On parameter estimation for delay models with discontinuous right-hand sides

We study delay models with discontinuous right-hand side. Lack of smoothness in the solutions of such problems may have serious consequences for parameters estimation using gradient-based approaches. Additionally, it may cause ambiguities in the parameter determinability analysis applied on the parameter estimates. In order to overcome these difficulties, we suggest a standard regularization technique to make the model continuous. We prove the convergence of the solution of the regularized model to the solution of the original problem. As a consequence of that, parameter estimates inferred from the regularized model converge to the corresponding estimates of the original problem. We support our findings with numerical illustrations for simple test problems.