Control policies for multi-inventory systems with uncertain demand and setup

We consider multi-inventory systems in the presence of unknown but bounded demand and uncertain setups. 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 of the case in which there are no setups. 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.