TIME OPTIMAL PROBLEM OF MULTIDIMENSIONAL DISTRIBUTED PARAMETER SYSTEM

Abstract

Distributed Parameter System (DPS) is a system in which mass or energy is distributed over all the spatial dimen-sions. Such systems arise in various application areas, such as a Bending of beama, Heat transfer, chemical process systems, communication systems. Dynamics of. such systems is described by partial differentia. equations. Compared to ordinary differential equations, very small amount of work has been done towards the solution of partial differential equations. Owing to these difficulties study of optimal control of DPS is formidable compared to its counterpart in Lumped Parameter Systems (LPS). There are many physical systems which are described by diffusion equations, for example, heating of solids, flow of viscous fluids, diffusion of gases, flux distribution in a solid rotor. Very often it is da4ribeI to achieve a particular type of distribution in such systems by applying manipulative control on its boundaries. It is also desirable to achieve such distributions by suitably designing the controller, in shortest possible time. From physical point of view, the control may sometimes have physical constraints.