Guaranteed Overapproximations of Unsafe Sets for Continuous and Hybrid Systems: Solving the Hamilton-Jacobi Equation Using Viability Techniques
نویسندگان
چکیده
We show how reachable sets of constrained continuous and simple hybrid systems may be computed using the minimum time-toreach function. We present an algorithm for computing a discrete approximation to the minimum time-to-reach function, which we prove to be a converging underapproximation to the actual function. We use the discrete minimum time-to-reach function for simple hybrid systems to compute overapproximations of unsafe zones for aircraft in a sector of the Oakland Air Traffic Control Center, leading to the automatic generation of conflict-free aircraft maneuvers.
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