Robust model predictive control of Wiener systems

Abstract

Block-oriented models (BOMs) have shown to be appealing and efficient as nonlinear representations for many applications. They are at the same time valid and simple models in a more extensive region than time-invariant linear models. In this work, Wiener models are considered. They are one of the most diffused BOMs, and their structure consists in a linear dynamics in cascade with a nonlinear static block. Particularly, the problem of control of these systems in the presence of uncertainty is treated. The proposed methodology makes use of a robust identification procedure in order to obtain a robust model to represent the uncertain system. This model is then employed to design a model predictive controller. The mathematical problem involved in the controller design is formulated in the context of the existing linear matrix inequalities (LMI) theory. The main feature of this approach is that it takes advantage of the static nature of the nonlinearity, which allows to solve the control problem by focusing only in the linear dynamics. This formulation results in a simplified design procedure, because the original nonlinear model predictive control (MPC) problem turns into a linear one.

A new multimodel approach by Laguerre filters on sliding window for nonlinear system identification and control

“…Therefore, the reduced complexity model that approximate a high order for nonlinear systems received great attention in recent years such as the nonlinear block-structure models (Biagiola and Figueroa, 2011; Bloemena et al, 2001; Kazemi and Arefi, 2017; Wiener and Hammerstein), the Volterra models with reduced complexity by expanding Volterra kernels on independent orthonormal function bases such as Laguerre basis and generalized orthonormal basis (GOB) to yield Laguerre-Volterra model (Bernussou and Oustaloup, 2002; Campello et al, 2004; Soni, 2006; Zhang et al, 2009) and GOB-Volterra model (Hacioglu and Williamson, 2001; Kibangou et al, 2003, 2005; Nelles, 2000), the tensor decomposition based Volterra models (Favier et al, 2012; Khouaja et al, 2006, 2016), the bilinear-Laguerre model resulting from the complexity reduction of the bilinear model (Garna et al, 2013; Sarah et al, 2014) and the Laguerre-multimodel (Marouani et al, 2015; Sbarbaro, 1995; Sbarbaro and Johansen, 1997). This latter model is based on the exploitation of the Laguerre filters for each operating region in the multimodel approach (Gasso, 2000; Orjuela, 2008) by using the filtering of the input by Laguerre orthonormal functions.…”

Controlling the Movement of a Human Forearm based on Finite Time Optimal Regulator and Nonlinear Control System

“…The performance index is selected to give the best trade-off between performance and cost of control. The performance index that is widely used in optimal control design is known as the quadratic performance index and is based on minimumerror and minimum-energy criteria [11][12][13][14]. Consider the plant described by…”

Smooth switching in a scheduled robust model predictive controller

“…Meanwhile, some researchers investigated approaches to decrease computational time and complexity [3,4], reduce conservativeness [5][6][7][8], or simplify the representation of the uncertainties [9][10][11][12]. In [9] the nonlinear system was represented * Corresponding author.…”