  In this work we seek for an approach to integrate safety in the learning
process that relies on a partly known state-space model of the system and
regards the unknown dynamics as an additive bounded disturbance. We introduce a
framework for safely learning a control strategy for a given system with an
additive disturbance. On the basis of the known part of the model, a safe set
in which the system can learn safely, the algorithm can choose optimal actions
for pursuing the target set as long as the safety-preserving condition is
satisfied. After some learning episodes, the disturbance can be updated based
on real-world data. To this end, Gaussian Process regression is conducted on
the collected disturbance samples. Since the unstable nature of the law of the
real world, for example, change of friction or conductivity with the
temperature, we expect to have the more robust solution of optimal control
problem.
  For evaluation of approach described above we choose an inverted pendulum as
a benchmark model. The proposed algorithm manages to learn a policy that does
not violate the pre-specified safety constraints. Observed performance is
improved when it was incorporated exploration set up to make sure that an
optimal policy is learned everywhere in the safe set. Finally, we outline some
promising directions for future research beyond the scope of this paper.
