Controller Design for a Class of Delayed and Constrained Systems: Application to Supply Chains

This chapter aims to investigate the construction of efficient controllers for some input time delay systems, subjected to strict constraints of positivity and saturating limitations, in presence of some exogenous bounded disturbances. The results are presented through the application of supply chains, for which controller design is a challenging issue trading-off between stabilising properties in presence of time lags, and constraints due to the physical limitations and specificities of the plants of the supply chain. We show that the stabilization of such flow systems can be tackled by the stabilization of input time delay systems, using a predictor based feedback approach. This classical control method, which permits to overcome the delays, is enriched by using saturation terms that allow the consideration of the physical constraints of the system resources composing the serial supply chains.