Difference between revisions of "Brachistochrone problem (TACO)"

# ----------------------------------------------------------------
# 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;