Optimal Model Reference Sliding Mode Control of Perishable Inventory Systems

Abstract

In this article, a new optimal model-based sliding mode controller is proposed and applied to a perishable inventory system. The sliding variable of the real plant is forced to follow the reference trajectory generated by the model of the plant. This model is controlled by a linear quadratic (LQ) optimal controller. The control structure proposed in this article allows on one hand to maintain the advantages of the optimal controller, such as limiting and smoothing out the initial control signal, which, in the considered scenario, is the replenishment order sent to the suppliers. On the other hand, once the model converges to the vicinity of the desired state, the sliding mode controller can react significantly faster to the unknown disturbance, i.e., consumers’ demand. Since the reference trajectory is unperturbed by the disturbance, this allows to combine the advantages of both approaches: limited and smooth initial control signal and good robustness in the quasi-steady state. Those properties are analytically demonstrated, as well as in computer simulations. Note to Practitioners —This article is motivated by the need of effective supply chain management. For that purpose, we apply the paradigm of sliding mode control, which is well known for its robustness and computational efficiency. Unfortunately, the initial orders generated by the “basic” sliding mode controller strongly depend on the warehouse capacity and can exhibit rapid changes. On the other hand, optimal controllers can ensure limited and smooth orders; however, their robustness is inferior to sliding mode controllers. The approach proposed in this article uses a model of the supply chain controlled by an optimal controller and forces the real supply chain to follow the model. Because of this, the proposed strategy allows on one hand to significantly reduce the required warehouse capacity and the operating cost but on the other hand ensures smooth and limited orders.