Towards a unified theory of parameter adaptive control. I. Tunability

A conceptual framework is proposed in which a parameter adaptive control system is taken to be a particular interconnection of a process, a parameterized controller, and a tuner. Emphasis is placed on the importance of a tuning error in the adaptation process. The concept of tunability is defined, characterized, and shown to be necessary for adaptive stabilization. Tunability also proves to be sufficient for adaptive stabilization for systems using tuning algorithms with certain typical capabilities