A game theoretic approach to controller design for hybrid systems
Tomlin, C.J.
Lygeros, J.
Shankar Sastry, S.
Dept. of Aeronaut. & Astronaut., Stanford Univ., CA;
This paper appears in: Proceedings of the IEEE
Publication Date: Jul 2000
Volume: 88,
Issue: 7
On page(s): 949-970
ISSN: 0018-9219
References Cited: 62
CODEN: IEEPAD
INSPEC Accession Number: 6740317
Digital Object Identifier: 10.1109/5.871303
Current Version Published: 2002-08-06
Abstract
We present a method to design controllers for safety
specifications in hybrid systems. The hybrid system combines discrete
event dynamics with nonlinear continuous dynamics: the discrete event
dynamics model linguistic and qualitative information and naturally
accommodate mode switching logic, and the continuous dynamics model the
physical processes themselves, such as the continuous response of an
aircraft to the forces of aileron and throttle. Input variables model
both continuous and discrete control and disturbance parameters. We
translate safety specifications into restrictions on the system's
reachable sets of states. Then, using analysis based on optimal control
and game theory for automata and continuous dynamical systems, we derive
Hamilton-Jacobi equations whose solutions describe the boundaries of
reachable sets. These equations are the heart of our general controller
synthesis technique for hybrid systems, in which we calculate feedback
control laws for the continuous and discrete variables, which guarantee
that the hybrid system remains in the “safe subset” of the
reachable set. We discuss issues related to computing solutions to
Hamilton-Jacobi equations. Throughout, we demonstrate out techniques on
examples of hybrid automata modeling aircraft conflict resolution,
autopilot flight mode switching, and vehicle collision avoidance
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