# Computing Controllers for Nonlinear Hybrid Systems

Conference paper

- First Online:

DOI: 10.1007/3-540-48983-5_22

- Cite this paper as:
- Tomlin C., Lygeros J., Sastry S. (1999) Computing Controllers for Nonlinear Hybrid Systems. In: Vaandrager F.W., van Schuppen J.H. (eds) Hybrid Systems: Computation and Control. HSCC 1999. Lecture Notes in Computer Science, vol 1569. Springer, Berlin, Heidelberg

## 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.

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## Copyright information

© Springer-Verlag Berlin Heidelberg 1999