Advertisement

Environmental Modeling & Assessment

, Volume 17, Issue 1–2, pp 7–18 | Cite as

Dynamical Allocation Method of Emission Rights of Pollutants by Viability Constraints Under Tychastic Uncertainty

  • Jean-Pierre AubinEmail author
  • Luxi Chen
  • Marie-Hélène Durand
Article

Abstract

This study proposes a method of dynamic decentralization by constraints and its associated software. It can be used to allocate pollutant emissions rights among the different polluters such that they achieve both given global and local emission thresholds not to be transgressed. Knowing the maximum growth rates of polluting emissions of each polluter in the worst case, this method provides the rule of a dynamic allocation of pollutant emissions rights as well as the required initial emissions of each polluters assuring that, whatever the growth rates of the emissions below the maximum growth rates, the resulting emissions will be, both globally and locally, under their thresholds. These guaranteed initial emissions supply each polluter with a measure of risk insurance. This problem, formulated as a “tychastic” regulated system with viability constraints, is solved with mathematical and algorithmic tools of viability theory and numerical results obtained by a dedicated software are presented.

Keywords

Polluting emissions Decentralizing constraints Dynamic regulation Viability Tychastic 

References

  1. 1.
    Aubin, J. P. (1991). Viability theory. Cambridge: Birkhäuser.Google Scholar
  2. 2.
    Aubin, J.-P. (1997). Dynamic economic theory: A viability approach. Berlin: Springer.Google Scholar
  3. 3.
    Aubin, J. P. (1998). Optima and equilibria. Berlin: Springer.Google Scholar
  4. 4.
    Aubin, J.-P. (2001). Viability kernels and capture basins of sets under differential inclusions. SIAM Journal of Control and Optimization, 40, 853–881.CrossRefGoogle Scholar
  5. 5.
    Aubin, J.-P. (2003). Regulation of the evolution of the architecture of a network by connectionist tensors operating on coalitions of actors. Journal of Evolutionary Economics, 13, 95–124.CrossRefGoogle Scholar
  6. 6.
    Aubin, J.-P. (2008). Ockham’s razor: Deriving cyclic evolutions from viability and inertia constraints. ARIMA, 9, 17–31.Google Scholar
  7. 7.
    Aubin, J.-P. (2010). La mort du devin, l’émergence du démiurge. Essai sur la contingence et la viabilité des systèmes. Éditions Beauchesne.Google Scholar
  8. 8.
    Aubin, J.-P. (2010). Une approche viabiliste du couplage des systèmes climatiques et économiques. Natures, Sciences, Sociétés.Google Scholar
  9. 9.
    Aubin, J.-P., Bayen, A., & Saint-Pierre, P. (2010). Viability theory. New directions. Berlin: Springer.Google Scholar
  10. 10.
    Aubin, J.-P., Bernardo, T., & Saint-Pierre, P. (2004). A viability approach to global climate change issues. In A. Haurie, & L. Viguier (Eds.), Advances in global change research. Dordrecht: Klüwer.Google Scholar
  11. 11.
    Aubin, J.-P., & Da Prato, G. (1995). Stochastic Nagumo’s viability theorem. Stochastic Analysis and Applications, 13, 1–11.CrossRefGoogle Scholar
  12. 12.
    Aubin, J.-P., & Da Prato G., (1998). The viability theorem for stochastic differential inclusions. Stochastic Analysis and Applications, 16, 1–15.CrossRefGoogle Scholar
  13. 13.
    Aubin, J.-P., Da Prato, G., & Frankowska, H. (2000). Stochastic invariance for differential inclusions. Journal of Set-Valued Analysis, 8, 181–201.CrossRefGoogle Scholar
  14. 14.
    Aubin, J.-P., & Dordan, O. (1996). Fuzzy systems, viability theory and toll sets. In H. Nguyen (Ed.), Handbook of fuzzy systems, modeling and control (pp. 461–488). Dordrecht: Kluwer.Google Scholar
  15. 15.
    Aubin, J.-P., & Doss, H. (2003). Characterization of stochastic viability of any nonsmooth set involving its generalized contingent curvature. Stochastic Analysis and Applications, 25, 951–981.Google Scholar
  16. 16.
    Aubin, J.-P., & Frankowska, H. (1990). Set-valued analysis. Boston: Birkhäuser.Google Scholar
  17. 17.
    Aubin, J.-P., & Haddad, G. (2001). Cadenced runs of impulse and hybrid control systems. International Journal Robust and Nonlinear Control, 11, 401–415.CrossRefGoogle Scholar
  18. 18.
    Aubin, J.-P., & Haddad, G. (2001). Path-dependent impulse and hybrid control systems. In M.D. Di Benedetto, & A.L. Sangiovanni-Vincentelli (Eds.), Hybrid systems: computation and control. Proceedings of the HSCC 2001 conference, LNCS 2034 (pp. 119–132). Berlin: Springer.CrossRefGoogle Scholar
  19. 19.
    Aubin, J.-P., & Haddad, G. (2002). History (path) dependent optimal control and portfolio valuation and management. Journal of Positivity, 6, 331–358.CrossRefGoogle Scholar
  20. 20.
    Aubin, J.-P., & Haddad, G. (2002). Impulse capture basins of sets under impulse control systems. Journal of Mathematical Analysis and Applications, 275, 676–692.CrossRefGoogle Scholar
  21. 21.
    Aubin, J.-P., Lygeros, J., Quincampoix, M., Sastry, S., & Seube, N. (2002). Impulse differential inclusions: a viability approach to hybrid systems. IEEE Transactions on Automatic Control, 47, 2–20.CrossRefGoogle Scholar
  22. 22.
    Aubin, J.-P., & Saint-Pierre, P. (2006), Guaranteed inertia functions in dynamical games. International Game Theory Review (IGTR), 8, 185–218.CrossRefGoogle Scholar
  23. 23.
    Babonneau, F., Vial, J.-P., & Apparigliato, R. (2010). Robust optimization for environmental and energy planning. In J. A. Filar, & A. Haurie (Eds.), Handbook on “Uncertainty and environmental decision making”. International series in operations research and management science (pp. 79–126). Berlin: Springer.Google Scholar
  24. 24.
    Bahn, O., Haurie, A., & Malhamé, R. (2008). A stochastic control model for optimal timing of climate policies. Automatica, 44, 1545–1558.CrossRefGoogle Scholar
  25. 25.
    Blanchard, O. (2002). Scenarios for differentiating commitments. In K. Baumert, O. Blanchard, S. Llosa, & J. Perkaus (Eds.), Options for protecting the climate (pp. 203–222). Washington: WRI.Google Scholar
  26. 26.
    Cardaliaguet, P., Quincampoix, M., & Saint-Pierre, P. (1999). Set-valued numerical methods for optimal control and differential games. In Stochastic and differential games. Theory and numerical methods. Annals of the International Society of Dynamical Games (pp. 177–247). Cambridge: Birkhäuser.Google Scholar
  27. 27.
    Da Prato, G., & Frankowska, H. (1994). A stochastic Filippov theorem. Stochastic Calculus, 12, 409–426.CrossRefGoogle Scholar
  28. 28.
    Da Prato, G., & Frankowska, H. (2001). Stochastic viability for compact sets in terms of the distance function. Dynamics Systems Applications, 10, 177–184.Google Scholar
  29. 29.
    Da Prato, G., & Frankowska, H. (2004). Invariance of stochastic control systems with deterministic arguments. Journal of Differential Equations, 200, 18–52CrossRefGoogle Scholar
  30. 30.
    Den Elzen, M., Berk, M., Lucas, P., Eickhout, B., & van Vuuren, D. (2003). Exploring climate regimes for differentiation of commitments to achieve The EU climate target. RIVM Report, Netherland Environmental Assessment Agency.Google Scholar
  31. 31.
    Den Elzen, M., & Höhne, N. (2008). Reductions of greenhouse gas emissions in Annex 1 and non-Annex 1 countries for meeting concentration stabilization targets. Climatic Change, 91, 249–274.CrossRefGoogle Scholar
  32. 32.
    Den Elzen, M., Schaeffer, M., & Lucas, P. (2005). Differentiating future commitments on the basis of countries’relative historical responsabilities for climate change: Uncertainties in the Brazilina Proposal in the context of a policy implementation. Climatic Change, 71, 277–301.CrossRefGoogle Scholar
  33. 33.
    Doss, H. (1977). Liens entre équations différentielles stochastiques et ordinaires. Annales de l’Institut Henri Poincaré. Section B. Calcul des Probabilités et Statistiques, 23, 99–125.Google Scholar
  34. 34.
    Doyen, L., & Gabay, D. (1997). Viabilité et régulation d’un modèle de croissance prenant en compte le risque climatique. In Actes des Journées du PIREVS du CNRS Toulouse, Session 2, (p. 249).Google Scholar
  35. 35.
    Doyen, L., & Gabay, D. (1999). Viable regulation of a dynamic climate–economic model. In Proceedings of the symposium planetary garden in Chambery, session B9, (p. 386).Google Scholar
  36. 36.
    Greiner, A., Grüne, L., & Semmler, W. (2010). Growth and climate change: Threshold and multiple equilibria. In J. Crespo Cuaresma, T. Palokangas, & A. Tarasyev (Eds.), Dynamic systems, economic growth, and the environment (pp. 63–79). Berlin: Springer.Google Scholar
  37. 37.
    Grüne, L., & Worthmann, K. (2011). A distributed NMPC scheme without stabilizing terminal constraints. In LCCC Workshop on Distributed Model Predictive Control and Supply Chains” Lund, 18–21 May 2010 Google Scholar
  38. 38.
    Haurie, A., Scéia, A., & Thénié, J. (2009). Inland transport and climate change: A literature review. UNECE Working Paper, WP29-149-23.Google Scholar
  39. 39.
    Haurie, A., & Viguier, L. (Eds.) (2005). The coupling of climate and economic dynamic. Dordrecht: Springer.Google Scholar
  40. 40.
    Höhne, N., Blum, H., Fuglestvedt, J., Bieltvedt Skeie, R., Kurosawa, A., Hu, G., et al. (2011). Contributions of individual countries’emissions to climate change and their uncertainty. Climatic Change, (in press)Google Scholar
  41. 41.
    IPCC (2004). Describing scientific uncertainties in climate change to support analysis of risk and of options. In M. Manning, M. Petit, D. Easterling, J. Murphy, H.-H. Rogner, R. Swart, et al. (Eds.), IPCC workshop report.Google Scholar
  42. 42.
    IPCC (2007). Fourth assessment report: climate change 2007 (AR4). Cambridge: Cambridge University Press.Google Scholar
  43. 43.
    Jancovici, J.-M. (2002). L’avenir climatique. Quel temps ferons-nous? Éditions du seuil.Google Scholar
  44. 44.
    Jorgensen, S., Martin-Herran, G., & Zaccour, G. (2010). Dynamic games in the economics and management of pollution. Environmental Modeling and Assessment, 15, 433–467CrossRefGoogle Scholar
  45. 45.
    Karousakis, K., Guay, B., & Philibert, C. (2008). Differentiating countries in terms of mitigation commitments, action and support. OCDE/IEA.Google Scholar
  46. 46.
    Lempert, R., Scheffran, J., & Sprinz, D. F. (2009). Methods for long-term environmental policy challenges. Global Environmental Politics, 9, 106–132.CrossRefGoogle Scholar
  47. 47.
    LeTreut, H., et al. (2004). Science du changement climatique (105 pp.). Paris: IDDRI édition.Google Scholar
  48. 48.
    Le Treut, H., & Jancovici, J.-M. (2004) L’effet de serre. Flammarion.Google Scholar
  49. 49.
    Martin, S. (2004). The cost of restoration as a way of defining resilience: A viability approach applied to a model of lake eutrophication. Ecology and Society, 9(2), 8. [Online] URL: http://www.ecologyandsociety.org/vol9/iss2/art8.Google Scholar
  50. 50.
    Saint-Pierre, P. (1994), Approximation of the viability kernel. Applied Mathematics & Optimisation, 29, 187–209.CrossRefGoogle Scholar
  51. 51.
    Scheffran, J. (2004). Interaction in climate games: The case of emissions trading. In J. Geldermann, & M. Treitz (Eds.), Entscheidungstheorie und -praxis in industrieller Produktion und Umweltforschung (pp. 1–18). Aachen: Shaker.Google Scholar
  52. 52.
    Scheffran, J. (2008). Adaptive management of energy transitions in long-term climate change. Computational Management Science, 5, 259–286.CrossRefGoogle Scholar
  53. 53.
    Stern, N., et al. (2006). The economics of climate change: the Stern review. Cambridge: Cambridge University Press.Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • Jean-Pierre Aubin
    • 1
    Email author
  • Luxi Chen
    • 1
  • Marie-Hélène Durand
    • 2
  1. 1.Société VIMADES (Viabilité, Marchés, Automatique et Décision)ParisFrance
  2. 2.IRDBondyFrance

Personalised recommendations