The deployment of advanced real-time control and optimization strategies in socially-integrated

engineering systems could significantly improve our quality of life while

creating jobs and economic opportunity. However, in cyber-physical systems such as

smart grids, transportation networks, healthcare, and robotic systems, there still exist

several challenges that prevent the implementation of intelligent control strategies.

These challenges include the existence of limited communication networks, dynamic

and stochastic environments, multiple decision makers interacting with the system,

and complex hybrid dynamics emerging from the feedback interconnection of physical

processes and computational devices.

In this dissertation, we study the problem of designing robust control and optimization

algorithms for cyber-physical systems using the framework of hybrid dynamical

systems. We propose different theoretical frameworks for the design and analysis of

feedback mechanisms that optimize the performance of dynamical systems without requiring

an explicit characterization of their mathematical model, i.e., in a model-free

way. The closed-loop system that emerges of the interconnection of the plant with the

feedback mechanism describes, in general, a set-valued hybrid dynamical system. These

types of systems combine continuous-time and discrete-time dynamics, and they usually

lack the uniqueness of solutions property. The framework of set-valued hybrid

dynamical systems allows us to study many complex dynamical systems that emerge in

different engineering applications, such as networked multi-agent systems with switching graphs, non-smooth mechanical systems, dynamic pricing mechanisms in transportation

systems, autonomous robots with logic-based controllers, etc. We propose

a step-by-step approach to the design of different types of discrete-time, continuous-time,

hybrid, and stochastic controllers for different types of applications, extending

and generalizing different results in the literature in the area of extremum seeking control,

sampled-data extremization, robust synchronization, and stochastic learning in

networked systems. Our theoretical results are illustrated via different simulations and

numerical examples.