Adaptation is amongst the most familiar and wide spread phenomena in nature. Since the early days of the nineteenth century it has puzzled researchers in broad areas of science. Since it had often been observed in responsive behaviors of biological systems, adaptation was initially understood as a regulatory mechanism that helps an animal to survive in a changing environment. Later the notion of adaptation was adopted in wider fields of science and engineering.

As a theoretical discipline it began to emerge as a branch of control theory during the first half of the twentieth century. Its beginning was marked by publications discussing basic principles of adaptation and its merits for engineering. Imprecise technology and mechanisms were, perhaps, amongst the strongest practical motivations for such a theory at that time. Various notions of adaptation were adopted by engineers and theoreticians in order to grasp, understand, and implement relevant features of this phenomenon in practice. The first applications of the new theory were simple schemes for extremal control of mechanical systems; these systems could be described by just a few linear ordinary differential equations. Since then adaptive controllers have evolved to encompass substantially more complex devices. The controlling devices themselves can now be viewed as nonlinear dynamical systems with specific input–output properties. Methods for the design and analysis of such systems are currently recognized by many in terms of the theory of adaptive control and systems identification.