On the smoothness of nonlinear system identification

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We shed new light on the \textit{smoothness} of optimization problems arising in prediction error parameter estimation of linear and nonlinear systems.

• We show that for regions of the parameter space where the model is not contractive, the Lipschitz constant and $\beta$-smoothness of the objective function might blow up exponentially with the simulation length, making it hard to numerically find minima within those regions or, even, to escape from them.
• In addition to providing theoretical understanding of this problem, this paper also proposes the use of multiple shooting as a viable solution.
• The proposed method minimizes the error between a prediction model and the observed values.