Set-Membership Estimation Theory for Coupled MIMO Wiener-like Models

Abstract

In this paper, an approach for identifying coupled multiple input multiple output (MIMO) Wiener like models in presented. Each multiple input, single output (MISO) model structure contained in the MIMO model is parameterized using finite set of discrete Laguerre transfer functions followed by a High Level Canonical Piecewise Linear (HLCPWL) that represents the static memoryless nonlinear block. For each MISO model, the parameters of the HLCPWL functions are found via Set Membership (SM) estimation theory, under mild error constrains. In this way, each MISO Wiener like model is described as a set of parameters for the nonlinear static subsystem, whose values are obtained by solving linear programming problem. The MIMO Wiener like model structure is then represented as a set of coupled input output MISO models, converting the identification of a coupled MIMO system into the identification of MISO systems. In order to validate the proposed identification algorithm, an illustrative example is provided.