Toy NMPC problem (TACO)

This page contains a model of a small Toy NMPC problem in AMPL format, making use of the TACO toolkit for AMPL control optimization extensions. Here, it is used for off-line optimal control only. This problem can be found in the thesis <bibref>Diehl2001</bibref>. 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 toy_taco.mod

# ----------------------------------------------------------------
# Toy NMPC problem using AMPL and TACO
# (c) Christian Kirches, Sven Leyffer
#
# Source: M. Diehl, 2001
# ----------------------------------------------------------------
include OptimalControl.mod;
 
var tf := 3, >= 2, <= 3;
var t;
 
var x := -0.5;
 
var u >= -1.0, <= 1.0, := 0.0;
let u.type := "u0";
 
var p := 1.0;
 
minimize LagrangeObjective:
	integral (x^2 + u^2, tf);
 
subject to 
 
ODE: diff(x,t) = (x + p) * x + u;
SPC: eval(x,0) = -0.5;
EPC: eval(x,tf) = 0.0;
 
option solver ...;
 
solve;

Other Descriptions

Other descriptions of this problem are available in

• Mathematical notation at Toy NMPC problem