The objective of this work is to generate new fundamental science for hybrid dynamical systems that enables systematic design of algorithms for learning the parameters, dynamics, and constraints of such complex systems, using experimental data. Hybrid systems are dynamical systems with intertwined continuous and discrete behavior. Hybrid controllers are algorithms that involve logic variables, timers, memory states, along with the associated decision-making logic. The combination of such mixed behavior, both in the system to control and in the algorithms, is embodied in key future engineering systems. The future autonomous systems will have variables that change continuously according to physics laws, exhibit jumps due to controlled switches, replanning of maneuvers, on-the-fly redesign, and failures, while the control algorithms require logic to adapt to such abrupt changes. Hybrid behavior also emerges in such engineering systems due to their complexity. In fact, communication events, abrupt changes in connectivity, and the cyber-physical interaction between vehicles, humans, robots, their environment, and communication networks lead to impulsive behavior that interacts with physics and computing. The intellectual impact of the proposed research plan stems from a novel use of hybrid control theory, one that leads to experimental data-driven learning algorithms for hybrid systems that are not only robust but also optimal. The proposed combination of hybrid control and optimization in- formed by real-time data exploits–in a holistic manner–key robust stabilization capabilities of hybrid feedback control and optimality guarantees of receding horizon control for com- plex autonomous systems of interest to AFOSR that are part of the broad mission of the DoD.