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In this paper, a novel model reference adaptive control (MRAC) architecture for nonlinear, time-varying, hybrid dynamical systems is applied for the first time to design the control system of a multi-rotor unmanned aerial vehicle (UAV). The proposed control system is specifically designed to address problems of practical interests involving autonomous UAVs transporting unknown, unsteady payloads and subject to instantaneous variations both in their state and in their dynamics. These variations can be due, for instance, to the payload’s dynamics, impacts between the payload and its casing, and sudden payload dropping and pickup. The proposed hybrid MRAC architecture improves the UAV’s trajectory tracking performance over classical MRAC also in the presence of motor failures. The applicability of the proposed framework is validated numerically through the first use of the high-fidelity simulation environment PyChrono for autonomous UAV control system testing.