Identification of Monotone Wiener Systems
Abstract:
This presentation reviews some of the developments in the design and analysis of tools for estimating nonparameteric monotone Wiener systems from observed data. This problem is interesting as it calls for an extension of tools from system identification for linear systems towards nonlinear estimation, while still relating very closely to linear systems theory. Specifically, we argue that the role of complexity control becomes more pronounced than in traditional parametric problems. It is indicated how methods of convex optimization and regularization provide a satisfactory approach for the batch case. Secondly, it is reviewed how methods of online learning provide an efficient approach to recursive identification of such systems. Throughout, it is indicated how this problem occurs in practical cases of identification and automatic control, involving such phenomena as quantization, transformation or saturation of the measurements.