Catalyst mixing problem - Revision history

ClemensZeile at 19:15, 12 January 2018

2018-01-12T19:15:36Z

← Older revision		Revision as of 19:15, 12 January 2018
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	<math>		<math>
	\begin{array}{llcl}		\begin{array}{llcl}
	\displaystyle \min_{x, u} &-1 + x_1(t_f) + x_2(t_f) \\[1.5ex]		\displaystyle \min_{x, w} &-1 + x_1(t_f) + x_2(t_f) \\[1.5ex]
	\mbox{s.t.}		\mbox{s.t.}
	& \dot{x}_1 & = & u ( 10 x_2(t) - x_1(t)), \\		& \dot{x}_1 & = & w(t) ( 10 x_2(t) - x_1(t)), \\
	& \dot{x}_2 & = & u ( x_1(t) - 10 x_2(t)) - (1 - u(t)) \, x_2(t) , \\		& \dot{x}_2 & = & w(t) ( x_1(t) - 10 x_2(t)) - (1 - w(t)) \, x_2(t) , \\
	& x(t_0) &=& (1, 0)^T, \\		& x(t_0) &=& (1, 0)^T, \\
	& u(t) &\in& \{0,1\}.		& w(t) &\in& \{0,1\}.
	\end{array}		\end{array}
	</math>		</math>
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	In this model the parameters used are <math> t_0 = 0, \, \, t_f = 1 </math>.		In this model the parameters used are <math> t_0 = 0, \, \, t_f = 1 </math>.

			== Reference Solution ==
			If the problem is relaxed, i.e., we demand that w(t) be in the continuous interval [0, 1] instead of the binary choice \{0,1\}, the optimal solution can be determined by means of direct optimal control.

			<gallery caption="Reference solution plots" widths="180px" heights="140px" perrow="2">
			Image:Catalyst_Mixing_Problem_Performance.png\| Results with relaxed controls and collocation from the [http://www.mcs.anl.gov/~more/cops/ COPS library]
			Image:Catalyst Mixing Controls.png\| Optimal relaxed controls showing a bang-bang structure.
			</gallery>

	== Source Code ==		== Source Code ==

2018-01-12T18:47:46Z

Mathematical formulation

← Older revision		Revision as of 18:47, 12 January 2018
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	\displaystyle \min_{x, u} &-1 + x_1(t_f) + x_2(t_f) \\[1.5ex]		\displaystyle \min_{x, u} &-1 + x_1(t_f) + x_2(t_f) \\[1.5ex]
	\mbox{s.t.}		\mbox{s.t.}
	& \dot{x}_1 & = & u ( 10 x_2 - x_1), \\		& \dot{x}_1 & = & u ( 10 x_2(t) - x_1(t)), \\
	& \dot{x}_2 & = & u ( x_1 - 10 x_2) - (1 - u \, x_2) , \\		& \dot{x}_2 & = & u ( x_1(t) - 10 x_2(t)) - (1 - u(t)) \, x_2(t) , \\
	& x(t_0) &=& (1, 0)^T, \\		& x(t_0) &=& (1, 0)^T, \\
	& u(t) &\in& [0,1].		& u(t) &\in& \{0,1\}.
	\end{array}		\end{array}
	</math>		</math>

2016-09-29T19:21:02Z

← Older revision		Revision as of 19:21, 29 September 2016
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	[[Category:MIOCP]]		[[Category:MIOCP]]
	[[Category:ODE model]]		[[Category:ODE model]]
			[[Category:Chemical engineering]]

2016-07-27T08:28:28Z

← Older revision		Revision as of 08:28, 27 July 2016
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	\|nx = 2		\|nx = 2
	\|nu = 1		\|nu = 1
	\|nc = 1		\|nc = 2
	\|nre = 2		\|nre = 2
	}}<!-- Do not insert line break here or Dimensions Box moves up in the layout...		}}<!-- Do not insert line break here or Dimensions Box moves up in the layout...

2016-07-27T08:25:46Z

← Older revision		Revision as of 08:25, 27 July 2016
Line 3:		Line 3:
	\|nx = 2		\|nx = 2
	\|nu = 1		\|nu = 1
			\|nc = 1
	\|nre = 2		\|nre = 2
	}}<!-- Do not insert line break here or Dimensions Box moves up in the layout...		}}<!-- Do not insert line break here or Dimensions Box moves up in the layout...

2016-06-27T22:00:51Z

← Older revision		Revision as of 22:00, 27 June 2016
Line 2:		Line 2:
	\|nd = 1		\|nd = 1
	\|nx = 2		\|nx = 2
	\|nw = 1		\|nu = 1
	\|nre = 2		\|nre = 2
	}}<!-- Do not insert line break here or Dimensions Box moves up in the layout...		}}<!-- Do not insert line break here or Dimensions Box moves up in the layout...

2016-05-05T18:03:41Z

← Older revision		Revision as of 18:03, 5 May 2016
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	\begin{array}{llcl}		\begin{array}{llcl}
	\displaystyle \min_{x, u} &-1 + x_1(t_f) + x_2(t_f) \\[1.5ex]		\displaystyle \min_{x, u} &-1 + x_1(t_f) + x_2(t_f) \\[1.5ex]
	\mbox{s.t.} & \dot{x}_1 & = & u ( 10 x_2 - x_1), \\		\mbox{s.t.}
			& \dot{x}_1 & = & u ( 10 x_2 - x_1), \\
	& \dot{x}_2 & = & u ( x_1 - 10 x_2) - (1 - u \, x_2) , \\		& \dot{x}_2 & = & u ( x_1 - 10 x_2) - (1 - u \, x_2) , \\
	& x(t_0) &=& (1, 0)^T, \\		& x(t_0) &=& (1, 0)^T, \\

2016-04-10T09:49:02Z

← Older revision		Revision as of 09:49, 10 April 2016
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	{{Dimensions		{{Dimensions
	\|nd = 1		\|nd = 1
	\|nx = 3		\|nx = 2
	\|nw = 1		\|nw = 1
	\|nre = 3		\|nre = 2
	}}<!-- Do not insert line break here or Dimensions Box moves up in the layout...		}}<!-- Do not insert line break here or Dimensions Box moves up in the layout...

2016-04-10T09:48:33Z

Mathematical formulation

2016-04-10T09:47:59Z

Mathematical formulation