Model Predictive Control of Hybrid Systems with Applications to Supply Chain Management

Hybrid systems are dynamical systems whose behavior is determined by the interaction of continuous and discrete dynamics. Such systems arise in many real contexts, including automotive systems, chemical processes, communication networks, and supply chain management. A supply chain, whose goal is to transform ideas and raw materials into delivered products and services, is an example of a heterogeneous interconnection between continuous dynamics (inventory levels, material flows, etc.) and discrete dynamics (connection graphs, precedences, priorities, etc.). In general, in order to maximize a certain benefit or minimize certain costs, we have to optimally control all the heterogeneous components of the hybrid system. Model predictive control (MPC) is a well-known technique used in industry to (sub)optimally control dynamical processes, and is usually based on linear models. This paper presents an overview of MPC techniques for hybrid systems. After giving a brief introduction to hybrid system models, model predictive control, and standard computation techniques, the paper summarizes recent results in using symbolic techniques and event-based formulations that exploit the particular structure of the hybrid process to come up with improved numerical computation schemes. The concepts are illustrated through application examples in centralized management of supply chains.