Robust Hybrid Model Reference Adaptive Control and Output-Feedback Linearization with Applications to Quadcopter UAVs

Abstract

This chapter presents the first robust model reference adaptive control (MRAC) system for hybrid, time-varying plants affected by parametric, matched, and unmatched uncertainties as well as uncertainties in the plant’s discrete-time dynamics. This continuous-time component of this MRAC system comprises both an adaptive law and a control law that are analogous to the adaptive law and control law of classical MRAC systems. The discrete-time component of the proposed MRAC system comprises a resetting mechanism that counters the effect of resetting events in the plant dynamics. The mechanisms that guarantee robustness to unmatched uncertainties extend the well-known σ-modification and e-modification of MRAC as well as the use of continuous projection operators to a hybrid systems framework. This adaptive control framework is applied to the problem of controlling output-feedback linearized dynamical models while switching among multiple feedback-linearizing output signals according to any user-defined algorithm that is compatible with the conditions sufficient for the existence of the linearizing diffeomorphism. As an example, we solve the problem of controlling the dynamics of a quadcopter unmanned aerial vehicle (UAV) tasked with following both a user-defined trajectory and a user-defined attitude, and not just a user-defined yaw angle as it occurs in the overwhelming majority of works on this topic.