Difference between revisions of "Brachistochrone problem (TACO)"
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| − | This page contains a model of the classical [[Brachistochrone problem]] in [http://www.ampl.org AMPL] format, making use of the TACO toolkit for AMPL control optimization extensions. | + | This page contains a model of the classical [[Brachistochrone problem]] (Johann Bernoulli, 1696), see e.g. [http://en.wikipedia.org/wiki/Brachistochrone_curve Wikipedia] or <bib id="Betts1993" />, in [http://www.ampl.org AMPL] format, making use of the TACO toolkit for AMPL control optimization extensions. |
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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== References == | == References == | ||
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[[Category:AMPL/TACO]] | [[Category:AMPL/TACO]] | ||
Latest revision as of 21:32, 30 December 2015
This page contains a model of the classical Brachistochrone problem (Johann Bernoulli, 1696), see e.g. Wikipedia or [Betts1993]Author: J.T. Betts; S. Eldersveld; W.P. Huffman
Institution: Boeing Computer Services
Title: Sparse nonlinear programming test problems (Release 1.0)
Year: 1993
, in AMPL format, making use of the TACO toolkit for AMPL control optimization extensions.
Note that you will need to include a generic 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 brac_taco.mod
# ---------------------------------------------------------------- # Brachistochrone problem using AMPL and TACO # (c) Christian Kirches, Sven Leyffer # ---------------------------------------------------------------- include OptimalControl.mod; var t; var tf := 1.0, >= 0.1, <= 1.0; let tf.scale := 0.5; # improves convergence var x := 0, >= 0, <= 1; var y := 0, >= 0, <= 1; var v := 0, >= 0, <= 8; var a := 0.5, >= 0, <= 1.57079327; let a.type := "u1"; let a.slope_min := -10.0; let a.slope_max := +10.0; param gravity := 32.174; # in ft/s^2 minimize EndTime: eval (t,tf); let EndTime.scale := 0.1; subject to ODE_x: diff(x,t) = v*cos(a); ODE_y: diff(y,t) = v*sin(a); ODE_v: diff(v,t) = gravity*sin(a); IVC_x: eval(x,0) = 0; IVC_y: eval(y,0) = 0; IVC_v: eval(v,0) = 0; TC_x: eval(x,tf) = 1.0; # treating IVCs as boundary constraints improves convergence let IVC_x.type := "dpc"; let IVC_y.type := "dpc"; let IVC_v.type := "dpc"; option solver ...; solve;
Other Descriptions
Other descriptions of this problem are available in
- Mathematical notation at Brachistochrone problem
References
There were no citations found in the article.
