Mario Milanese (Modelway Srl)
SMT: Set Membership Theory for Identification, Prediction, Filtering & Control of Nonlinear Systems
The talk will present a theory of inference-making from noisy data measured on nonlinear systems, showing that identification, prediction, filtering and control are specific instances of the theory. The theory is developed within a Set Membership (SM) framework, an alternative view to the classical Parametric Statistical (PS) framework, widely used in investigating the above specific problems.
In the SM framework, a bound only on the gradient of the system regression function is assumed, at difference from PS methods which assume a parametric functional form of the regression function. Moreover, the SM theory assumes only that the noises corrupting the data are bounded, in contrast with PS approaches, which rely on noise assumptions such as stationarity, uncorrelation, type of distribution, etc.
The basic notions of the theory are presented and main results that can be obtained for the specific cases of identification, prediction, filtering and control are reviewed.
The talk will conclude with a discussion of two basic questions:
– what may be gained by using the presented SM theory instead of the widely diffused PS theory?
– is the theory practically viable, allowing to efficiently deal with complex real world applications?
The discussion will be based both on theoretical as well as experimental results