Hierarchical MPC for Multiple Commodity Transportation Networks
Transportation networks are large scale complex systems spatially distributed whose objective is to deliver commodities at the agreed time and at the agreed location. These networks appear in different domain fields, such as communication, water distribution, traffic, logistics and transportation. A transportation network has at the macroscopic level storage capability (located in the nodes) and transport delay (along each connection) as main features. Operations management at transportation networks can be seen as a flow assignment problem. The problem dimension to solve grows exponentially with the number of existing commodities, nodes and connections. In this work we present a Hierarchical Model Predictive Control (H-MPC) architecture to determine flow assignments in transportation networks, while minimizing exogenous inputs effects. This approach has the capacity to keep track of commodity types while solving the flow assignment problem. A flow decomposition of the main system into subsystems is proposed to diminish the problem dimension to solve in each time step. Each subsystem is managed by a control agent. Control agents solve their problems in a hierarchical way, using a so-called push-pull flow perspective. Further problem dimension reduction is achieved using contracted projection sets. The framework proposed can be easily scaled to network topologies in which hundreds of commodities and connections are present.
KeywordsControl Agent Center Node Transportation Network Container Terminal Quay Crane
This work was supported by the Portuguese Government, through Fundação para a Ciência e a Tecnologia, under the project PTDC/EEACRO/102102/2008 - AQUANET, through IDMEC under LAETA and by the VENI project “Intelligent multi-agent control for flexible coordination of transport hubs” (project 11210) of the Dutch Technology Foundation STW, a subdivision of the Netherlands Organisation for Scientific Research (NWO).
- 1.R.K. Ahuja, T.L. Magnanti, J.B. Orlin, Network Flows (Prentice Hall, Upper Saddle River, 1993)Google Scholar
- 4.T.G. Crainic, K.H. Kim, Intermodal transportation, in Transportation, Handbooks in Operations Research and Management Science, ed. by C. Barnhart, G. Laporte (Elsevier, North-Holland, 2007), pp. 467–537Google Scholar
- 5.ECT Publications. Fast forward 52, Winter 2011Google Scholar
- 7.M. Kvasnica, P. Grieder, M. Baotić. Multi-parametric toolbox (mpt). http://control.ee.ethz.ch/~mpt/
- 8.S. Leirens, C. Zamora, R.R. Negenborn, B. De Schutter, Coordination in urban water supply networks using distributed model predictive control, in Proceedings of the 2010 American Control Conference (ACC10), pp. 3957–7104, Baltimore, Maryland, June 2010Google Scholar
- 9.J.M. Maciejowski, Predictive Control with Constraints (Prentice-Hall, Harlow, 2002)Google Scholar
- 10.J.M. Maestre, D. Mu noz de la Pena, E.F. Camacho, Distributed mpc: a supply chain case, in 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference, pp. 7099–7104, Shanghai, China, Dec 2009Google Scholar
- 11.J.L. Nabais, R.R. Negenborn, M.A. Botto, Hierarchical model predictive control for optimizing intermodal container terminal operations, Submitted to a conference 2012Google Scholar
- 12.J.L. Nabais, R.R. Negenborn, M.A. Botto, A novel predictive control based framework for optimizing intermodal container terminal operations, in Proceedings of the 3rd International Conference on Computational Logistics (ICCL), pp. 53–71, Shanghai, China, September 2012Google Scholar
- 15.J. Ottjes, H. Veeke, M. Duinkerken, J. Rijsenbrij, G. Lodewijks, Simulation of a multiterminal system for container handling, in Container Terminals and Cargo Systems, edited by K. Hwan Kim, H.-O. Gunther (Springer, Berlin, 2007), pp. 15–36Google Scholar
- 16.M.E. Sezer, D.D. Šiljak, Decentralized control, in The Control Handbook, edited by W.S. Levine (CRC Press, New York, 1996), pp. 779–793Google Scholar