Convex Hulls of Reachable Sets

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We study the structure of the convex hulls of reachable sets of nonlinear systems with bounded disturbances (dx/dt=f(x)+g(x)w). Reachable sets play an important role in control. For example, they are often used in the robustness analysis of controllers. However, efficiently computing accurate approximations of reachable sets of nonlinear systems remains difficult. Is there additional structure that we can use to design faster and more accurate algorithms?

We extend our previous characterization results by accounting for uncertain initial conditions and analyzing more general classes of dynamical systems and sets of disturbances. We also provide second-order error bounds for a sampling-based estimation algorithm.