Particle steering problem (TACO) - Revision history

JonasSchulze: Text replacement - "\(.*)\<\/bibref\>" to ""

2015-12-30T20:32:09Z

Text replacement - "\<bibref\>(.*)\<\/bibref\>" to "<bib id="$1" />"

← Older revision		Revision as of 20:32, 30 December 2015
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	This page contains a model of the [[Particle steering problem]] in [http://www.ampl.org AMPL] format, making use of the TACO toolkit for AMPL control optimization extensions. This classical problem can e.g. be found in <~~bibref>~~Bryson1975</~~bibref~~>. The original model using a collocation formulation can be found in the [http://www.mcs.anl.gov/~more/cops/ COPS library].		This page contains a model of the [[Particle steering problem]] in [http://www.ampl.org AMPL] format, making use of the TACO toolkit for AMPL control optimization extensions. This classical problem can e.g. be found in <bib id="Bryson1975" />. The original model using a collocation formulation can be found in the [http://www.mcs.anl.gov/~more/cops/ COPS library].
	Note that you will need to include a generic [[support AMPL files\|AMPL/TACO support file]], OptimalControl.mod.		Note that you will need to include a generic [[support AMPL files\|AMPL/TACO support file]], OptimalControl.mod.
	To solve this model, you require an optimal control or NLP code that uses the TACO toolkit to support the AMPL optimal control extensions.		To solve this model, you require an optimal control or NLP code that uses the TACO toolkit to support the AMPL optimal control extensions.

JonasSchulze: Text replacement - "" to ""

2015-12-30T20:28:26Z

Text replacement - "<bibreferences/>" to "<biblist />"

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	== References ==		== References ==
	<~~bibreferences~~/>		<biblist />

	[[Category:AMPL/TACO]]		[[Category:AMPL/TACO]]

Ckirches: Reference for particle steering problem (TACO)

2011-09-29T20:58:41Z

Reference for particle steering problem (TACO)

← Older revision		Revision as of 20:58, 29 September 2011
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	This page contains a model of the [[Particle steering problem]] in [http://www.ampl.org AMPL] format, making use of the TACO toolkit for AMPL control optimization extensions. The original model using a collocation formulation can be found in the [http://www.mcs.anl.gov/~more/cops/ COPS library].		This page contains a model of the [[Particle steering problem]] in [http://www.ampl.org AMPL] format, making use of the TACO toolkit for AMPL control optimization extensions. This classical problem can e.g. be found in <bibref>Bryson1975</bibref>. The original model using a collocation formulation can be found in the [http://www.mcs.anl.gov/~more/cops/ COPS library].
	Note that you will need to include a generic [[support AMPL files\|AMPL/TACO support file]], OptimalControl.mod.		Note that you will need to include a generic [[support AMPL files\|AMPL/TACO support file]], OptimalControl.mod.
	To solve this model, you require an optimal control or NLP code that uses the TACO toolkit to support the AMPL optimal control extensions.		To solve this model, you require an optimal control or NLP code that uses the TACO toolkit to support the AMPL optimal control extensions.
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	let u.type := "u1";		let u.type := "u1";

	minimize time:		minimize time: eval(t,tf);
	eval(t,tf);

	subject to		subject to

	dy1: diff (y[1],t) = y[2];		dy1: diff (y[1],t) = y[2];
	dy2: diff (y[2],t) = a*cos(u);		dy2: diff (y[2],t) = a*cos(u);
	dy3: diff (y[3],t) = y[4];		dy3: diff (y[3],t) = y[4];
	dy4: diff (y[4],t) = a*sin(u);		dy4: diff (y[4],t) = a*sin(u);

	ivc{i in 1..4}: eval(y[i],0) = 0;		ivc{i in 1..4}: eval(y[i],0) = 0;

	by1d: eval(y[2],tf) = 45;		by1d: eval(y[2],tf) = 45;
	by2: eval(y[3],tf) = 5;		by2: eval(y[3],tf) = 5;
	by2d: eval(y[4],tf) = 0;		by2d: eval(y[4],tf) = 0;

	option solver ...;		option solver ...;
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	* Mathematical notation at [[Particle steering problem]]		* Mathematical notation at [[Particle steering problem]]
	* [[:Category:AMPL \| AMPL]] (using a fixed discretization) at the [http://www.mcs.anl.gov/~more/cops/ COPS library]		* [[:Category:AMPL \| AMPL]] (using a fixed discretization) at the [http://www.mcs.anl.gov/~more/cops/ COPS library]

			== References ==
			<bibreferences/>

	[[Category:AMPL/TACO]]		[[Category:AMPL/TACO]]

Ckirches: Particle steering problem (TACO)

2011-09-29T19:19:17Z

Particle steering problem (TACO)

New page

This page contains a model of the [[Particle steering problem]] in [http://www.ampl.org AMPL] format, making use of the TACO toolkit for AMPL control optimization extensions. The original model using a collocation formulation can be found in the [http://www.mcs.anl.gov/~more/cops/ COPS library].
Note that you will need to include a generic [[support AMPL files|AMPL/TACO support file]], OptimalControl.mod.
To solve this model, you require an optimal control or NLP code that uses the TACO toolkit to support the AMPL optimal control extensions.

=== AMPL ===

This is the source file particle_taco.mod
<source lang="AMPL">
# ----------------------------------------------------------------
# Particle steering problem using AMPL and TACO
# (c) Christian Kirches, Sven Leyffer
#
# Source: COPS 3.1 collocation formulation - March 2004
# ----------------------------------------------------------------
include OptimalControl.mod;

param Pi := 3.14159265358979;
param a := 100.0;

var t;
var tf := 1, >= 0, <=10;
var y{1..4};
var u >= -Pi/2, <= +Pi/2;
let u.type := "u1";

minimize time:
eval(t,tf);

subject to

dy1: diff (y[1],t) = y[2];
dy2: diff (y[2],t) = a*cos(u);
dy3: diff (y[3],t) = y[4];
dy4: diff (y[4],t) = a*sin(u);

ivc{i in 1..4}: eval(y[i],0) = 0;

by1d: eval(y[2],tf) = 45;
by2: eval(y[3],tf) = 5;
by2d: eval(y[4],tf) = 0;

option solver ...;

solve;

</source>

== Other Descriptions ==

Other descriptions of this problem are available in

* Mathematical notation at [[Particle steering problem]]
* [[:Category:AMPL | AMPL]] (using a fixed discretization) at the [http://www.mcs.anl.gov/~more/cops/ COPS library]

[[Category:AMPL/TACO]]