Abstract
Array algebra and array optimization technique are concisely reviewed. The array is a natural generalization of the vector-matrix and it provides the more convenient tool than the vector-matrix does. It is shown that a wide class of distributed parameter systems (DPS) is approximately transformed into array dynamical systems in a unified manner. In the array system formulation, the well-systematized lumped parameter theory is available, at the same time, the spatial structure of the DPS is preserved and it is easy to utilize the SpatialState-Distribution-Pattern (SSDP) to control. The optimal regulator problem for the linear array systems is formulated and controllers for the problem are optimally designed by use of array optimization technique. The resultant controller realizes the most basic SSDP feedback in the sense that the structured states are feedbacked. The array formulation, in other words, the discretization of continuous distributions into forms suitable for computer management with their spatial structure preserved, provides a methodology for SSDP analysis and design, and it can be applied to various fields other than DPS approximation.
