A Tutorial on Hybrid Feedback Control

This tutorial paper introduces hybrid feedback control through a self-contained examination of hybrid control systems modeled by the combination of differential and difference equations with constraints. Using multiple examples, it illustrates the power of hybrid feedback control, which stems from the integration of continuous and discrete dynamics, where state variables update instantaneously at specific events while flowing continuously otherwise. The paper defines hybrid closed-loop systems as interconnected hybrid plants and controllers with designated inputs and outputs, and formalizes their solutions. It summarizes key properties of hybrid systems and reviews various control strategies, including supervisory control with logic variables to select feedback controllers, event-triggered control to minimize control input updates, and strategies using multiple Lyapunov-like functions for stabilization. Pointers to further reading and other strategies in the literature are provided.