Abstract
We consider adaptive control of discrete-time nonlinear systems with unknown parameters and with bounded noise. In the single parameter case, we demonstrate that the necessary and sufficient condition for the existence of a robust feedback stabilizer is that the nonlinear growth rate of the system dynamics is less than 4. This result further confirms the conclusion of (Guo, 1997) where Gaussian noise were considered. In the multiple parameter case, the necessary and sufficient condition turns out to be governed by a polynomial rule, which is identical to the one obtained in (Xie and Guo, 1999) where also Gaussian noise were considered but only the necessity part was proved. To the authors’ knowledge, the stabilizing controller constructed in this paper seems the first capable of dealing with any nontrivial noise in the multiple parameter case.
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