Introduction to Adaptive Control for Multiple Time Scale Systems

Abstract

Multiple time scale systems are a noteworthy class of dynamical systems. Adaptive control has not been studied in the context of multiple time scale systems because it is not robust to time scale separation. This paper introduces and evaluates three methods of adaptive control for multiple time scale systems. Each method is a framework that is valid for a wide class of adaptive control methods. Full-Order Adaptive Control (FOAC) applies adaptive control to the system as a whole. It is straightforward but sensitive to time scale uncertainty. Reduced-Order Adaptive Control (ROAC) applies adaptive control to either the fast or slow modes only. This simplifies synthesis but can also constrain the range of valid time scale separation. [K]Control of Adaptive Multiple Time Scale Systems (KAMS) fuses two adaptive control signals using multiple time scale techniques. Generalized formal definitions, stability criteria, and examples are developed and presented for each method. Results show that [K]Control of Adaptive Multiple Time Scale Systems has the best performance because each reduced-order model is stabilized separately and because the fast dynamics converge to the manifold more quickly than the other methods. It also takes advantage of model reduction and relaxes the stability requirements of the other methods.