Papers › Reachability of weakly nonlinear systems using Carleman linearization
Reachability of weakly nonlinear systems using Carleman linearization
Marcelo Forets, Christian Schilling
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In this article we introduce a solution method for a special class of nonlinear initial-value problems using set-based propagation techniques. The novelty of the approach is that we employ a particular embedding (Carleman linearization) to leverage recent advances of high-dimensional reachability solvers for linear ordinary differential equations based on the support function. Using a global error bound for the Carleman linearization abstraction, we are able to describe the full set of behaviors of the system for sets of initial conditions and in dense time.
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