Slow Timescale Adaptive Control for Multiple-Timescale Systems

Abstract

Multiple-timescale systems are a noteworthy class of dynamic systems that can be modeled with singularly perturbed differential equations. Adaptive control has not been studied in the context of singularly perturbed plants. This paper introduces and evaluates three methods of adaptive control for multiple-timescale 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 can be sensitive to timescale effects. 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 timescale separation. [K]Control of Adaptive Multiple-Timescale Systems (KAMS) fuses two adaptive control signals using multiple-timescale techniques. KAMS takes advantage of model reduction unlike FOAC, and allows for unstable fast dynamics unlike ROAC. Generalized formal definitions, stability criteria, and examples are developed and presented for each method. Results presented in the paper for the control of a Boeing 747-100/200 on approach show that KAMS has a desirable blend of performance and robustness because each reduced-order model is stabilized separately.