  This paper proposes a receding horizon active learning and control problem
for dynamical systems in which Gaussian Processes (GPs) are utilized to model
the system dynamics. The active learning objective in the optimization problem
is presented by the exact conditional differential entropy of GP predictions at
multiple steps ahead, which is equivalent to the log determinant of the GP
predictive covariance matrix. The resulting non-convex and complex optimization
problem is solved by the Successive Convex Programming algorithm that exploits
the first-order approximations of non-convex functions. Simulation results of
an autonomous racing car example verify that using the proposed method can
significantly improve data quality for model learning while solving time is
highly promising for real-time applications.
