Adaptation Is Unnecessary in L1-Adaptive Control: What Makes an Adaptive Controller "Adaptive"?

The basic premise upon which adaptive control is based is the existence of a parameterized controller that achieves the control objective. Moreover, it is assumed that these parameters are not known but that they can be estimated online from measurements of the plant signals. Toward this end, an identifier is added to generate the parameter estimates. Then, applying a certainty equivalence principle, these estimates are directly applied in the aforementioned control law. The purpose of this article is to prove, via a proposition that adaptation is unnecessary in L
₁
-Adaptive Control.