Optimal management with hybrid dynamics: The shallow lake problem

P.V. Reddy; Hans Schumacher; Jacob Engwerda

doi:10.1007/978-3-319-20988-3_7

Optimal management with hybrid dynamics: The shallow lake problem

P.V. Reddy
, Hans Schumacher
, Jacob Engwerda

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Scientific › peer-review

6 Citations (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 language	English
Title of host publication	Mathematical Control Theory
Subtitle of host publication	Nonlinear and Hybrid Control Systems
Editors	M.K. Camlibel, A.A. Julius, R. Pasumarthy, J.M.A. Scherpen
Place of Publication	Heidelberg
Publisher	Springer International Publishing
Pages	111-136
Number of pages	26
Volume	I
ISBN (Print)	9783319209876
DOIs	https://doi.org/10.1007/978-3-319-20988-3_7
Publication status	Published - 2015

Publication series

Name	Lecture Notes in Control and Information Sciences
Publisher	Springer
Volume	461

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 8 Decent Work and Economic Growth

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

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

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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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.",

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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 proceeding › Chapter › Scientific › peer-review

TY - CHAP

T1 - Optimal management with hybrid dynamics

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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

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T3 - Lecture Notes in Control and Information Sciences

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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 ). doi: 10.1007/978-3-319-20988-3_7

Optimal management with hybrid dynamics: The shallow lake problem

Abstract

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