Annals of Operations Research

, Volume 220, Issue 1, pp 25–48 | Cite as

Model predictive control, the economy, and the issue of global warming

  • Thierry BréchetEmail author
  • Carmen Camacho
  • Vladimir M. Veliov


This study is motivated by the evidence of global warming, which is caused by human activity but affects the efficiency of the economy. We employ the integrated assessment Nordhaus DICE-2007 model (Nordhaus, A question of balance: economic modeling of global warming, Yale University Press, New Haven, 2008). Generally speaking, the framework is that of dynamic optimization of the discounted inter-temporal utility of consumption, taking into account the economic and the environmental dynamics. The main novelty is that several reasonable types of behavior (policy) of the economic agents, which may be non-optimal from the point of view of the global performance but are reasonable form an individual point of view and exist in reality, are strictly defined and analyzed. These include the concepts of “business as usual”, in which an economic agent ignores her impact on the climate change (although adapting to it), and of “free riding with a perfect foresight”, where some economic agents optimize in an adaptive way their individual performance expecting that the others would perform in a collectively optimal way. These policies are defined in a formal and unified way modifying ideas from the so-called “model predictive control”. The introduced concepts are relevant to many other problems of dynamic optimization, especially in the context of resource economics. However, the numerical analysis in this paper is devoted to the evolution of the world economy and the average temperature in the next 150 years, depending on different scenarios for the behavior of the economic agents. In particular, the results show that the “business as usual”, although adaptive to the change of the atmospheric temperature, may lead within 150 years to increase of temperature by 2°C more than the collectively optimal policy.


Environmental economics Dynamic optimization Optimal control Global warming Model predictive control Integrated assessment 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Allgöwer, F., & Zheng, A. (2000). Progress in systems theory: Vol. 26. Nonlinear model predictive control. Basel: Birkhäuser. CrossRefGoogle Scholar
  2. Bréchet, Th., Eyckmans, J., Gerard, F., Marbaix, Ph., Tulkens, H., & van Ypersele, J.-P. (2010). The impact of the unilateral EU commitment on the stability of international climate agreements. Climate Policy, 10, 148–166. CrossRefGoogle Scholar
  3. Bréchet, Th., Gerard, F., & Tulkens, H. (2011). Efficiency vs. stability of climate coalitions: a conceptual and computational appraisal. The Energy Journal, 32(1), 49–76. CrossRefGoogle Scholar
  4. Bosetti, V., Carraro, C., De Cian, E., Duval, R., Massetti, E., & Tavoni, M. (2009). The incentives to participate in, and the stability of, international climate coalitions: a game-theoretic analysis using the Witch model. 2009.064 Note di lavoro, FEEM. Google Scholar
  5. Carlson, D. A., Haurie, A. B., & Leizarowitz, A. (1991). Infinite horizon optimal control. Berlin: Springer. CrossRefGoogle Scholar
  6. Diehl, M., Bock, H. G., Schilder, J. P., Findeisen, R., Nagy, Z., & Allgöwer, F. (2002). Real-time optimization and nonlinear model predictive control of processes governed by differential-algebraic equations. Journal of Process Control, 12, 577–585. CrossRefGoogle Scholar
  7. Dontchev, A. L., & Rockafellar, R. T. (2009). Springer monographs in mathematics. Implicit functions and solution mappings. A view from variational analysis. Berlin: Springer. CrossRefGoogle Scholar
  8. Eyckmans, J., & Tulkens, H. (2003). Simulating coalitionally stable burden sharing agreements for the climate change problem. Resource and Energy Economics, 25, 299–327. CrossRefGoogle Scholar
  9. Findeisen, R., Allgöwer, F., & Biegler, L. T. (Eds.) (2007). Lecture notes in control and information sciences: Vol. 358. Assessment and future directions of nonlinear model predictive control. Berlin: Springer. Google Scholar
  10. Greiner, A., & Semmler, W. (2005). Economic growth and global warming: a model of multiple equilibria and thresholds. Journal of Economic Behavior and Organization, 57, 430–447. CrossRefGoogle Scholar
  11. Greiner, A., Grüne, L., & Semmler, W. (2009). Growth and climate change: threshold and multiple equilibria. In J. Crespo Cuaresma, T. Palokangas, & A. Tarasyev (Eds.), Dynamic modeling and econometrics in economics and finance: Vol. 12. Dynamic systems, economic growth, and the environment (pp. 63–78). Berlin: Springer. ISBN:978-3-642-02131-2. CrossRefGoogle Scholar
  12. Haurie, A. (2003). Integrated assessment modeling for global climate change: an infinite horizon optimization viewpoint. Environmental Modeling and Assessment, 8, 117–132. CrossRefGoogle Scholar
  13. Haurie, A. (2005). A multigenerational game model to analyze sustainable development. Annals of Operational Research, 137, 369–386. CrossRefGoogle Scholar
  14. Kriegler, E., Hall, J. W., Held, H., Dawson, R., & Schellnhuber, H. J. (2009). Imprecise probability assessment of tipping points in the climate system. Proceedings of the National Academy of Sciences, 106, 5041–5046. CrossRefGoogle Scholar
  15. Nordhaus, W. D. (1992). An optimal transition path for controlling greenhouse gases. Science, 258(5086), 1315–1319. CrossRefGoogle Scholar
  16. Nordhaus, W. D. (1993). Rolling the DICE: an optimal transition path for controlling greenhouse gases. Resource and Energy Economics, 15, 27–50. CrossRefGoogle Scholar
  17. Nordhaus, W. D. (1993). Optimal greenhouse gas reductions and tax policy in the DICE model. The American Economic Review, 83, 313–317. Google Scholar
  18. Nordhaus, W. D. (2008). A question of balance: economic modeling of global warming. New Haven: Yale University Press. Google Scholar
  19. Nordhaus, W. D., & Boyer, J. (2000). Warming the world. Cambridge: MIT Press. Google Scholar
  20. Solomon, S., Qin, D., Manning, M., Chen, Z., Marquis, M., Averyt, K. B., Tignor, M., & Miller, H. L. (Eds.) (2007). Contribution of working group I to the fourth assessment report of the intergovernmental panel on climate change. Cambridge: Cambridge University Press. Google Scholar
  21. Stern, N. (2006). The economics of climate change: the Stern review. Cambridge: Cambridge University Press. Google Scholar
  22. Yang, Z. (2008). Strategic bargaining and cooperation in greenhouse gas mitigations—an integrated assessment modeling approach. Cambridge: MIT Press. CrossRefGoogle Scholar
  23. Wolenski, P. (1990). The exponential formula for the reachable set of Lipschitz differential inclusion. SIAM Journal on Control and Optimization, 28, 1148–1161. CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Thierry Bréchet
    • 1
    Email author
  • Carmen Camacho
    • 2
  • Vladimir M. Veliov
    • 3
  1. 1.CORE and Louvain School of Management, Chair Lhoist Berghmans in Environmental Economics and ManagementUniversité catholique de LouvainLouvain-la-NeuveBelgium
  2. 2.Belgian National Foundation of Scientific Research and Economics DepartmentUniversité catholique de LouvainLouvain-la-NeuveBelgium
  3. 3.ORCOS, Institute of Mathematical Methods in EconomicsVienna University of TechnologyViennaAustria

Personalised recommendations