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Reachability analysis of nonlinear dynamical systems is a challenging andcomputationally expensive task. Computing the reachable states for linearsystems, in contrast, can often be done efficiently in high dimensions. In thispaper, we explore verification methods that leverage a connection between thesetwo classes of systems based on the concept of the Koopman operator. TheKoopman operator links the behaviors of a nonlinear system to a linear systemembedded in a higher dimensional space, with an additional set of so-calledobservable variables. Although, the new dynamical system has lineardifferential equations, the set of initial states is defined with nonlinearconstraints. For this reason, existing approaches for linear systemsreachability cannot be used directly. In this paper, we propose the firstreachability algorithm that deals with this unexplored type of reachabilityproblem. Our evaluation examines several optimizations, and shows the proposedworkflow is a promising avenue for verifying behaviors of nonlinear systems.

Reachability of Black-Box Nonlinear Systems after Koopman Operator Linearization