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Modeling and Management of Resources under Uncertainty pp 167–185Cite as

Uncertain Dynamical Systems: An Application to River Pollution Control

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Part of the book series: Lecture Notes in Biomathematics ((LNBM,volume 72))

Abstract

There is an extensive literature dealing with the modelling and management of water quality systems. However, only a few treatments include the effects of uncertain disturbances, and those are stochastic in nature. In the present treatment, we employ a deterministic approach in dealing with uncertain disturbances. We consider uncertain but bounded disturbances and allow for two possibilities, the bounds are known and the bounds are not known.

We introduce controls in the form of effluent rate and in-stream aeration to manage a simple water quality system whose state consists of biochemical oxygen demand and dissolved oxygen, and which is subject to uncertain disturbances. These controls, which are either of the feedback (memoryless) or of the adaptive (learning) type, require knowledge of the system’s current state; thus, we allow also for measurement error in the state. The theory is illustrated by numerous simulations.

Research supported by NSF and AFOSR.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Malaya, Kuala Lumpur, 22-11, Malaysia

    C. S. Lee

  2. Department of Mechanical Engineering, University of California, Berkeley, California, 94720, USA

    G. Leitmann

Authors
  1. C. S. Lee
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  2. G. Leitmann
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Editor information

Editors and Affiliations

  1. Aerospace and Mechanical Engineering, University of Arizona, Tucson, AZ, 85721, USA

    Thomas L. Vincent

  2. Department of Fisheries and Wildlife, University of Minnesota, St. Paul, MN, 55108, USA

    Yosef Cohen

  3. Department of Mechanical and Materials Engineering, Washington State University, Pullman, WA, 99164-2920, USA

    Walter J. Grantham

  4. Division of Fisheries Research, CSIRO Marine Laboratories, GPO Box 1538, Hobart, Tasmania, Australia

    Geoffrey P. Kirkwood

  5. Department of Mathematics, University of Queensland, St. Lucia, Queensland, 4067, Australia

    Jan M. Skowronski

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© 1987 Springer-Verlag Berlin Heidelberg

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Lee, C.S., Leitmann, G. (1987). Uncertain Dynamical Systems: An Application to River Pollution Control. In: Vincent, T.L., Cohen, Y., Grantham, W.J., Kirkwood, G.P., Skowronski, J.M. (eds) Modeling and Management of Resources under Uncertainty. Lecture Notes in Biomathematics, vol 72. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-93365-3_13

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  • DOI: https://doi.org/10.1007/978-3-642-93365-3_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-17999-3

  • Online ISBN: 978-3-642-93365-3

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