Analysis of a class of infinite dimensional systems based on model decomposition

Authors:	Smieja Jaroslaw, Silesian University of Technology, Poland Swierniak Andrzej, Silesian University of Technology, Poland
Topic:	1.1 Modelling, Identification & Signal Processing
Session:	Image Processing and Biomedical Applications
Keywords:	Systems methodology, optimal control, biomedical systems, bilinear systems

Abstract

This paper is concerned with modeling and control of a class of bilinear systems. They are described by infinite number of ODEs. After introduction of model applications, the methodology of analysis of such models, based on system decomposition, is presented. The model description is transformed into a vector integro-differential equation, which makes it possible to analyze its behavior and address a particular optimization problem arising in the given model application. The optimization problem is stated and necessary conditions of optimal control are derived. Subsequently, the gradient method for finding optimal control is shown, illustrated by an example. Finally, some remarks on the model applicability are presented.