Fast diffeomorphic matching to learn globally asymptotically stable nonlinear dynamical systems

We propose a new diffeomorphic matching algorithm and use it to learn nonlinear dynamical systems with the guarantee that the learned systems have global asymptotic stability. For a given set of demonstration trajectories, and a reference globally asymptotically stable time-invariant system, we compute a diffeomorphism that maps forward orbits of the reference system onto the demonstrations. The same diffeomorphism deforms the whole reference system into one that reproduces the demonstrations, and is still globally asymptotically stable.