Adaptive algorithm structure: impacts on stability and performance

The structures of adaptive algorithms are examined for their impact on input-output stability and performance measures. Three general algorithm structures are considered: the a priori form, the a posteriori form, and the proportional integral (PI) form. A parallel development is used to directly compare continuous- and discrete-time versions of the algorithms considered. The standard a priori and a posteriori algorithm forms are shown to be special cases of a more flexible proportional-plus-integral algorithm, which is implemented via normalization in the adaptive law. It is shown that this normalization can enhance algorithm stability and input-output performance of normalized errors, but the performance unnormalized errors may not be significantly affected. This direct comparison of simple algorithm structures serves to isolate the stability and performance properties due to these structures alone. It provides information for algorithm design, allowing the essential effects of design options to be traded off against the many other options