Optimal management with hybrid dynamics: The shallow lake problem

P.V. Reddy, Hans Schumacher, Jacob Engwerda

Research output: Chapter in Book/Report/Conference proceedingChapterScientificpeer-review

1 Citation (Scopus)

Abstract

In this article we analyze an optimal management problem that arises in ecological economics using hybrid systems modeling. First, we introduce a discounted autonomous infinite horizon hybrid optimal control problem and develop few tools to analyze the necessary conditions for optimality. Next, using these tools we study the classical shallow lake problem where the nonlinear lake dynamics is described by hybrid dynamics. We show that our results agree with earlier studies on the problem, that is, variation of system parameters induce bifurcations in the optimal solution.
Original languageEnglish
Title of host publicationMathematical Control Theory
Subtitle of host publicationNonlinear and Hybrid Control Systems
EditorsM.K. Camlibel, A.A. Julius, R. Pasumarthy, J.M.A. Scherpen
Place of PublicationHeidelberg
PublisherSpringer International Publishing
Pages111-136
Number of pages26
VolumeI
ISBN (Print)9783319209876
DOIs
Publication statusPublished - 2015

Publication series

NameLecture Notes in Control and Information Sciences
PublisherSpringer
Volume461

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  • Cite this

    Reddy, P. V., Schumacher, H., & Engwerda, J. (2015). Optimal management with hybrid dynamics: The shallow lake problem. In M. K. Camlibel, A. A. Julius, R. Pasumarthy, & J. M. A. S. (Eds.), Mathematical Control Theory : Nonlinear and Hybrid Control Systems (Vol. I, pp. 111-136). (Lecture Notes in Control and Information Sciences ; Vol. 461). Springer International Publishing. https://doi.org/10.1007/978-3-319-20988-3_7