Piecewise-Linear H∞ Inventory Control of Switched Production Systems

This paper focuses on the problem of inventory control of production systems. The main contribution of the paper is that production systems are modeled as constrained switched linear systems and the inventory control problem is formulated as a constrained switched H_∞ problem with a piecewise-affine (PWA) control law. The switching variable for the production systems modeled in this paper is the stock level. When the stock level is positive, some of the perishable produced parts are being stored and will deteriorate with time at a given rate. When the stock level is negative it leads to backorders, which means that orders for production of parts are coming in and there are no stocked parts to immediately meet the demand. A state feedback controller that forces the stock level to be kept close to zero (sometimes called a just-in-time policy), even when there are fluctuations in the demand, will be designed in this paper using H_∞ control theory and will be formulated as a set of linear matrix inequalities (LMIs). A numerical example is provided to show the effectiveness of the proposed method