Controller Synthesis for Hybrid Systems: the Hamilton-Jacobi Approach

C. Tomlin, J. Lygeros and S. Sastry

We present 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 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 present an example derived from aircraft conflict resolution.

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