George Haller

Blow-up of Koopman eigenfunctions at basin boundaries

Abstract We show that under non-degeneracy conditions on a dynamical system, all of its smooth, non-constant Koopman eigenfunctions blow up along the boundary of the basin of attraction of a fixed point. We give a simple, geometric version of this general result for the case of a...

Existence of Spectral Submanifolds in Time Delay Systems

Abstract Spectral submanifolds (SSMs) are invariant manifolds of a dynamical system, defined by the property of being tangent to a spectral subspace of the linearized dynamics at a steady state. We show existence, along with certain desirable properties such as smoothness, attrac...

Predicting subharmonic and superharmonic backbone curves in nonlinear mechanical systems

Abstract We show that conservative (or primary) backbone curves, defined as amplitude–frequency curves of conservative nonlinear normal modes, have a tight mathematical connection with all subharmonic and superharmonic (or secondary) backbone curves, defined as curves connecting...

Nonlinear spectral modeling and control of soft-robotic muscles from data

Abstract Artificial muscles are essential for compliant musculoskeletal robotics but complicate control due to nonlinear multiphysics dynamics. Electrohydraulic actuators, a class of soft artificial muscles, offer high performance but exhibit memory effects and hysteresis. Here w...