Hybrid Automata

Hybrid automata are mathematical models used to describe systems that involve both continuous processes and discrete events. Imagine a system that can change smoothly over time—like the temperature rising or falling—and can also switch between different modes or states—like turning a heater on or off. Hybrid automata capture these behaviors by combining equations that describe continuous changes with rules for switching between different modes. This framework is useful for understanding complex systems such as robotics, automotive control, and biological processes where both types of dynamics interact.