Consistent Measures and Bounds For Control Policies

Numerous solutions to control problems cannot be directly compared because the comparison measures depend upon solution specific quantities. Information theoretic approaches use entropy as a consistent measure which is independent of implementation specifics. This paper use state entropy, control entropy, and average work - measures inspired by Source Coding Theory - to characterize the environment complexity, solution complexity, and solution performance in an implementation independent fashion. The paper demonstrates that a trade-off exists between a solution's complexity and its performance. It further presents the Shannon Bound which characterizes the relationship between solution complexity and performance and describes the realization of the bound using Blahut's Algorithm. Finally, it demonstrates that Blahut's Algorithm may be useful in computing optimal policies subject to system constraints.