# Particle steering problem (TACO)

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This page contains a model of the Particle steering problem in AMPL format, making use of the TACO toolkit for AMPL control optimization extensions. This classical problem can e.g. be found in [Bryson1975]Address: New York
Author: Bryson, A.E.; Ho, Y.-C.
Publisher: Wiley
Title: Applied Optimal Control
Year: 1975 . The original model using a collocation formulation can be found in the COPS library. 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 particle_taco.mod

```# ----------------------------------------------------------------
# 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,t) = y;
dy2: diff (y,t) = a*cos(u);
dy3: diff (y,t) = y;
dy4: diff (y,t) = a*sin(u);

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

by1d: eval(y,tf) = 45;
by2:  eval(y,tf) = 5;
by2d: eval(y,tf) = 0;

option solver ...;

solve;```

## Other Descriptions

Other descriptions of this problem are available in