  In this work, we present a learning-based nonlinear $H^\infty$ control
algorithm that guarantee system performance under learned dynamics and
disturbance estimate. The Gaussian Process (GP) regression is utilized to
update the nominal dynamics of the system and provide disturbance estimate
based on data gathered through interaction with the system. A soft-constrained
differential game associated with the disturbance attenuation problem in
nonlinear $H^\infty$ control is then formulated to obtain the nonlinear
$H^\infty$ controller. The differential game is solved through the min-max
Game-Theoretic Differential Dynamic Programming (GT-DDP) algorithm in
continuous time. Simulation results on a quadcopter system demonstrate the
efficiency of the learning-based control algorithm in handling external
disturbances.
