$\mathcal{L}_1$ Adaptive Control for Switching Reference Systems: Application to Flight Control

Abstract: This paper presents a framework for the design and analysis of an $\mathcal{L}_1$ adaptive controller with a switching reference system. The use of a switching reference system allows the desired behavior to be scheduled across the operating envelope, which is often required in aerospace applications. The analysis uses a switched reference system that assumes perfect knowledge of uncertainties and uses a corresponding non-adaptive controller. Provided that this switched reference system is stable, it is shown that the closed-loop system with unknown parameters and disturbances and the $\mathcal{L}_1$ adaptive controller can behave arbitrarily close to this reference system. Simulations of the short period dynamics of a transport class aircraft during the approach phase illustrate the theoretical results.