrid dynamics emerging from the feedback interconnection of physicalprocesses and computational devices.In this dissertation, we study the problem of designing robust control and optimizationalgorithms for cyber-physical systems using the framework of hybrid dynamicalsystems. We propose different theoretical frameworks for the design and analysis offeedback mechanisms that optimize the performance of dynamical systems without requiringan explicit characterization of their mathematical model, i.e., in a model-freeway. The closed-loop system that emerges of the interconnection of the plant with thefeedback mechanism describes, in general, a set-valued hybrid dynamical system. Thesetypes of systems combine continuous-time and discrete-time dynamics, and they usuallylack the uniqueness of solutions property. The framework of set-valued hybriddynamical systems allows us to study many complex dynamical systems that emerge indifferent engineering applications, such as networked multi-agent systems with switching graphs, non-smooth mechanical systems, dynamic pricing mechanisms in transportationsystems, autonomous robots with logic-based controllers, etc. We proposea step-by-step approach to the design of different types of discrete-time, continuous-time,hybrid, and stochastic controllers for different types of applications, extendingand generalizing different results in the literature in the area of extremum seeking control,sampled-data extremization, robust synchronization, and stochastic learning innetworked systems. Our theoretical results are illustrated via different simulations andnumerical examples