  Quadrotors are one of the popular unmanned aerial vehicles (UAVs) due to
their versatility and simple design. However, the tuning of gains for quadrotor
flight controllers can be laborious, and accurately stable control of
trajectories can be difficult to maintain under exogenous disturbances and
uncertain system parameters. This paper introduces a novel robust and adaptive
control synthesis methodology for a quadrotor robot's attitude and altitude
stabilization. The developed method is based on the fuzzy reinforcement
learning and Strictly Negative Imaginary (SNI) property. The first stage of our
control approach is to transform a nonlinear quadrotor system into an
equivalent Negative-Imaginary (NI) linear model by means of the feedback
linearization (FL) technique. The second phase is to design a control scheme
that adapts online the Strictly Negative Imaginary (SNI) controller gains via
fuzzy Q-learning, inspired by biological learning. The proposed controller does
not require any prior training. The performance of the designed controller is
compared with that of a fixed-gain SNI controller, a fuzzy-SNI controller, and
a conventional PID controller in a series of numerical simulations.
Furthermore, the stability of the proposed controller and the adaptive laws are
proofed using the NI theorem.
