On learning the input-output behaviour of nonlinear fading memory systems from finite data

This paper deals with system identification for the class of nonlinear fadi ng memory systems from input-output noisy data. It is distinct from traditi onal formulations in two respects: (1) We are motivated by the class of sys tems where no finite parameterization can cover the class arbitrarily close ly. Since finite data can only resolve finitely many parameters and so resi dual dynamics becomes an important issue in identification; (2) Our objecti ve is to characterize the behaviour uniformly over the class of all bounded inputs. The primary focus of the paper is to establish a framework for learning the behaviour for the class of nonlinear fading memory systems uniformly over all inputs. The main idea is to separate the components of identification i nto estimation of a parametric part followed by a coarse description of the residual dynamics and the objective is to estimate a model that gives the tightest description. The principle difficulty arises on account of our nee d to characterize the behaviour uniformly over the set of all bounded input s,a requirement motivated from control applications. Although, this goal is unachievable, it is possible to still characterize the 'essential' input-o utput behaviour over the class of dithered inputs. We show that this notion is directly applicable for robust control situations. Moreover, system ide ntification with finite input-output data also becomes tractable, Tradeoff between dithering, size of uncertainty and sample-complexity is also develo ped. Copyright (C) 2000 John Wiley & Sons, Ltd.