Optimal pollution control of a lake

  • F. X. Litt
  • H. Smets
Human Environment (Water Pollution)
Part of the Lecture Notes in Computer Science book series (LNCS, volume 40)


This paper considers a lake in which a pollutant is dumped at a rate whose maximum value is constant. We assume that the quantity of pollutant eliminated by natural processes is proportional to the total amount of pollutant contained into the lake. With this process we associate a cost which is the sum of two terms : the first one represents the cost of cleaning up a fraction of the pollutant and the second term is a measure of the damage done to the environment.

We then determine the optimal dumping policy, i.e., the policy which minimizes that cost integrated over a fixed period of time by solving an optimal control problem.


Optimal Control Problem Optimal Policy Discount Factor Terminal Time Horizontal Asymptote 
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    HALKIN H., "Necessary conditions for optimal control problems with infinite horizons", Econometrica, vol. 42, No. 2, 1974.Google Scholar
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    LITT F.X., "Politique optimale de dépollution dans un système accumulatif", RART 74/01, Université de Liège, juillet 1974.Google Scholar
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    LITT F.X., "Politique optimale de dépollution dans un système non strictement cumulatif", RART 74/03, Université de Liège, septembre 1974.Google Scholar
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    LITT F.X., "Politique optimale de dépollution dans un système non strictement cumulatif: suite. Conclusions de l'étude", RART 74/05, Université de Liège, novembre 1974.Google Scholar

Copyright information

© Springer-Verlag 1976

Authors and Affiliations

  • F. X. Litt
    • 1
  • H. Smets
    • 1
    • 2
  1. 1.Université de LiègeBelgium
  2. 2.OECDParis

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