Set Membership methods in identification, prediction and filtering of nonlinear systems

The problem of making inference on nonlinear systems starting from finite and noise-corrupted data is considered. In particular, the inference of identification, prediction and filtering are treated. The inference making problem is approached by means of a Set Membership (SM) method. The main feature of this method is that it assumes a bound on the gradient of the model regression function. On the contrary, most of the existing methods need the choice of a functional form of the regression function. The search of the functional form may be quite time consuming, and lead only to approximate model structures, whose errors may be responsible of large inference errors. Moreover, the SM method assumes only that the noise is bounded, in contrast with statistical approaches, which rely on noise assumptions such as stationarity, ergodicity, uncorrelation, type of distribution, etc. The validity of these assumptions may be difficult to test in many applications and is certainly lost in presence of approximate modeling. In the paper, some of the main results developed by the authors, i.e. an optimal identification algorithm, two almost-optimal prediction algorithms and an almost-optimal filtering algorithm are presented within the presented unified SM inference making problem.