Suboptimal Periodical Control for the Infinite Dimensional Systems with Application to Biomedical Modeling

Despite long history of research and rich literature devoted to optimization problems, relatively few works concerning optimal control for infinite dimensional systems can be found. Moreover, they mostly present approaches suitable for PDE models. This paper is concerned with optimal control problem for certain class of infinite dimensional systems as well as some dynamical properties of such systems. Models based on infinite number of state equations may be applied to a variety of systems. They may describe e.g. RC ladders, which are approximation of long transmission lines, model of drug resistance evolution caused by gene amplification or certain queuing systems (e.g. M/M/1 [2]). This paper presents analysis of bilinear models with infinite dimensional, tridiagonal system matrix, represented by equation ) ( )) ( ( ) ( ) ( t u t x B t Ax t x + = & , (1) where