Feedback linearization with Neural Network augmentation applied to X-33 attitude control

Abstract

In the application of adaptive flight control, significant issues arise due to vehicle input characteristics such as actuator position limits, actuator position rate limits, and linear input dynamics. The concept of modifying a reference model to prevent an adaptation law from "seeing" and adapting-to these system characteristics is introduced. A specific adaptive control method based on this concept, termed Pseudo-Control Hedging, is introduced that accomplishes this for any Model Reference Adaptive Controller that includes approximate feedback linearization. This method enables continued adaptation while the plant input is saturated. Acceptance and flight certification of an online Neural Network adaptive control law for the X-33 Reusable Launch Vehicle technology demonstrator is discussed as motivation for this work. Simulation results applying the method to the X-33 are described.

Historical Overview of Research in Reconfigurable Flight Control

“…The first term is derived from the Lyapunov stability approach, and the second term ensures the boundedness of the neural-network weights. Variations of this approach were applied by Calise and students of Calise to a wide variety of systems including missiles [57], a tilt-rotor aircraft [58], reusable launch vehicles [59], and munitions [60]. Several important theoretical advances were made in the course of this work, including a stability proof for adaptive multi-layer sigmoidal neural-networks in McFarland and Calise [57] and a pseudo-control hedging technique to allow adaptation to continue during actuator saturation in Johnson et al [59].…”

Hybrid Adaptive Flight Control with Model Inversion Adaptation

“…Thus, the development of verifiable metrics for adaptive control will be important in order to mature adaptive control technologies in the future. Over the past several years, various model-reference adaptive control (MRAC) methods have been investigated (Cao & Hovakimyan, 2008;Eberhart & Ward, 1999;Hovakimyan et al, 2001;Johnson et al, 2000;Kim & Calise, 1997;Lavretsky, 2009;Nguyen et al, 2008;Rysdyk & Calise, 1998;Steinberg, 1999). The majority of MRAC methods may be classified as direct, indirect, or a combination thereof.…”

“…In contrast, direct adaptive control methods adjust control parameters to account for system uncertainties directly without identifying unknown plant parameters explicitly. MRAC methods based on neural networks have been a topic of great research interest (Johnson et al, 2000;Kim & Calise, 1997;Rysdyk & Calise, 1998). Feedforward neural networks are capable of approximating a generic class of nonlinear functions on a compact domain within arbitrary tolerance (Cybenko, 1989), thus making them suitable for adaptive control applications.…”

“…This method is the basis for the intelligent flight control system that has been developed for the F-15 test aircraft by NASA. Johnson et al introduced a pseudo-control hedging approach for dealing with control input characteristics such as actuator saturation, rate limit, and linear input dynamics (Johnson et al, 2000). Hovakimyan et al developed an output feedback adaptive control to address issues with parametric uncertainties and unmodeled dynamics (Hovakimyan et al, 2001).…”

Optimal Control Modification for Robust Adaptation of Singularly Perturbed Systems with Slow Actuators

“…There has been a steady increase in the number of adaptive control applications in a wide range of settings such as aerospace, robotics, process control, etc. 1,2 The ability to accommodate system uncertainties and to improve fault tolerance of a control system is a major advantage of adaptive control. Nonetheless, adaptive control still faces significant challenges in providing robustness in the presence of unmodeled dynamics and parametric uncertainties.…”