Robust optimization method for the identification of nonlinear state-space models

A partially constrained optimization method is presented to estimate the parameters of a discrete-time nonlinear state-space model. Its advantage is its robustness towards instabilities: it can even be used to model unstable systems. A nonlinear least-squares optimization strategy is used, allowing to estimate the model parameters together with a user-selected set of states. The fraction (over time) of selected states determines the number of constraints in the optimization. Depending on this fraction, the algorithm is more robust towards instabilities but rather slow (many constraints), or faster but less robust (few constraints). A strategy (with effective state selection) is proposed that benefits from the advantages of both situations. An experimental data example illustrates how large data sets can be handled via this strategy, and that unstable regions can be crossed.