Data from Numerical Continuation in Nonlinear Experiments using Local Gaussian Process Regression

Control-based continuation is a new methodology that allows experimenters to systematically investigate the dynamic behaviour of laboratory-based nonlinear systems, whether they are engineered devices or biological systems. The focus is on finding boundaries between qualitatively different types of behaviour; these boundaries (so-called bifurcations) are then automatically tracked as system parameters are varied, using a range of ideas from control theory, dynamical systems and numerical analysis. The success of this proposal will enable the widespread uptake of control-based continuation, across engineering and the applied sciences, thus greatly easing the difficulties of experimentally characterising nonlinear systems. Three key objectives will be addressed: 1) estimation of the local linearisation of a steady-state directly from the controlled experiment; 2) making the underlying numerical methods fast and robust to experimental noise; and 3) demonstrating the methodology on a multi-degree-of-freedom system.