Simulation-Based Reachability Analysis for Nonlinear Systems Using Componentwise Contraction Properties

  • Murat ArcakEmail author
  • John Maidens
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10760)


A shortcoming of existing reachability approaches for nonlinear systems is the poor scalability with the number of continuous state variables. To mitigate this problem we present a simulation-based approach where we first sample a number of trajectories of the system and next establish bounds on the convergence or divergence between the samples and neighboring trajectories that are not explicitly simulated. We compute these bounds using contraction theory and reduce the conservatism by partitioning the state vector into several components and analyzing contraction properties separately in each direction. Among other benefits this allows us to analyze the effect of constant but uncertain parameters by treating them as state variables and partitioning them into a separate direction. We next present a numerical procedure to search for weighted norms that yield a prescribed contraction rate, which can be incorporated in the reachability algorithm to adjust the weights to minimize the growth of the reachable set. The proposed reachability method is illustrated with examples, including a magnetic resonance imaging application.


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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.University of California, BerkeleyBerkeleyUSA

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