Counts as:

Experimental Course Offered:

Spring 2008

Catalog Description:

Description 1: Hybrid systems are dynamical systems with both continuous and discrete dynamics. Developed jointly by the computer science and control communities, they are finding increasing applications in a variety of engineering fields, even in scientific fields such as biological systems. This course will cover some basic aspects of hybrid systems, including their modeling, reachability and stability analysis, controller synthesis, optimization, and simulation tools, that are important in applying hybrid systems to engineering problems. Description 2: 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 CAD, real-time software, robotics and automation, mechatronics, aeronautics, air and ground transportation systems, 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 have been developed to model hybrid systems, to analyze their behaviors, and to synthesize controllers that guarantee closed-loop safety and performance specifications. These advances have also been complemented by computational tools for the automatic verification and simulation of hybrid systems. This course will present an overview of the recent advances in modeling, analysis, control, and verification of hybrid systems. Topics covered in this course include the following aspects of hybrid systems: 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.

Course Objectives:

Objective: 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.

Lecture Outline:

Assessment Method:

none