Robust adaptive regulation of polynomial systems with dynamic uncertainties

This paper studies the global regulation problem for a class of nonlinear polynomial systems subject to both dynamic uncertainty and static uncertainty. The dynamic uncertainty does not vanish at the origin of the state space and thus is not input-to-state stable (ISS). As a result, the small gain theory based robust control technique alone cannot handle this problem. We manage to integrate both robust control and adaptive control techniques to overcome the difficulty. The problem studied here is motivated from the global robust servomechanism problem for the lower triangular systems subject to an uncertain exosystem. An example is given to illustrate this point.