Least inventory control of multistorage systems with non-stochastic unknown inputs

We consider multiinventory production systems with control and state constraints dealing with unknown demand or supply levels. Unlike most contributions in the literature concerning this class of systems, we cope with uncertainties in an “unknown-but-bounded” fashion, in the sense that each unknown quantity may take any value in an assigned interval. For these situations, we perform a worst-case analysis. We show that a “smallest worst-case inventory level” exists, and it is associated to a steady-state control strategy. Then we consider the problem of driving the inventory levels to their smallest worst-case values. For this problem, we first give necessary and sufficient conditions, then we show that convergence occurs in a finite number of steps, and we give an upper bound for such a number