DETERMINISTIC ADAPTIVE-CONTROL WITH SLOWLY VARYING PARAMETERS - AN AVERAGING ANALYSIS

In this work averaging methods are used to analyse the behaviour of an adaptive controller with slowly varying parameters. The incorporation of time varying parameters into a stability analysis of an adaptive c ontroller leads to certain perturbation terms in the error system. The type of averaging results so far applied to adaptive control cannot d eal with these perturbations. Thus, some new averaging theorems are ne eded. These results are known in the averaging literature. However, he re a very simple proof technique has been found which gives finite and infinite interval averaging results under weaker conditions. The aver aging analysis shows that, with regard to parameter tracking, the adap tive algorithm behaves like a first-order filter. It is also clear tha t successful tracking then requires knowledge of the true speed of par ameter change.