Multivariable MRAC using Nussbaum gains for aircraft with abrupt damages

This paper derives a stable multivariable model reference adaptive control (MRAC) scheme for systems with abrupt parameter variations (which may cause uncertain sign changes in the system’s high frequency gain matrix), motivated by the application to in-flight aircraft systems with damages. Such sign changes are illustrated by an aircraft model with asymmetric abrupt damages, and their uncertainty is handled by a Nussbaum gain based adaptive control design to control the aircraft for both healthy and post-damage situations, by adapting controller parameters autonomously after the damages occur, for which the knowledge of time instants, structures and values of the damages is not required. A piecewise continuous Lyapunov function is utilized to prove the desired system stability and tracking properties in the presence of damages.