View source for Time optimal car problem (TACO)

This page contains a model of the [[Time optimal car problem]] in [http://www.ampl.org AMPL] format, making use of the TACO toolkit for AMPL control optimization extensions. The model can be found e.g. in
<bibref>Cuthrell1987</bibref> and <bibref>Logsdon1992</bibref>.
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 tocar1_taco.mod
<source lang="AMPL">
# ----------------------------------------------------------------
# Time optimal car problem using AMPL and TACO
# (c) Christian Kirches, Sven Leyffer
#
# Source: Cuthrell/Biegler'87, Logsdon/Biegler'92
# ----------------------------------------------------------------
include OptimalControl.mod;

var t;
var tf := 20, >= 5, <= 50;

var s := 0, >= 0, <= 330;
var v := 0, >= 0, <= 30;
var gas := 0.0, >= -2.0, <= 1.0;
let gas.type := "u0";

var p := 0.05, >= 0, <= 0.1;

minimize EndTime:
	eval(t,tf);
let EndTime.scale := 10.0;

subject to 

ODE_s:	diff(s,t) = v;
ODE_v:	diff(v,t) = gas - p;

IVC_s:	eval(s,0) = 0;
IVC_v: 	eval(v,0) = 0;

 TC_s:	eval(s,tf) = 300.0;
let TC_s.scale := 100.0;

TC_v:	eval(v,tf) = 0;
let TC_v.scale := 10.0;

let IVC_s.type := "dpc";
let IVC_v.type := "dpc";

option solver ...;

solve;

</source>

== Other Descriptions ==

Other descriptions of this problem are available in

* Mathematical notation at [[Time optimal car problem]]
 
[[Category:AMPL/TACO]]

== References ==

<biblist />