  Stochastic dynamic control systems relate in a prob- abilistic fashion the
space of control signals to the space of corresponding future states.
Consequently, stochastic dynamic systems can be interpreted as an information
channel between the control space and the state space. In this work we study
this control-to-state informartion capacity of stochastic dynamic systems in
continuous-time, when the states are observed only partially. The
control-to-state capacity, known as empowerment, was shown in the past to be
useful in solving various Artificial Intelligence & Control benchmarks, and was
used to replace problem-specific utilities. The higher the value of empowerment
is, the more optional future states an agent may reach by using its controls
inside a given time horizon. The contribution of this work is that we derive an
efficient solution for computing the control-to-state information capacity for
a linear, partially-observed Gaussian dynamic control system in continuous
time, and discover new relationships between control-theoretic and
information-theoretic properties of dynamic systems. Particularly, using the
derived method, we demonstrate that the capacity between the control signal and
the system output does not grow without limits with the length of the control
signal. This means that only the near-past window of the control signal
contributes effectively to the control-to-state capacity, while most of the
information beyond this window is irrelevant for the future state of the
dynamic system. We show that empowerment depends on a time constant of a
dynamic system.
