LPV Design of Charge Control for an SI Engine Based on LFT Neural State-Space Models

This paper is one of two joint papers, each presenting and utilizing a different representation of a feedforward neural network for controller design. Here a neural state-space model is transformed into a linear fractional transformation (LFT) representation to obtain a discrete-time quasi-linear parameter-varying (LPV) model of a nonlinear plant, whereas in the joint paper (Abbas and Werner [2008]) a method is proposed to transform the neural state-space into a discrete-time polytopic quasi-LPV model. As a practical application, air charge control of a Spark-Ignition (SI) engine is used in both papers as example to illustrate two different synthesis methods for fixed structure low-order discrete-time LPV controllers. In this paper, a method that combines modelling using a multilayer perceptron network and controller synthesis using linear matrix inequalities (LMIs) and evolutionary search is proposed. In the first step a neural state-space model is transformed into a linear fractional transformation (LFT) representation to obtain a discrete-time quasi-LPV model of a nonlinear plant from input-output data only. Then a hybrid approach using LMI solvers and genetic algorithm, which is based on the concept of quadratic separators, is used to synthesize a discrete-time LPV controller.