  In previous work, using a process we call meshing, the reachable state spaces
for various continuous and hybrid systems were approximated as a discrete set
of states which can then be synthesized into a Markov chain. One of the
applications for this approach has been to analyze locomotion policies obtained
by reinforcement learning, in a step towards making empirical guarantees about
the stability properties of the resulting system. In a separate line of
research, we introduced a modified reward function for on-policy reinforcement
learning algorithms that utilizes a "fractal dimension" of rollout
trajectories. This reward was shown to encourage policies that induce
individual trajectories which can be more compactly represented as a discrete
mesh. In this work we combine these two threads of research by building meshes
of the reachable state space of a system subject to disturbances and controlled
by policies obtained with the modified reward. Our analysis shows that the
modified policies do produce much smaller reachable meshes. This shows that
agents trained with the fractal dimension reward transfer their desirable
quality of having a more compact state space to a setting with external
disturbances. The results also suggest that the previous work using mesh based
tools to analyze RL policies may be extended to higher dimensional systems or
to higher resolution meshes than would have otherwise been possible.
