Reaching Law Based Discrete Time Sliding Mode Inventory Management Strategy

In this paper, a new reaching law for uncertain discrete time systems is presented. The proposed reaching law is designed to ensure a limited sliding variable rate of change and at least asymptotic convergence of the variable to zero. The law is utilized to design a control strategy, which is then applied to an inventory management system with multiple suppliers and limited warehouse capacity. The strategy is proved to ensure all the desirable properties of the system. On the one hand, it guarantees that the suppliers are never forced to send more goods than they are capable of and that warehouse capacity is never exceeded. On the other hand, it ensures that the consumers' demand is always fully satisfied.