# Particle steering problem (TACO)

From mintOC

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[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;

## Other Descriptions

Other descriptions of this problem are available in

- Mathematical notation at Particle steering problem
- AMPL (using a fixed discretization) at the COPS library

## References

[Bryson1975] | Bryson, A.E.; Ho, Y.-C. (1975): Applied Optimal Control. (%edition%). Wiley, New York, %pages% |