Ocean - Revision history

RobertLampel: /* Mathematical formulation */

2026-01-29T10:50:03Z

Mathematical formulation

← Older revision		Revision as of 10:50, 29 January 2026
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	<math>		<math>
	\begin{array}{lll}		\begin{array}{lll}
	\displaystyle \min_{w} && y(t_f) \\		\displaystyle \min_{w} && -y(t_f) \\
	\text{subject to} \\		\text{subject to} \\
	\quad \dot{y}(t) & = & \exp(-\rho \cdot t) \cdot (U(t)- A(t) - u_1(t) \cdot C(t) - D(t)),\\		\quad \dot{y}(t) & = & \exp(-\rho \cdot t) \cdot (U(t)- A(t) - u_1(t) \cdot C(t) - D(t)),\\

2026-01-29T10:18:32Z

Parameters

2025-11-28T13:45:40Z

Reference Solutions

← Older revision		Revision as of 13:45, 28 November 2025
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	Here is one local solution to the above control problem.		Here is one local solution to the above control problem.

	<gallery caption="Reference solution plots" widths="~~180px~~" heights="~~140px~~" perrow="1">		<gallery caption="Reference solution plots" widths="500px" heights="300px" perrow="1">
	Image:Ocean.png\| States and discretized control for a local optimum. Due to the explicit time dependence the time <math>t</math> was added as an additional state.		Image:Ocean.png\| States and discretized control for a local optimum. Due to the explicit time dependence the time <math>t</math> was added as an additional state.
	</gallery>		</gallery>

2025-08-22T06:52:02Z

2025-08-21T14:19:03Z

References

← Older revision		Revision as of 14:19, 21 August 2025
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	== References ==		== References ==
	<span id="PersonalComm">[1]</span> W. Rickels and S. Sager. Personal communication. 2015. <br>		<span id="PersonalComm">[1]</span> W. Rickels and S. Sager. Personal communication. 2015. <br>
	<span id="JankaPhD">[1]</span> Janka, D.: Sequential quadratic programming with indefinite Hessian approximations for nonlinear optimum experimental design for parameter estimation in differential-algebraic equations. Ph.D. thesis, Ruprecht-Karls-Universität Heidelberg (2015). URL https://mathopt.de/publications/Janka2015.pdf <br>		<span id="JankaPhD">[2]</span> Janka, D.: Sequential quadratic programming with indefinite Hessian approximations for nonlinear optimum experimental design for parameter estimation in differential-algebraic equations. Ph.D. thesis, Ruprecht-Karls-Universität Heidelberg (2015). URL https://mathopt.de/publications/Janka2015.pdf <br>


	[[Category:MIOCP]]		[[Category:MIOCP]]
	[[Category:Sensitivity-seeking arcs]]		[[Category:Sensitivity-seeking arcs]]

2025-08-21T14:18:54Z

← Older revision		Revision as of 14:18, 21 August 2025
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	}}		}}

	The '''Ocean problem''' describes fossil fuel consumption and sequestration into the ocean [~~169~~]. It is a		The '''Ocean problem''' describes fossil fuel consumption and sequestration into the ocean [[#PersonalComm \| [1]]]. It is a
	two box model where <math>S</math> describes the carbon stock in the atmosphere and upper layer ocean,		two box model where <math>S</math> describes the carbon stock in the atmosphere and upper layer ocean,
	<math>R</math> describes the carbon stock in fossil reserve and <math>D_L</math> the carbon stock in the deeper layer. The dynamics are given by an [[:Category:ODE model\|ODE model]].		<math>R</math> describes the carbon stock in fossil reserve and <math>D_L</math> the carbon stock in the deeper layer. The dynamics are given by an [[:Category:ODE model\|ODE model]].
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	== Miscellaneous and Further Reading ==		== Miscellaneous and Further Reading ==
	The problem description and further references can be found in the PhD thesis of Dennis Janka [[#JankaPhD\|[1]]].		The problem description and further references can be found in the PhD thesis of Dennis Janka [[#JankaPhD\|[2]]].

	== References ==		== References ==

2025-08-21T14:18:06Z

← Older revision		Revision as of 14:18, 21 August 2025
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	== Miscellaneous and Further Reading ==		== Miscellaneous and Further Reading ==
	The problem description and further references can be found in the PhD thesis of ~~Michael Ernst Geiger~~ [[#~~GeigerPhD~~\|[1]]].		The problem description and further references can be found in the PhD thesis of Dennis Janka [[#JankaPhD\|[1]]].

	== References ==		== References ==
	<span id="~~GeigerPhD~~">[1]</span> "~~Adaptive Multiple Shooting~~ for ~~Boundary Value Problems and Constrained Parabolic Optimization Problems" by M~~. E. ~~Geiger~~ <br>		<span id="PersonalComm">[1]</span> W. Rickels and S. Sager. Personal communication. 2015. <br>
			<span id="JankaPhD">[1]</span> Janka, D.: Sequential quadratic programming with indefinite Hessian approximations for nonlinear optimum experimental design for parameter estimation in differential-algebraic equations. Ph.D. thesis, Ruprecht-Karls-Universität Heidelberg (2015). URL https://mathopt.de/publications/Janka2015.pdf <br>


	[[Category:MIOCP]]		[[Category:MIOCP]]
	[[Category:Sensitivity-seeking arcs]]		[[Category:Sensitivity-seeking arcs]]

2025-08-21T14:13:59Z

Reference Solutions

← Older revision		Revision as of 14:13, 21 August 2025
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	<gallery caption="Reference solution plots" widths="180px" heights="140px" perrow="1">		<gallery caption="Reference solution plots" widths="180px" heights="140px" perrow="1">
	Image:Ocean.png\| States and discretized control for a local optimum. Due to the explicit time dependence, the time <math>t</math> was added as an additional state.		Image:Ocean.png\| States and discretized control for a local optimum. Due to the explicit time dependence the time <math>t</math> was added as an additional state.
	</gallery>		</gallery>

2025-08-21T14:13:46Z

Reference Solutions

← Older revision		Revision as of 14:13, 21 August 2025
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	<gallery caption="Reference solution plots" widths="180px" heights="140px" perrow="1">		<gallery caption="Reference solution plots" widths="180px" heights="140px" perrow="1">
	Image:~~Rao_Mease~~.png\| States and discretized control for a local optimum.		Image:Ocean.png\| States and discretized control for a local optimum. Due to the explicit time dependence, the time <math>t</math> was added as an additional state.
	</gallery>		</gallery>

2025-08-21T14:05:56Z

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 </math>
 </p>
 == Reference Solutions ==