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Stochastic dynamic control systems relate in a prob- abilistic fashion thespace of control signals to the space of corresponding future states.Consequently, stochastic dynamic systems can be interpreted as an informationchannel between the control space and the state space. In this work we studythis control-to-state informartion capacity of stochastic dynamic systems incontinuous-time, when the states are observed only partially. Thecontrol-to-state capacity, known as empowerment, was shown in the past to beuseful in solving various Artificial Intelligence & Control benchmarks, and wasused to replace problem-specific utilities. The higher the value of empowermentis, the more optional future states an agent may reach by using its controlsinside a given time horizon. The contribution of this work is that we derive anefficient solution for computing the control-to-state information capacity fora linear, partially-observed Gaussian dynamic control system in continuoustime, and discover new relationships between control-theoretic andinformation-theoretic properties of dynamic systems. Particularly, using thederived method, we demonstrate that the capacity between the control signal andthe system output does not grow without limits with the length of the controlsignal. This means that only the near-past window of the control signalcontributes effectively to the control-to-state capacity, while most of theinformation beyond this window is irrelevant for the future state of thedynamic system. We show that empowerment depends on a time constant of adynamic system.

Control Capacity of Partially Observable Dynamic Systems in Continuous Time