Comparison of a nonlinear adaptive controller with certainty-equivalence type adaptive controllers

Recently a new class of adaptive controllers for linear time invariant minimum phase plants has been proposed and analysed. The design of these controllers is based on nonlinear tools and appears to be different from that of the more traditional adaptive controllers developed using the certainty-equivalence approach. The purpose of this paper is to compare the two classes of adaptive controllers by analysing their design and stability properties. It is shown that for plants with relative degree 1, the new class of adaptive controllers is a special case of a class of indirect model reference adaptive controllers developed using the certainty-equivalence approach. For relative degree greater that 1, the two classes of controllers are different.