The article discusses a method to efficiently analyze reachability in high-dimensional systems using conservative linear envelopes and antagonistic error. It introduces the concept of Hamilton-Jacobi reachability analysis and its applications in various domains. The authors propose a novel approach to overcome the curse of dimensionality by utilizing the Hopf formula for linear time-varying systems. By transforming nonlinear system errors into bounded artificial disturbances, they achieve guaranteed conservative reachability analysis and control synthesis. Several technical methods are presented to reduce conservativeness in the analysis, demonstrated through examples like the Van der Pol system and pursuit-evasion games with Dubins cars.
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by Will Sharple... alle arxiv.org 03-22-2024
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