Chapter

Hybrid Systems: Computation and Control

Volume 1569 of the series Lecture Notes in Computer Science pp 238-255

Date:

Computing Controllers for Nonlinear Hybrid Systems

  • Claire TomlinAffiliated withDepartment of Aeronautics and Astronautics, Stanford University
  • , John LygerosAffiliated withDepartment of Electrical Engineering and Computer Sciences, University of California
  • , Shankar SastryAffiliated withDepartment of Electrical Engineering and Computer Sciences, University of California

* Final gross prices may vary according to local VAT.

Get Access

Abstract

We discuss a procedure for synthesizing controllers for safety specifications for hybrid systems. The procedure depends on the construction of the set of states of a continuous dynamical system that can be driven to a subset of the state space, avoiding another subset of the state space (the Reach-Avoid set). We present a new characterization of the Reach-Avoid set in terms of the solution of a pair of coupled Hamilton-Jacobi partial differential equations. We also discuss a computational algorithm for solving such partial differential equations and demonstrate its effectiveness on numerical examples.