2017/01/18 by Stas Tiomkin, Daniel Polani, Tiomkin, Stas +3
Computer Science · Engineering · Mathematics · #93C41 #Bayesian Modeling and Causal Inference #FOS: Computer and information sciences #Fault Detection and Control Systems #Information Theory (cs.IT) #Smart Grid Security and Resilience #cs.IT #math.IT #msc:93C41
paper · pdf · doi:10.48550/arxiv.1701.04984
11 [ages, 7 figures
arxiv created 2017/01/18 · openalex publication_date 2017/01/18 · arxiv updated 2017/01/19 · openalex created_date 2017/02/03 · openalex updated_date 2026/07/28
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.