Consistent Measures and BoundsFor Control

Many procedures exist for nding solutions to optimal control problems. Measures characterizing each method describe the method's performance as functions of quantities that the method utilizes. However, the measures are not usually consistent across solutions so as to allow unbiased comparison of diierent solutions to the same problem. This paper presents state entropy, control entropy, and average work | measures inspired by Source Coding Theory | that characterize the complexity of solutions, the solution environments, and the performance of a solution, all in a consistent fashion. It demonstrates that there is a trade-oo between the complexity of a solution and its performance. It further presents a lower bound on the measures (Shannon's Bound) and presents Blahut's Algorithm that computes the bound. Finally, it demonstrates that Blahut's Algorithm may be useful in computing optimal policies subject to system constraints.