System transformations and adaptive systems

The purpose of this paper is to formulate the concept of system transformation and the concept of adaptive system in the framework of general systems theory, and to characterize both concepts as well as mutual relationships between them from a qualitative viewpoint. We define a system transformation as a mapping on the class of all systems under consideration in a general and unified manner, and especially consider the variety of system behavior under parallel, cascade, and feedback transformation for linear functional time systems. We introduce the notion of open system in terms of system transformation. We then formulate class controllability and adaptability of an open system under system transformation, and characterize them in terms of basic system properties. In particular, we obtain a necessary and sufficient condition under which an open system is adaptive.