Control variation as a source of uncertainty: Single input case

This paper presents a theoretical framework and the control strategy for single input discrete-time stochastic systems for which the control variations increase state uncertainty (CVIU systems). This type of system model can be useful in many practical situations, such as in monetary policy problems, medicine and biology, and, in general, in problems for which a complete dynamic model is too complex to be feasible. The optimal control strategy for a single-input CVIU system associated with a convex cost functional is devised using dynamic programming and tools from nonsmooth analysis. Furthermore, this strategy points to a region in the state space in which the optimal action is of no variation, as expected from the cautionary nature of controlling underdetermined systems. In addition, a specific result for the case when the cost functional is differentiable is obtained and discussed. These results are illustrated through a numerical example in economics.