Input estimation in nonlinear dynamical systems using differential algebra techniques

The paper considers the problem of estimating the unknown input of a nonlinear dynamical system, described by polynomial or rational differential equations, from a finite set of noisy output samples. Without additional information this problem is ill-posed since the unknown function may belong to an arbitrary infinite-dimensional space. We tackle this difficulty by designing a novel class of fast regularization algorithms that relies upon differential algebra techniques. Monte Carlo studies are used to demonstrate the effectiveness of the new approach.