Adaptive Control for Singularly Perturbed Systems

Singularly perturbed systems are a class of mathematical systems that are not well approximated by their limits and can be used to model plants with multiple fast and slow states. Multiple-timescale systems are very common in engineering applications, but adaptive control can be sensitive to timescale effects. Recently a method called [K]control of Adaptive Multiple-timescale Systems (KAMS) has shown improved performance and increased robustness for singularly perturbed systems, but it has only been studied on systems using adaptive control for the slow states. This article extends KAMS to the general case when adaptive control is used to stabilize both the slow and fast states simultaneously. This causes complex interactions between the fast state reference model and the manifold to which the fast states converge. It is proven that under certain conditions the system still converges to the reference model despite these complex interactions. This method is demonstrated on a nonlinear, nonstandard, numerical example.