Applied Math Seminar
Winter Quarter 2002
3:15 - 4:15 p.m.
Sloan Mathematics Corner
Building 380, Room 380-C

Friday, February 15, 2002


Claire Tomlin
Department of Aeronautics and Astronautics
Stanford University

Computational Methods for Analyzing
and Controlling Hybrid Systems

Abstract:

Hybrid system theory lies at the intersection of the two traditionally distinct fields of engineering control theory and computer science verification, and is defined as the modeling, analysis, and control of systems which involve the interaction of both discrete state systems, modeled by finite automata, and continuous state dynamics, modeled by differential equations. Embedded systems, or physical systems controlled by a discrete logic, such as the autopilot logic for controlling an aircraft, or an air traffic management system for controlling thousands of aircraft, are prime examples of systems in which event sequences are determined by continuous state dynamics. These systems use discrete logic in control because discrete abstractions make it easier to manage system complexity and discrete representations more naturally accommodate linguistic and qualitative information in controller design.

In this talk, I will present a method that we have designed for analyzing and controlling hybrid systems, and will focus on the numerical methods and software toolkits that we have developed for efficient application of these techniques. These methods will be presented in the context of three large scale hybrid systems: air traffic system analysis and control (with NASA Ames and Oakland Air Route Traffic Control Center), the design of provably safe autopilot logic (with Boeing), and the analysis of biological cell networks (with the Stanford Medical School).

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