Computing Controllers for Nonlinear Hybrid Systems

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.

• Type: Conference
• Year: 1999
• Where: HYBRID
• Authors: Claire Tomlin, John Lygeros, Shankar Sastry
• Keywords: Control Systems, HYBRID 1999, Partial Differential Equations, Reach-Avoid Set, State Space