Kernel methods for regression in continuous time over subsets and manifolds

This paper derives error bounds for regression in continuous time over subsets of certain types Riemannian manifolds. The problem is typically driven by a nonlinear evolution law taking values on the manifold, and it cast as one optimal estimation reproducing kernel Hilbert space. A new notion persistency excitation (PE) defined rates convergence estimates are derived using PE condition. We discuss analyze two approximation methods exact solution. then conclude with some numerical simulations that illustrate qualitative character computed function estimates. Examples generated trajectory Lorenz system based experimental motion capture data included.