A shortcoming of existing reachability approaches for nonlinear systems isthe poor scalability with the number of continuous state variables. To mitigatethis problem we present a simulation-based approach where we first sample anumber of trajectories of the system and next establish bounds on theconvergence or divergence between the samples and neighboring trajectories. Wecompute these bounds using contraction theory and reduce the conservatism bypartitioning the state vector into several components and analyzing contractionproperties separately in each direction. Among other benefits this allows us toanalyze the effect of constant but uncertain parameters by treating them asstate variables and partitioning them into a separate direction. We nextpresent a numerical procedure to search for weighted norms that yield aprescribed contraction rate, which can be incorporated in the reachabilityalgorithm to adjust the weights to minimize the growth of the reachable set.
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