AAE 66800: Hybrid Systems: Theory and Applications


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. Important applications of hybrid systems include aeronautics, air and ground transportation systems, CAD, real-time software, robotics and automation, mechatronics, process control, as well as biological systems. Recently, hybrid systems have been at the center of intense research activity in the control theory, computer-aided verification, and artificial intelligence communities, and methodologies and computational tools have been developed to model hybrid systems, to analyze their behaviors, and to synthesize controllers that guarantee closed-loop safety and performance specifications.

Format: 3 hrs of lectures per week
Credit Hours: 3
Offered: Fall (even years)
Pre-Requisite: AAE564 (ECE602 or equivalent) and MA511 (or equivalent)
Co-Requisite: None
Inseok Hwang and Jianghai Hu (ECE)
URL: https://engineering.purdue.edu/AAE/Academics/Courses/aae690b/
Course Goal & Objectives:

To introduce the basic concepts and theory of hybrid systems; to acquaint the students with their analysis and numerical simulation tools; to familiarize the students with the current state of art of hybrid systems research frontier; and to encourage the students to apply the hybrid systems model to problems in their own fields of study and other multidisciplinary areas.

Necessary Background:
  1. Linear system theory
  2. Linear algebra
  1. Introduction
  2. Background
  3. Model of hybrid systems (hybrid automata)
  4. Applications
  5. Reachability analysis of hybrid systems
  6. Stability of hybrid systems
  7. Simulations of hybrid systems
  8. Optimal control of hybrid systems
  9. Estimation and identification of hybrid systems
  10. Controller synthesis of hybrid systems
  11. Advanced topics: a geometric theory of hybrid systems
  12. Advanced topics: stochastic hybrid systems (SHSs)
  13. Advanced topics: game theory

Prepared by: I. Hwang
Date: November 7, 2014