Robust adaptive control: stability and asymptotic performance

Robust stability and asymptotic performance results are provided for adaptive control in the presence of both compact real parametric uncertainty and frequency-weighted bounded unstructured uncertainty. It is shown that a class of parameter adaptive control systems is robustly stable. The asymptotic robust performance bound can be made arbitrarily close to that of the nonadaptive design which would result from perfect parameter estimation. The key assumptions are: (1) the unknown parameters lie in a known compact convex set, (2) a certain bound on the initial state of the system is known, (3) the control design rule is Lipschitzian, and (4) the control design rule would produce a robust controller if given perfect parameter information. In addition, the location of the parametric and nonparametric uncertainty within the known system dynamic must satisfy certain structural assumptions