A new linear adaptive controller: design, analysis and performance

The certainty equivalence and polynomial approach, widely used for designing adaptive controllers, leads to "simple" adaptive control designs that guarantee stability, asymptotic error convergence, and robustness, but not necessarily good transient performance. Backstepping and tuning functions techniques, on the other hand, are used to design adaptive controllers that guarantee stability and good transient performance at the expense of a highly nonlinear controller. In this paper, we use elements from both design approaches to develop a new certainty equivalence based adaptive controller by combining backstepping based control law with a normalized adaptive law. The new adaptive controller guarantees stability and performance, as well as parametric robustness for the nonadaptive controller, that are comparable with the tuning functions scheme, without the use of higher order nonlinearities.