Multiple-Timescale Adaptive Control for Uncertain Nonlinear Dynamical Systems

Abstract

Adaptive control is a field of control theory dedicated to addressing uncertain and time-varying system models. Multiple-timescale control is dedicated to addressing systems with some states evolving quickly and others evolving slowly. Multiple-timescale control has been shown to have difficulty with uncertain systems and adaptive control has been shown to have difficulty with multiple-timescale systems. This dissertation describes a novel control methodology called [K]control of Adaptive Multiple-timescale Systems (KAMS). KAMS seeks to address systems that simultaneously exhibit uncertain and multiple-timescale behaviors. Unlike traditional multiple-timescale control literature, KAMS uses adaptive control to stabilize the subsystems. The reference models and adapting parameters used in adaptive control significantly complicate the stability analysis. KAMS is a flexible theory and framework. The stability proofs apply to a wide array of adaptive algorithms and multiple-timescale fusion techniques. The examples in this dissertation include the adaptive control methods Model Reference Adaptive Control and Adaptive Nonlinear Dynamic Inversion. The multiple-timescale fusion techniques of Composite Control, Sequential Control, and Simultaneous Slow and Fast Tracking are all used. The primary novel contributions of this dissertation are 1.) a formal development and analysis of KAMS theory and its design methodology; 2.) a set of theoretical tools for stability analyses of KAMS including proofs of sufficient conditions for asymptotic stability; 3.) demonstration of the benefits of KAMS, including formal and numerical validation of how KAMS can relax the minimum phase assumption for a multitude of common adaptive control methods. KAMS is demonstrated and evaluated on examples consisting of stabilization and attitude control of a quadrotor Unmanned Air System; fuel-efficient orbital transfer maneuvers; and preventing inlet unstart on hypersonic aircraft. Results presented in the dissertation demonstrate that KAMS has better performance overall, and improved robustness to uncertainty in the time scale separation parameter than traditional approaches like adaptive control alone, or multiple-timescale control alone.