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We present a parameter estimation method in Ordinary Differential Equation(ODE) models. Due to complex relationships between parameters and states theuse of standard techniques such as nonlinear least squares can lead to thepresence of poorly identifiable parameters. Moreover, ODEs are generallyapproximations of the true process and the influence of misspecification oninference is often neglected. Methods based on control theory have emerged toregularize the ill posed problem of parameter estimation in this context.However, they are computationally intensive and rely on a nonparametric stateestimator known to be biased in the sparse sample case. In this paper, weconstruct criteria based on discrete control theory which are computationallyefficient and bypass the presmoothing step of signal estimation while retainingthe benefits of control theory for estimation. We describe how the estimationproblem can be turned into a control one and present the numerical methods usedto solve it. We show convergence of our estimator in the parametric andwell-specified case. For small sample sizes, numerical experiments with modelscontaining poorly identifiable parameters and with various sources of modelmisspecification demonstrate the acurracy of our method. We finally test ourapproach on a real data example.

A regularization method for the parameter estimation problem in ordinary differential equations via discrete optimal control theory