Identification of nonlinear systems and optimality analysis in Sobolev spaces

In this paper, we propose a novel approach for the identification from data of an unknown nonlinear function together with its derivatives. This approach can be useful, for instance, in the context of nonlinear system identification for obtaining models that are more reliable than the traditional ones, based on plain function approximation. Indeed, models identified by accounting for the derivatives can provide a better performance in several tasks, such as multi-step prediction, simulation, and control design. We also develop an optimality analysis, showing that models derived using this approach enjoy suitable optimality properties in Sobolev spaces. We finally demonstrate the effectiveness of the approach with a numerical example.