@inbook{6a43bd66a04849ddab8c05cd86545f0c,
title = "Optimal management with hybrid dynamics: The shallow lake problem",
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.",
author = "P.V. Reddy and Hans Schumacher and Jacob Engwerda",
year = "2015",
doi = "10.1007/978-3-319-20988-3_7",
language = "English",
isbn = "9783319209876",
volume = "I",
series = "Lecture Notes in Control and Information Sciences ",
publisher = "Springer International Publishing",
pages = "111--136",
editor = "M.K. Camlibel and A.A. Julius and R. Pasumarthy and {J.M.A. Scherpen}",
booktitle = "Mathematical Control Theory",
address = "Switzerland",
}