On repetitive control and the behaviour of a middle-aged consumer

This paper studies the relationship between repetitive control effectiveness as measured by a performance index, and the parameters of a simple discrete linear-quadratic model with imperfect state information. The results indicate the existence of processes for which a properly designed repetitive control has substantial advantages over a classical stochastically optimal solution. In particular, it is shown that repetitive control, which for a consumer means repetitive adjustments of consumption to the actual level of wealth, may result in values of the expected loss function that are lower than those obtained for the stochastically optimal imperfect-state-information solution.