Optimal control of oscillatory systems by iterative dynamic programming

Oscillatory inputs have been observed to increase the yield of chemical reactors beyond the level possible by steady inputs. To obtain the optimal inputs, iterative dynamic programming is well suited, because a very large number of time stages can be used without encountering computational problems. To observe the benefits of oscillatory inputs, the effects of the initial state and the final state can be eliminated by normalizing the average yields with respect to the yield from a shorter final time. Two examples show that optimal oscillatory control policy can improve the yield substantially. The third example shows that there are situations where oscillatory behaviour is optimal, but the benefits are negligible. The optimal control policies can be readily established with iterative dynamic programming with the use of a large number of time stages of flexible length.