Stabilization of multi-inventory systems with uncertain demand and setups

Abstract

In this paper, we consider different aspects of the problem of controlling a multi-inventory system in the presence of uncertain demand and setups. The demand is unknown but bounded in an assigned compact set. The control input is assumed to be constant in its operating regime and to incur setup whenever a variation of this regime is required. Both setup times and setup configurations are unknown. We provide necessary and sufficient stabilizability conditions which turn out to be the same in the case in which there are no setups. Stabilization can be achieved, provided that the planning horizon is large enough and a computable lower bound is given. We also face the problem of ultimately confining the state in an assigned constraint set and provide conditions on this set for the problem to be feasible. Furthermore, we consider the case in which the controls are quantized, as in the case of systems which work in a switching mode. Finally, we deal with the case in which multiple setups may happen during the planning horizon.