ECE 69500 - Hybrid Systems: Theory & Analysis

Lecture Hours: 3 

Credits: 3

Areas of Specialization(s): Automatic Control (AC)

Prerequisites: ECE602 (or AAE564 or equivalent) and MA511 (or equivalent) 

Catalog Description:
The revolution in digital technology has fueled a need for design techniques that can guarantee safety and performance specifications of embedded systems, or systems that couple discrete logics with analog physical environment. Such systems can be modeled by hybrid systems, which are dynamical systems that combine continuous-time dynamics modeled by differential equations and discrete-event dynamics modeled by finite automata.

This course will present an overview of the recent advances in modeling, analysis, control, and verification of hybrid systems. Topics covered include: continuous-time and discrete-event models; reachability analysis; safety specifications and model checking; optimal control and differential games; (Lyapunov) stability analysis and verification tools; stochastic hybrid systems; numerical simulations; and a range of engineering applications.

Required Text(s): NA

Recommended Text(s): A book draft currently in preparation by John Lygeros, Claire Tomlin, and Shankar Sastry and selected readings from the literature.

Lecture Outline:

Lectures	Principal Topics
1	Introduction: Motivating examples and outline
3	Background on continuous and discrete time dynamical systems
5	Model of hybrid systems (hybrid automata)
4	Some scientific and engineering applications
5	Reachability analysis of hybrid systems
5	Stability of hybrid systems
2	Software tools for the simulation of hybrid systems
6	Optimal control of hybrid systems
6	Estimation and identification of hybrid systems
3	Controller synthesis
1	Advanced topics: a geometric theory of hybrid systems
2	Advanced topics: stochastic hybrid systems (SHSs)
1	Advanced topics: game theory