Regression on Manifolds: Nonparametric system identification with applications in control and systems biology
Claire Tomlin, University of California at Berkeley
Abstract:
We discuss a method of system identification which uses nonparametric statistics to generate ordinary differential equation (ODE) models. The method is well suited to identifying system dynamics which evolve on a manifold of dimension lower than that of the ambient space. In this case, the gradient of the vector field may not be well defined, yet the regression coefficients may be interpreted as the exterior derivative of the vector field. The method generates local linear models from time series data: we discuss its application to systems biology and control of autonomous systems.