Robust stability of discrete-time adaptive nonlinear control

We consider adaptive control of discrete-time nonlinear systemswith unknown parameters and with bounded noise. In the singleparameter case, we demonstrate that the necessary and sufficientcondition for the existence of a robust feedback stabilizer isthat the nonlinear growth rate of the system dynamics is less than4. This result further confirms the conclusion of (Guo, 1997)where Gaussian noise were considered. In the multiple parametercase, the necessary and sufficient condition turns out to begoverned by a polynomial rule, which is identical to the oneobtained in (Xie and Guo, 1999) where also Gaussian noise wereconsidered but only the necessity part was proved. To the authors'knowledge, the stabilizing controller constructed in this paperseems the first capable of dealing with any nontrivial noise inthe multiple parameter case.