Towards a unified theory of parameter adaptive control: tunability

The author illustrates some of the advantages of thinking of a parameter adaptive control system as a system consisting of a process, a parameterized controller, and a tuner interconnected in a particular way. The proposed structure has the virtue of being general enough to describe many different kinds of adaptive systems, including those of the model-reference, self-tuning, and high-gain feedback types. While error models are not used in this setting, special emphasis is placed on the importance of a tuning error. Within this framework, the concept of weak tunability is defined, characterized, and shown to be necessary for adaptive stabilization. The main result is to prove that a slightly stronger property called tunability is sufficient for adaptive stabilization, provided a tuning algorithm which possesses certain typical capabilities is used