LinearMetabolic - Revision history

VeronicaHaritonova: /* Data */

2023-10-23T05:17:39Z

Data

← Older revision		Revision as of 05:17, 23 October 2023
Line 55:		Line 55:
	\|parameters <math>p_1, p_2, p_3</math>		\|parameters <math>p_1, p_2, p_3</math>
	\|noise		\|noise
			\|number of time intervals <math>N</math>
			\|final time <math>T^*</math>
	\|data <math>\eta</math>		\|data <math>\eta</math>
	\|-		\|-
Line 60:		Line 62:
	\|[1,1,1]		\|[1,1,1]
	\| 0		\| 0
			\|20
			\|4.3
	\|		\|
	[[1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0],		[[1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0],
Line 69:		Line 73:
	\|[1,1,1]		\|[1,1,1]
	\|0.2		\|0.2
			\|20
			\|4.3
	\|		\|
	[[1., 0.9590812,0.82266497,0.95877308,0.60614596,1.20781224, 0.92205471,1.0215116 ,0.89080449,1.05747735,1.04019676,1.06665347, 0.78545416,1.17084962,1.08658091,1.01467309,0.91098074,1.10349004, 0.83411596,0.73187308,0.70399766],		[[1., 0.9590812,0.82266497,0.95877308,0.60614596,1.20781224, 0.92205471,1.0215116 ,0.89080449,1.05747735,1.04019676,1.06665347, 0.78545416,1.17084962,1.08658091,1.01467309,0.91098074,1.10349004, 0.83411596,0.73187308,0.70399766],
Line 78:		Line 84:
	\|[1,1,1]		\|[1,1,1]
	\|0		\|0
			\|20
			\|4.226
	\|		\|
	[[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],		[[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
Line 87:		Line 95:
	\|[1,1,1]		\|[1,1,1]
	\|0.1		\|0.1
			\|20
			\|4.226
	\|		\|
	[[1.,0.98392517,1.02825092,1.0127091 ,1.21814838,1.03987996, 1.17367563,1.0721497 ,1.11254303,0.91560159,0.92664064,0.93069442, 1.01285111,1.10017347,0.9952073 ,1.05616016,1.12564585,1.02743444, 0.93306189,1.04808763,0.87659083],		[[1.,0.98392517,1.02825092,1.0127091 ,1.21814838,1.03987996, 1.17367563,1.0721497 ,1.11254303,0.91560159,0.92664064,0.93069442, 1.01285111,1.10017347,0.9952073 ,1.05616016,1.12564585,1.02743444, 0.93306189,1.04808763,0.87659083],

SebastianSager at 11:35, 20 October 2023

2023-10-20T11:35:17Z

← Older revision		Revision as of 11:35, 20 October 2023
Line 2:		Line 2:
	\|nd = 1		\|nd = 1
	\|nx = 4		\|nx = 4
	\|nw = 3		\|nu = 3
	\|nc = 2		\|nc = 1
	\|nri = 2		\|nri = 0
	\|nre = 5		\|nre = 5
	}}<!-- 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...
Line 43:		Line 43:
	</math>		</math>

	Here the four differential states and three control functions stand for the metabolite concentrations (<math> x_1, x_2, x_3, x_4 </math>) and the enzyme concentrations (<math> u_1, u_2, u_3 </math>). The objective function candidates are the sum of intermediate metabolite concentrations and the transition time. The parameters (<math> ~~k_1~~, ~~k_2~~, ~~k_3~~ </math>) are kinetic parameters in mass action expressions.		Here the four differential states and three control functions stand for the metabolite concentrations (<math> x_1, x_2, x_3, x_4 </math>) and the enzyme concentrations (<math> u_1, u_2, u_3 </math>). The two objective function candidates are the sum of intermediate metabolite concentrations and the transition time. The three model parameters <math>p_1, p_2, p_3</math> are kinetic parameters in mass action expressions.

	== Data ==		== Data ==

SebastianSager at 11:28, 20 October 2023

2023-10-20T11:28:15Z

← Older revision		Revision as of 11:28, 20 October 2023
Line 96:		Line 96:

	== Examples ==		== Examples ==
	~~Here are two~~ plots ~~with~~ noise free data for weights ~~[0.232, 0.768] to compare with the solution of different~~ optimal control problems.		The plots show noise free data for different weights from forward optimal control problems.
	<gallery caption="Solution plots" widths="280px" heights="240px" perrow="3">		<gallery caption="Solution plots" widths="280px" heights="240px" perrow="3">
	Image:LPN3B_min_sum_data.png\| OCP with weights [0.232, 0.768].		Image:LPN3B_min_sum_data.png\| OCP with weights [0.232, 0.768].

SebastianSager at 11:27, 20 October 2023

2023-10-20T11:27:04Z

← Older revision		Revision as of 11:27, 20 October 2023
Line 37:		Line 37:
	x_i(t) &\ge& 0 \; \forall \; i \in \{1,2,3,4\} \\		x_i(t) &\ge& 0 \; \forall \; i \in \{1,2,3,4\} \\
	u_i(t) &\in& [0,1] \; \forall \; i \in \{1,2,3\} \\		u_i(t) &\in& [0,1] \; \forall \; i \in \{1,2,3\} \\
	1 &\ge& u_1 + u_2 + u_3 \\		1 &\ge& u_1(t) + u_2(t) + u_3(t) \\
	w_1, w_2 \in [0,1] \\		w_1, w_2 \in [0,1] \\
	w_1 + w_2 = 1		w_1 + w_2 = 1

SebastianSager: Edited the data table

2023-10-20T11:26:21Z

Edited the data table

← Older revision		Revision as of 11:26, 20 October 2023
Line 16:		Line 16:

	== Mathematical formulation ==		== Mathematical formulation ==

	~~Under construction...~~

	The gIOC is given by		The gIOC is given by
Line 48:		Line 46:

	== Data ==		== Data ==

			The following table gives different values for <math>\eta</math>, componentwise for all four entries of <math>x</math> as time series, for different combinations of weights and noise levels that were used to produce the synthetic data via solution of forward optimal control problems.

	{\| class="wikitable"		{\| class="wikitable"
	\|+Data		\|+Data
	\|-		\|-
	\|weights		\|weights <math>w_1, w_2</math>
	\|parameters		\|parameters <math>p_1, p_2, p_3</math>
	\|noise		\|noise
	\|data		\|data <math>\eta</math>
	\|-		\|-
	\|[0.232, 0.768]		\|[0.232, 0.768]
	\|[1,1,1]		\|[1,1,1]
	\| 0		\| 0
	\|[[1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0],		\|
	[0, 0.215, 0.4298, 0.6446, 0.8593, 1.074, 1.2885, 1.503, 1.6591, 1.3381, 1.0792, 0.8704, 0.7021, 0.5662, 0.4849, 0.4846, 0.4844, 0.4842, 0.484, 0.4838, 0.4836],		[[1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0],
	[0, 0.0, 0.0002, 0.0004, 0.0007, 0.001, 0.0015, 0.002, 0.0391, 0.36, 0.6186, 0.827, 0.9948, 1.1301, 1.1405, 0.92, 0.7423, 0.5989, 0.4832, 0.3899, 0.3147],		[0, 0.215, 0.4298, 0.6446, 0.8593, 1.074, 1.2885, 1.503, 1.6591, 1.3381, 1.0792, 0.8704, 0.7021, 0.5662, 0.4849, 0.4846, 0.4844, 0.4842, 0.484, 0.4838, 0.4836],
	[0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0001, 0.0004, 0.0008, 0.0013, 0.0019, 0.0729, 0.2935, 0.4715, 0.6152, 0.731, 0.8245, 0.9]]		[0, 0.0, 0.0002, 0.0004, 0.0007, 0.001, 0.0015, 0.002, 0.0391, 0.36, 0.6186, 0.827, 0.9948, 1.1301, 1.1405, 0.92, 0.7423, 0.5989, 0.4832, 0.3899, 0.3147],
			[0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0001, 0.0004, 0.0008, 0.0013, 0.0019, 0.0729, 0.2935, 0.4715, 0.6152, 0.731, 0.8245, 0.9]]
	\|-		\|-
	\|[0.232, 0.768]		\|[0.232, 0.768]
	\|[1,1,1]		\|[1,1,1]
	\|0.2		\|0.2
	\|[[1. ,0.9590812 ,0.82266497,0.95877308,0.60614596,1.20781224,		\|
	0.92205471,1.0215116 ,0.89080449,1.05747735,1.04019676,1.06665347,		[[1., 0.9590812,0.82266497,0.95877308,0.60614596,1.20781224, 0.92205471,1.0215116 ,0.89080449,1.05747735,1.04019676,1.06665347, 0.78545416,1.17084962,1.08658091,1.01467309,0.91098074,1.10349004, 0.83411596,0.73187308,0.70399766],
	0.78545416,1.17084962,1.08658091,1.01467309,0.91098074,1.10349004,		[0.,0.37493181,0.10514573,0.79448823,0.44666767,1.19676033,1.14532119,1.64453389,1.93572019,1.37435635,0.92790967,1.11928728, 0.52061388,0.43837628,0.31518386,0.50300858,0.52891948,0.74255261, 0.07589526,0.64051491,0.47184952],
	0.83411596,0.73187308,0.70399766],[0. ,0.37493181,0.10514573,0.79448823,0.44666767,1.19676033,		[ 0., 0.23680072, 0.05047157,-0.03770305, 0.34603556,-0.45259701,0.25340369, 0.25177705, 0.16210031, 0.34367395, 0.96197961, 1.10224845, 1.21656021, 1.38442255, 1.02149302, 0.68818982, 0.7921558 , 0.32238544, 0.30229594, 0.43876605, 0.22073986],
	1.14532119,1.64453389,1.93572019,1.37435635,0.92790967,1.11928728,		[ 0.,-0.01591557,-0.12432336,-0.17669569,-0.21325853,-0.2489822 , -0.22989873,-0.0564741 ,-0.19961696,-0.16036058,-0.04386598, 0.25004781, -0.07279584, 0.09573081,-0.12329308,-0.03451486, 0.0173815 , 0.79895333, 0.8178261 , 0.53498205, 1.1021996]]
	0.52061388,0.43837628,0.31518386,0.50300858,0.52891948,0.74255261,
	0.07589526,0.64051491,0.47184952],[ 0. , 0.23680072, 0.05047157,-0.03770305, 0.34603556,-0.45259701,
	0.25340369, 0.25177705, 0.16210031, 0.34367395, 0.96197961, 1.10224845,
	1.21656021, 1.38442255, 1.02149302, 0.68818982, 0.7921558 , 0.32238544,
	0.30229594, 0.43876605, 0.22073986],[ 0. ,-0.01591557,-0.12432336,-0.17669569,-0.21325853,-0.2489822 ,
	-0.22989873,-0.0564741 ,-0.19961696,-0.16036058,-0.04386598, 0.25004781,
	-0.07279584, 0.09573081,-0.12329308,-0.03451486, 0.0173815 , 0.79895333,
	0.8178261 , 0.53498205, 1.1021996 ]]
	\|-		\|-
	\|[0,1]		\|[0,1]
	\|[1,1,1]		\|[1,1,1]
	\|0		\|0
	\|[[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],		\|
	[0, 0.211317, 0.422635, 0.633952, 0.845269, 1.05659, 1.2679, 1.47922, 1.69054, 1.90186, 1.95601, 1.58342, 1.2818, 1.03764, 0.839981, 0.685458, 0.685458, 0.685458, 0.685458, 0.685458, 0.685458],		[[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
	[0, 3.40252e-10, 2.02262e-09, 6.04129e-09, 1.32631e-08, 2.47434e-08, 4.23248e-08, 6.98021e-08, 1.16723e-07, 2.20847e-07, 0.103509, 0.476095, 0.777716, 1.02188, 1.21954, 1.36367, 1.10391, 0.893635, 0.72341, 0.58561, 0.474061],		[0, 0.211317, 0.422635, 0.633952, 0.845269, 1.05659, 1.2679, 1.47922, 1.69054, 1.90186, 1.95601, 1.58342, 1.2818, 1.03764, 0.839981, 0.685458, 0.685458, 0.685458, 0.685458, 0.685458, 0.685458],
	[0, 2.79389e-19, 2.05361e-18, 7.26553e-18, 1.82666e-17, 3.77412e-17, 6.87107e-17, 1.14894e-16, 1.82155e-16, 2.86358e-16, 3.73778e-11, 7.31532e-10, 5.75723e-09, 2.28945e-08, 7.3467e-08, 0.0103927, 0.270148, 0.480425, 0.65065, 0.78845, 0.9]]		[0, 3.40252e-10, 2.02262e-09, 6.04129e-09, 1.32631e-08, 2.47434e-08, 4.23248e-08, 6.98021e-08, 1.16723e-07, 2.20847e-07, 0.103509, 0.476095, 0.777716, 1.02188, 1.21954, 1.36367, 1.10391, 0.893635, 0.72341, 0.58561, 0.474061],
			[0, 2.79389e-19, 2.05361e-18, 7.26553e-18, 1.82666e-17, 3.77412e-17, 6.87107e-17, 1.14894e-16, 1.82155e-16, 2.86358e-16, 3.73778e-11, 7.31532e-10, 5.75723e-09, 2.28945e-08, 7.3467e-08, 0.0103927, 0.270148, 0.480425, 0.65065, 0.78845, 0.9]]
	\|-		\|-
	\|[0,1]		\|[0,1]
	\|[1,1,1]		\|[1,1,1]
	\|0.1		\|0.1
	\|[[1. ,0.98392517,1.02825092,1.0127091 ,1.21814838,1.03987996,		\|
	1.17367563,1.0721497 ,1.11254303,0.91560159,0.92664064,0.93069442,		[[1.,0.98392517,1.02825092,1.0127091 ,1.21814838,1.03987996, 1.17367563,1.0721497 ,1.11254303,0.91560159,0.92664064,0.93069442, 1.01285111,1.10017347,0.9952073 ,1.05616016,1.12564585,1.02743444, 0.93306189,1.04808763,0.87659083],
	1.01285111,1.10017347,0.9952073 ,1.05616016,1.12564585,1.02743444,		[0.,0.19112834,0.6016258 ,0.70894548,0.86077117,0.95316772, 1.12244906,1.51535841,1.48548905,1.87282215,2.13181979,1.48523121, 1.14624017,1.06839771,0.8838448 ,0.72466348,0.61379013,0.70096009, 0.73549769,0.62452413,0.61907767],
	0.93306189,1.04808763,0.87659083],[0. ,0.19112834,0.6016258 ,0.70894548,0.86077117,0.95316772,		[0., 0.04514029,-0.06510522,-0.00304812,-0.01620013, 0.006101, 0.04992798, 0.29317191, 0.11305888, 0.2285637 , 0.26142926, 0.50457228, 0.87829835, 0.90900075, 1.32279588, 1.42225272, 1.18086941, 0.67720058, 0.61562944, 0.6339817 , 0.36613472],
	1.12244906,1.51535841,1.48548905,1.87282215,2.13181979,1.48523121,		[0.,-0.13882966, 0.18200648,-0.06629627,-0.01496019, 0.21349797,-0.10124824,-0.05505019, 0.23235014, 0.09448396, 0.06059911,-0.12137716, -0.00781841, 0.04355511, 0.1369212 ,-0.13011339, 0.2027646 , 0.51512985, 0.65331917, 0.78324169, 0.81304223]]
	1.14624017,1.06839771,0.8838448 ,0.72466348,0.61379013,0.70096009,
	0.73549769,0.62452413,0.61907767],[ 0. , 0.04514029,-0.06510522,-0.00304812,-0.01620013, 0.006101 ,
	0.04992798, 0.29317191, 0.11305888, 0.2285637 , 0.26142926, 0.50457228,
	0.87829835, 0.90900075, 1.32279588, 1.42225272, 1.18086941, 0.67720058,
	0.61562944, 0.6339817 , 0.36613472],[ 0. ,-0.13882966, 0.18200648,-0.06629627,-0.01496019, 0.21349797,
	-0.10124824,-0.05505019, 0.23235014, 0.09448396, 0.06059911,-0.12137716,
	-0.00781841, 0.04355511, 0.1369212 ,-0.13011339, 0.2027646 , 0.51512985,
	0.65331917, 0.78324169, 0.81304223]]

	\|-		\|-
	\|}		\|}

VeronicaHaritonova: /* Mathematical formulation */

2023-10-20T11:25:52Z

Mathematical formulation

← Older revision		Revision as of 11:25, 20 October 2023
Line 39:		Line 39:
	x_i(t) &\ge& 0 \; \forall \; i \in \{1,2,3,4\} \\		x_i(t) &\ge& 0 \; \forall \; i \in \{1,2,3,4\} \\
	u_i(t) &\in& [0,1] \; \forall \; i \in \{1,2,3\} \\		u_i(t) &\in& [0,1] \; \forall \; i \in \{1,2,3\} \\
			1 &\ge& u_1 + u_2 + u_3 \\
	w_1, w_2 \in [0,1] \\		w_1, w_2 \in [0,1] \\
	w_1 + w_2 = 1		w_1 + w_2 = 1

SebastianSager: Removed old code and p

2023-10-20T06:46:23Z

Removed old code and p

@@ Line 21: / Line 21: @@
 The gIOC is given by
-<p>
+   <math>
     \displaystyle \min_{(p, w, x^*, u^*, T^*)} \; \| x^* - \eta \|
     </math>
@@ Line 44: / Line 43: @@
                   \end{array}
                   </math>
-</p>
 Here the four differential states and three control functions stand for the metabolite concentrations (<math> x_1, x_2, x_3, x_4 </math>) and the enzyme concentrations (<math> u_1, u_2, u_3 </math>). The objective function candidates are the sum of intermediate metabolite concentrations and the transition time. The parameters (<math> k_1, k_2, k_3 </math>) are kinetic parameters in mass action expressions.
@@ Line 118: / Line 117: @@
 </gallery>
 == References ==

VeronicaHaritonova: /* Examples */

2023-10-20T06:12:01Z

Examples

← Older revision		Revision as of 06:12, 20 October 2023
Line 113:		Line 113:
	== Examples ==		== Examples ==
	Here are two plots with noise free data for weights [0.232, 0.768] to compare with the solution of different optimal control problems.		Here are two plots with noise free data for weights [0.232, 0.768] to compare with the solution of different optimal control problems.
	<gallery caption="Solution plots" widths="~~180px~~" heights="~~140px~~" perrow="3">		<gallery caption="Solution plots" widths="280px" heights="240px" perrow="3">
	Image:~~ElectricCar PrimalStates Plot~~.~~PNG~~\| OCP with weights [0.232, 0.768].		Image:LPN3B_min_sum_data.png\| OCP with weights [0.232, 0.768].
	Image:LPN3B_minT_x_data.png\| OCP with weights [0,1].		Image:LPN3B_minT_x_data.png\| OCP with weights [0,1].
	</gallery>		</gallery>

VeronicaHaritonova: /* Examples */

2023-10-20T06:09:26Z

Examples

← Older revision		Revision as of 06:09, 20 October 2023
Line 115:		Line 115:
	<gallery caption="Solution plots" widths="180px" heights="140px" perrow="3">		<gallery caption="Solution plots" widths="180px" heights="140px" perrow="3">
	Image:ElectricCar PrimalStates Plot.PNG\| OCP with weights [0.232, 0.768].		Image:ElectricCar PrimalStates Plot.PNG\| OCP with weights [0.232, 0.768].
	Image:~~ElectricCar Control PathConstraints SwitchingFunction Plot~~.~~PNG~~\| OCP with weights [0,1].		Image:LPN3B_minT_x_data.png\| OCP with weights [0,1].
	</gallery>		</gallery>

VeronicaHaritonova: /* Examples */

2023-10-20T06:05:17Z

Examples

← Older revision		Revision as of 06:05, 20 October 2023
Line 112:		Line 112:

	== Examples ==		== Examples ==
	<gallery caption="~~Reference solution~~ plots" widths="180px" heights="140px" perrow="3">		Here are two plots with noise free data for weights [0.232, 0.768] to compare with the solution of different optimal control problems.
	Image:ElectricCar PrimalStates Plot.PNG\| ~~Primal states of an optimal trajectory for the relaxed problem on a control discretization grid~~ with ~~<math> N = 1~~,~~000 </math>~~.		<gallery caption="Solution plots" widths="180px" heights="140px" perrow="3">
	Image:ElectricCar Control PathConstraints SwitchingFunction Plot.PNG\| ~~The optimal control and switching function. The dotted vertical lines show the switching times <math> \tau_i </math> where transitions between different kinds of arcs occur~~.		Image:ElectricCar PrimalStates Plot.PNG\| OCP with weights [0.232, 0.768].
			Image:ElectricCar Control PathConstraints SwitchingFunction Plot.PNG\| OCP with weights [0,1].
	</gallery>		</gallery>