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

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

Fingerprint

Lakes
Hybrid systems
Economics

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

Optimal management with hybrid dynamics : The shallow lake problem. / Reddy, P.V.; Schumacher, Hans; Engwerda, Jacob.

Mathematical Control Theory : Nonlinear and Hybrid Control Systems. ed. / M.K. Camlibel; A.A. Julius; R. Pasumarthy; J.M.A. Scherpen. Vol. I Heidelberg : Springer International Publishing, 2015. p. 111-136 (Lecture Notes in Control and Information Sciences ; Vol. 461).

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

TY - CHAP

T1 - Optimal management with hybrid dynamics

T2 - The shallow lake problem

AU - Reddy, P.V.

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AU - Engwerda, Jacob

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N2 - 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.

AB - 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.

U2 - 10.1007/978-3-319-20988-3_7

DO - 10.1007/978-3-319-20988-3_7

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T3 - Lecture Notes in Control and Information Sciences

SP - 111

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BT - Mathematical Control Theory

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PB - Springer International Publishing

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Reddy PV, Schumacher H, Engwerda J. Optimal management with hybrid dynamics: The shallow lake problem. In Camlibel MK, Julius AA, Pasumarthy R, JMAS, editors, Mathematical Control Theory : Nonlinear and Hybrid Control Systems. Vol. I. Heidelberg: Springer International Publishing. 2015. p. 111-136. (Lecture Notes in Control and Information Sciences ). https://doi.org/10.1007/978-3-319-20988-3_7