Bounded error parameter estimation for models described by ordinary and delay differential equations

In this paper, we focus on the problem of parameter identification for non-linear dynamical systems in the case when the number of data samples are too small for standard statistical analysis. The models are described by ordinary and delay differential equations with bounded errors. When the number of data samples is very small, standard validation methods are not applicable because classical statistical asymptotic theory relies on the behavior of the estimated parameter as the number of samples grows large. We present a new computational method that can be used to for solving this problem for a specific class of models. Although the assumptions lead to a restricted class of models, the new algorithm is computationally efficient for this class of problems. We introduce the basic ideas, provide some theoretical results needed for the convergence of the method and present numerical examples to illustrate the approach.