Goddart's rocket problem (Bocop)

This is a Bocop implementation of Goddart's rocket problem. The .def, .constants and .bounds files can be obtained through defining the problems dimensions in the GUI. The .tpp files need to be edited separately.

Problem.def

# This file defines all dimensions and parameters
# values for your problem :
 
# Initial and final time :
time.free string final
time.initial double 0
time.final double 1
 
# Dimensions :
state.dimension integer 3
control.dimension integer 1
algebraic.dimension integer 0
parameter.dimension integer 1
constant.dimension integer 6
boundarycond.dimension integer 4
constraint.dimension integer 1
 
# Discretization :
discretization.steps integer 100
discretization.method string gauss
 
# Optimization :
optimization.type string batch
batch.type integer 0
batch.index integer 5
batch.nrange integer 3
batch.lowerbound double 0.3
batch.upperbound double 0.9
batch.directory string Batch-C
 
# Initialization :
initialization.type string from_init_file
initialization.file string none
 
# Parameter identification :
paramid.type string false
paramid.separator string ,
paramid.file string no_directory
paramid.dimension integer 0
 
# Names :
state.0 string position
state.1 string speed
state.2 string mass
control.0 string acceleration_u
parameter.0 string finaltime
boundarycond.0 string r(0)
boundarycond.1 string v(0)
boundarycond.2 string m(0)
boundarycond.3 string r(f)
constraint.0 string drag_minus_C
constant.0 string Tmax
constant.1 string A
constant.2 string k
constant.3 string r0
constant.4 string b
constant.5 string C
 
# Solution file :
solution.file string problem.sol
 
# Iteration output frequency :
iteration.output.frequency integer 0

Problem.constants

# This file contains the values of the constants of your problem.
# Number of constants used in your problem : 
6
 
# Values of the constants : 
3.5
310
500
1
7
0.6

Problem.bounds

# This file contains all the bounds of your problem.
# Bounds are stored in standard format : 
# [lower bound]  [upper bound] [type of bound]
 
# Dimensions (i&f conditions, y, u, z, p, path constraints) :
4 3 1 0 1 1
 
# Bounds for the initial and final conditions :
1 1 equal
0 0 equal
1 1 equal
1.01 2e+020 lower
 
# Bounds for the state variables :
>0:1:0 1 2e+020 lower
>1:1:1 0 2e+020 lower
>2:1:2 0 2e+020 lower
 
# Bounds for the control variables :
0 1 both
 
# Bounds for the algebraic variables :
 
# Bounds for the optimization parameters :
0 2e+020 lower
 
# Bounds for the path constraints :
-2e+020 0 upper

criterion.tpp

#include "header_criterion"
{
	// CRITERION FOR GODDARD PROBLEM
 
	// MAXIMIZE FINAL MASS
	criterion = -final_state[2];
}

dynamics.tpp

#include "header_dynamics"
{
	// DYNAMICS FOR GODDARD PROBLEM
	// dr/dt = v
	// dv/dt = (Thrust(u) - Drag(r,v)) / m - grav(r)
	// dm/dt = -b*|u|
 
	double Tmax = constants[0];
	double A = constants[1];
	double k = constants[2];
	double r0 = constants[3];
	double b = constants[4];
 
	Tdouble r = state[0];
	Tdouble v = state[1];
	Tdouble m = state[2];
 
	state_dynamics[0] = v;
	state_dynamics[1] = (thrust(control[0],Tmax) - drag(r,v,A,k,r0)) / m - grav(r);
	state_dynamics[2] = - b * control[0];
}

boundarycond.tpp

#include "header_boundarycond"
{
	// INITIAL CONDITIONS FOR GODDARD PROBLEM
	// r0 = 1    v0 = 0   m0 = 1
	// MODELED AS 1 <= r0 <= 1, etc
	boundary_conditions[0] = initial_state[0];
	boundary_conditions[1] = initial_state[1];
	boundary_conditions[2] = initial_state[2];
 
	// FINAL CONDITIONS FOR GODDARD PROBLEM
  	// rf >= 1.01   MODELED AS   1.01 <= rf
	boundary_conditions[3] = final_state[0];
}

pathcond.tpp

#include "header_pathcond"
{
	// CONSTRAINT ON MAX DRAG FOR GODDARD PROBLEM
	// Drag <= C ie Drag - C <= 0
 
	double A = constants[1];
	double k = constants[2];
	double r0 = constants[3];
	double C = constants[5];
 
	Tdouble r = state[0];
	Tdouble v = state[1];
 
	path_constraints[0] = drag(r,v,A,k,r0) - C;
}

dependencies.tpp

The dependencies file is only needed if you use additional functions like the three following.

#include "./grav.tpp"
#include "./drag.tpp"
#include "./thrust.tpp"

drag.tpp

#include "adolc/adolc.h"
#include "adolc/adouble.h"
#include <cmath>
 
// FUNCTION FOR GODDARD DRAG
// drag = 310 v^2 exp (-500(r-1))
 
// Arguments:
// r: radius
// v: velocity
 
template<class Tdouble> Tdouble drag(Tdouble r, Tdouble v, double A, double k, double r0)
{
 
	Tdouble drag;
	drag = A * v * v * exp(-k*(fabs(r)-r0));
	return drag;
 
}

grav.tpp

#include "adolc/adolc.h"
#include "adolc/adouble.h"
#include <cmath>
 
// FUNCTION FOR GRAVITY 
// g = 1 / r^2
 
// Arguments:
// r: radius
 
template<class Tdouble> Tdouble grav(Tdouble r)
{
 
	Tdouble grav;
	grav = 1e0 / r / r;
	return grav;
 
}

thrust.tpp

#include "adolc/adolc.h"
#include "adolc/adouble.h"
#include <cmath>
 
// FUNCTION FOR THRUST (GODDARD)
// T = u * Tmax
 
// Arguments:
// r: radius
 
template<class Tdouble> Tdouble thrust(Tdouble u, double Tmax)
{
	Tdouble thrust;
	thrust = u * Tmax;
	return thrust;
}