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cost_fn_print.cpp
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cost_fn_print.cpp
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#include"agent_defn.hpp"
#include"dataTYPE.hpp"
#include"3bodyfunction.hpp"
#include"FullTrajSoln.hpp"
#include"varIsp_func.hpp"
#include<cmath>
#include<vector>
#include<fstream>
#include<boost/numeric/odeint.hpp>
/**< ******************************************** */
/**< GLOBAL LAMBDA EXPRESSIONS */
auto sqr=[](const auto &x){return x*x;};
auto cube=[](const auto &x){return x*x*x;};
std::fstream fileout("Output.txt",std::ios::out);
auto write_cout=[&](const std::vector<Agent_datatype> &x, const Agent_datatype t)
{
fileout.precision(17);
for(unsigned int i=0;i<x.size();i++){
fileout<<x.at(i)<<"\t";
}
fileout<<t<<std::endl;
};
/**< BIG FUNCTION FOR DIFFERENT COST FUNCTION DEFINITIONS */
template<typename Agent_data>
Agent_data Agent<Agent_data>::cost_fn_print(const int &selector)
{
cost_val=0;
/// for(double i=0;i<1e4;i++){double j=0;j++;}///MIMICKS EXPENSIVE COST FUNCTION EVALUATION
switch(selector)
{
case 1:{
/**< SPHERE */
for(unsigned int i=0;i<vals.size();i++){
cost_val+=sqr(vals.at(i));
}
break;
}
case 2:{
/**< ACKERLEY */
const Agent_data pi=acos(-1.0L);
Agent_data x1=vals.at(0);
Agent_data x2=vals.at(1);
cost_val=20.0+exp(1.0)-20.0*exp(-0.2*sqrt(0.5*(sqr(x1)+sqr(x2))))-exp(0.5*(cos(2*pi*x1)+cos(2*pi*x2)));///ACKERLEY
break;
}
case 3:{
/**< ROSENBROCK */
for(unsigned int i=0;i<vals.size()-1;i++){
cost_val+=(100*sqr(vals.at(i+1)-sqr(vals.at(i)))+sqr(vals.at(i)-1));
}
break;
}
case 4:{
/**< EASOM */
const Agent_data pi=acos(-1.0L);
cost_val=-cos(vals.at(0))*cos(vals.at(1))*exp(-(sqr(vals.at(0)-pi)+sqr(vals.at(1)-pi)));
break;
}
case 5:{
/**< SCHAFFER FUNCTION N. 2 */
cost_val=0.50+(sqr(sin(sqr(vals.at(0))-sqr(vals.at(1))))-0.50)/sqr(1.0+0.001*(sqr(vals.at(0))+sqr(vals.at(1))));
break;
}
case 6:{
/**< STYBLINSKI-TANG */
for(unsigned int i=0;i<vals.size();i++){
cost_val+=(sqr(sqr(vals.at(i)))-16.0*sqr(vals.at(i))+5.0*vals.at(i));
}
cost_val/=2.0;
break;
}
case 7:{
/**< EGGHOLDER FUNCTION */
cost_val=-(vals.at(1)+47.0)*sin(sqrt(abs(0.5*vals.at(0)+vals.at(1)+47.0)))-vals.at(0)*sin(sqrt(abs(vals.at(0)-vals.at(1)-47.0)));
break;
}
case 8:{
/**< HIMMELBLAU */
cost_val=sqr(sqr(vals.at(0))+vals.at(1)-11.0)+sqr(vals.at(0)+sqr(vals.at(1))-7);
break;
}
case 9:{
/**< RASTRIGIN */
const Agent_data pi=acos(-1.0L);
for(unsigned int i=0;i<vals.size();i++){
cost_val+=sqr(vals.at(i))-10.0*cos(2*pi*vals.at(i));
}
cost_val+=10.0*vals.size();
break;
}
case 10:{
/**< SCHWEFEL - difficult */
for(unsigned int i=0;i<vals.size();i++){
cost_val-=vals.at(i)*sin(sqrt(abs(vals.at(i))));
}
cost_val+=418.9829*vals.size();
///min is at all indept vars = 420.97
break;
}
case 11:{
/**< CROSS IN TRAY */
const Agent_data pi=acos(-1.0L);
Agent_data x=vals.at(0);Agent_data y=vals.at(1);
cost_val=-0.0001*pow(abs(sin(x)*sin(y)*exp(abs(100.0-sqrt(sqr(x)+sqr(y))/pi)))+1.0,0.1);
break;
}
case 12:{
/**< CHICHINADZE */
const Agent_data pi=acos(-1.0L);
Agent_data x=vals.at(0);Agent_data y=vals.at(1);
cost_val=sqr(x)-12.0*x+8.0*sin(2.5*pi*x)+10*cos(0.5*pi*x)+11.0-0.2*sqrt(5)/(exp(0.5*sqr(y-0.5)));
break;
}
case 13:{
/**< CUBE - similar to 2D Rosenbrock */
cost_val=100.0*sqr(vals.at(1)-cube(vals.at(0)))+sqr(1-vals.at(0));
break;
}
case 14:{
/**< DAMAVANDI - very difficult to arrive at global optimum */
const Agent_data pi=acos(-1.0L);
Agent_data x=vals.at(0);Agent_data y=vals.at(1);
cost_val=(1.0-abs(pow((sin(pi*(x-2.0))*sin(pi*(y-2.0)))/(sqr(pi)*(x-2.0)*(y-2.0)),5.0)))*(2.0+sqr(x-7.0)+2*sqr(y-7.0));
break;
}
case 15:{
/**< HOLDER TABLE FUNCTION */
const Agent_data pi=acos(-1.0L);
Agent_data x=vals.at(0);Agent_data y=vals.at(1);
cost_val=-abs(sin(x)*cos(y)*exp(abs(1.0-sqrt(sqr(x)+sqr(y))/pi)));
break;
}
case 16:{
/**< OPTIMAL TIME CAR ACCELERATION */
/**< 3D PROBLEM, 2 COSTATES 1 TIME VARIABLE */
/**< 2s IS OPTIMUM TIME */
using namespace boost::numeric::odeint;
typedef Agent_data state_type;
typedef runge_kutta_cash_karp54<std::vector<state_type>> stepper_type;
typedef controlled_runge_kutta<stepper_type> controlled_stepper_type;
auto rhs=[&](const std::vector<state_type> x, std::vector<state_type> &dxdt, const state_type){
dxdt.at(0)=x.at(1);
dxdt.at(1)=-1.0*copysign(1.0,static_cast<state_type>(x.at(2)));
dxdt.at(2)=-vals.at(0);
};
state_type abs_err = 1.0e-16,rel_err = 1.0e-16,a_x = 1.0,a_dxdt = 1.0;
controlled_stepper_type controlled_stepper(default_error_checker<state_type,
range_algebra,default_operations>(abs_err,rel_err,a_x,a_dxdt));
///SHIFT STATE VECTOR AS AGENT CLASS PRIVATE VARIABLE
///THAT'LL PROBABLY INCREASE SPEED
std::vector<state_type> x;
x.push_back(0.0);
x.push_back(0.0);
x.push_back(vals.at(1));
integrate_adaptive(controlled_stepper,rhs,x,0.0,vals.at(2),1e-3);
cost_val=abs(x.at(0)-1.0)+abs(x.at(1));
///cost_val-=vals.at(2)*(cost_val<=1e-9)?1.0:0.0;
break;
}
case 17:{
/**< 2D SOLAR ELECTRIC LOW THRUST MIN TIME */
using namespace boost::numeric::odeint;
typedef Agent_datatype state_type;
typedef runge_kutta_fehlberg78<std::vector<state_type>> stepper_type;
typedef controlled_runge_kutta<stepper_type> controlled_stepper_type;
static const double mu=1.32712440018e+20;
static const double g0=9.806;
static const double Isp=1500.0;
static const double g0Isp=g0*Isp;
static double mi=1000.0;
double re=149.6e+9;
double ve=sqrt(mu/re);
double rm=1.524*re;
double vm=sqrt(mu/rm);
static const double k=0.1*sqr(re);
static const double pi=acos(-1);
double r;double alph;double T;
double a1,b1,c1,a2,b2,c2;
double r4,r3,msq;
state_type abs_err=1.0e-16,rel_err=1.0e-16,a_x=1.0,a_dxdt=1.0;
controlled_stepper_type controlled_stepper(default_error_checker<state_type,
range_algebra,default_operations>(abs_err,rel_err,a_x,a_dxdt));
auto rhs=[&](const std::vector<state_type> x, std::vector<state_type> &dxdt, const state_type){
r=sqrt(sqr(x.at(0))+sqr(x.at(1)));///RADIUS
alph=pi+atan2(x.at(8),x.at(7));///OPTIMAL CONTROL ANGLE
T=k/sqr(r);
///STATE EQUATIONS
dxdt.at(0)=x.at(2);
dxdt.at(1)=x.at(3);
dxdt.at(2)=(-mu*x.at(0)/cube(r))+(T*cos(alph)/x.at(4));
dxdt.at(3)=(-mu*x.at(1)/cube(r))+(T*sin(alph)/x.at(4));
dxdt.at(4)=-T/(g0Isp);
///COSTATE EQUATIONS
r4=sqr(sqr(r));r3=cube(r);msq=sqr(x.at(4));
a1=(-mu/r3)+((3.0*mu*x.at(0)/(r4)*(x.at(0)/r))+(cos(alph)*-2.0*k*x.at(0)/(x.at(4)*r4)));
a2=(3.0*mu*x.at(0)/(r4)*(x.at(1)/r))+(cos(alph)*-2.0*k*x.at(1)/(x.at(4)*r4));
b1=(3.0*mu*x.at(1)/(r4)*(x.at(0)/r))+(sin(alph)*-2.0*k*x.at(0)/(x.at(4)*r4));
b2=(-mu/r3)+((3.0*mu*x.at(1)/(r4)*(x.at(1)/r))+(sin(alph)*-2.0*k*x.at(1)/(x.at(4)*r4)));
c1=-2.0*k*x.at(0)/(r4*g0Isp);
c2=-2.0*k*x.at(1)/(r4*g0Isp);
dxdt.at(5)=-x.at(7)*a1-x.at(8)*b1-x.at(9)*c1;
dxdt.at(6)=-x.at(7)*a2-x.at(8)*b2-x.at(9)*c2;
dxdt.at(7)=-x.at(5);
dxdt.at(8)=-x.at(6);
dxdt.at(9)=-x.at(7)*(-T*cos(alph)/msq)-x.at(8)*(-T*sin(alph)/msq);
};
std::vector<state_type> x;
x.push_back(re);///X COORDINATE
x.push_back(0.0);///Y COORDINATE
x.push_back(0.0);///X VELOCITY
x.push_back(ve);///Y VELOCITY
x.push_back(mi);///INIT MASS
for(unsigned int i=0;i<5;i++){
x.push_back(vals.at(i));
}
double endtime=86400.0*vals.at(5);
integrate_adaptive(controlled_stepper,rhs,x,0.0,endtime,endtime/1000.0);
cost_val=abs(-1.0+(sqr(x.at(0))+sqr(x.at(1)))/sqr(rm));///achieve position
cost_val+=abs(-1.0+(sqr(x.at(2))+sqr(x.at(3)))/sqr(vm));///achieve velocity
cost_val+=abs(-1.0+sqr(abs(x.at(0)*x.at(3)-x.at(1)*x.at(2))/(rm*vm)));///achieve angular momentum
break;
}
case 18:{
/**< 2D NUCLEAR ELECTRIC LOW THRUST MIN TIME */
using namespace boost::numeric::odeint;
typedef Agent_datatype state_type;
typedef runge_kutta_fehlberg78<std::vector<state_type>> stepper_type;
// typedef controlled_runge_kutta<stepper_type> controlled_stepper_type;
static const double mu=params.mu;//12440018e+20;
static const double g0=params.g0;
static const double Isp=params.Isp;
static const double g0Isp=g0*Isp;
double re=params.rinit;
// double ve=sqrt(mu/re);
double rm=params.rf_fac*params.rinit;
double vm=sqrt(mu/rm);
static double mi=params.mi;
static const double pi=acos(-1.0);
double r;double alph;double T;
double a1,b1,c1,a2,b2,c2;
double r4,r3,msq,cth,sth;
///state_type abs_err=1.0e-16,rel_err=1.0e-16,a_x=1.0,a_dxdt=1.0;
///controlled_stepper_type controlled_stepper(default_error_checker<state_type,
/// range_algebra,default_operations>(abs_err,rel_err,a_x,a_dxdt));
auto controlled_stepper=make_controlled(1.0e-16,1.0e-16,86400.0*params.maxstep,stepper_type());
auto rhs=[&](const std::vector<state_type> x, std::vector<state_type> &dxdt, const state_type){
r=sqrt(sqr(x.at(0))+sqr(x.at(1)));///RADIUS
alph=pi+atan2(x.at(8),x.at(7));///OPTIMAL CONTROL ANGLE
T=params.kfactor;//k;
cth=cos(alph);sth=sin(alph);
///STATE EQUATIONS
dxdt.at(0)=x.at(2);
dxdt.at(1)=x.at(3);
dxdt.at(2)=(-mu*x.at(0)/cube(r))+(T*cth/x.at(4));
dxdt.at(3)=(-mu*x.at(1)/cube(r))+(T*sth/x.at(4));
dxdt.at(4)=-T/(g0Isp);
///COSTATE EQUATIONS
r4=sqr(sqr(r));r3=cube(r);msq=sqr(x.at(4));
a1=(-mu/r3)+((3.0*mu*x.at(0)/(r4)*(x.at(0)/r)));
a2=(3.0*mu*x.at(0)/(r4)*(x.at(1)/r));
b1=(3.0*mu*x.at(1)/(r4)*(x.at(0)/r));
b2=(-mu/r3)+((3.0*mu*x.at(1)/(r4)*(x.at(1)/r)));
c1=0.0;
c2=0.0;
dxdt.at(5)=-x.at(7)*a1-x.at(8)*b1-x.at(9)*c1;
dxdt.at(6)=-x.at(7)*a2-x.at(8)*b2-x.at(9)*c2;
dxdt.at(7)=-x.at(5);
dxdt.at(8)=-x.at(6);
dxdt.at(9)=(-x.at(7)*(-T*cth/msq)-x.at(8)*(-T*sth/msq));
};
std::vector<state_type> x;
double a,rad,v,x0,y0,vx0,vy0;
a=re*params.rpfac/(1.0-params.ecc);
rad=a*(1.0-sqr(params.ecc))/(1.0+params.ecc*cos(params.nu*pi/180));
x0=rad*cos(params.nu*pi/180);
y0=rad*sin(params.nu*pi/180);
v=sqrt(mu*((2.0/rad)-(1.0/a)));
double gamma=atan2(params.ecc*sin(params.nu*pi/180.0),1.0+params.ecc*cos(params.nu*pi/180.0));
vx0=v*cos(0.5*pi-gamma+params.nu*pi/180.0);vy0=v*sin(0.5*pi-gamma+params.nu*pi/180.0);
x.push_back(x0);///X COORDINATE
x.push_back(y0);///Y COORDINATE
x.push_back(vx0);///X VELOCITY
x.push_back(vy0);///Y VELOCITY
x.push_back(mi);///INIT MASS
for(unsigned int i=0;i<5;i++){
x.push_back(vals.at(i));
}
double endtime=86400.0*vals.at(5);
integrate_adaptive(controlled_stepper,rhs,x,0.0,endtime,0.001,write_cout);
cost_val=sqr(-1.0+((sqr(x.at(0))+sqr(x.at(1)))/sqr(rm)));///achieve position
cost_val+=sqr(-1.0+((sqr(x.at(2))+sqr(x.at(3)))/sqr(vm)));///achieve velocity
cost_val+=sqr(-1.0+sqr(abs(x.at(0)*x.at(3)-x.at(1)*x.at(2))/(rm*vm)));///achieve angular momentum
massfrac=(mi-x.at(4))/mi;
break;
}
case 19:{
/**< 2D CONTINUOUS THRUST MIN FUEL */
using namespace boost::numeric::odeint;
typedef Agent_datatype state_type;
typedef runge_kutta_fehlberg78<std::vector<state_type>> stepper_type;
static const double mu=params.mu;
static const double g0=params.g0;
static const double Isp=params.Isp;
static const double g0Isp=g0*Isp;
static double mi=params.mi;
double re=params.rinit;
double rm=params.rf_fac*params.rinit;
double vm=sqrt(mu/rm);
static const double pi=acos(-1.0);
double r,alph,T;
double a1,b1,a2,b2,c1,c2;
double r2,r4,r3,msq,m;
double costsqrt,p,l1,l2,calp,salp;
double dTx,dTy;
// int NEP=params.NEP;
auto controlled_stepper=make_controlled(1.0e-16,1.0e-16,1.0*86400.0,stepper_type());
auto rhs=[&](const std::vector<state_type> x, std::vector<state_type> &dxdt, const state_type){
r=sqrt(sqr(x.at(0))+sqr(x.at(1)));///RADIUS
r2=sqr(r);r4=(sqr(r2));r3=cube(r);
m=x.at(4);msq=sqr(x.at(4));
if(params.NEP==1){
///NEP
T=params.kfactor;
dTx=0.0;dTy=0.0;
}
else{
///SEP INVERSE SQR LAW
T=params.kfactor*sqr(re/r);
if(r<0.25*re){///SATURATE THRUST
T=params.kfactor*sqr(1.0/0.25);
}
dTx=-2.0*T*x.at(0)/r2;dTy=-2.0*T*x.at(1)/r2;
}
///condition to prevent bad stuff
if(m<0.1*mi){
T=0.0;
}
costsqrt=sqrt(sqr(x.at(7))+sqr(x.at(8)));
alph=pi+atan2(x.at(8),x.at(7));
calp=cos(alph);salp=sin(alph);
p=1.0;
l1=T*((costsqrt/m)+(x.at(9)/g0Isp)-T);
///l2=-T*((costsqrt/m)+(x.at(9)/g0Isp));
l2=-l1-sqr(T);
if(l2>=0.0){
p=0.0;
}
else if(l1<0.0&&l2<0.0){
p=-l2/sqr(T);
}
///STATE EQUATIONS
dxdt.at(0)=x.at(2);
dxdt.at(1)=x.at(3);
dxdt.at(2)=(-mu*x.at(0)/r3)+(p*T*calp/m);
dxdt.at(3)=(-mu*x.at(1)/r3)+(p*T*salp/m);
dxdt.at(4)=-p*T/(g0Isp);
///COSTATE EQUATIONS
a1=(-mu/r3)+((3.0*mu*x.at(0)/(r4)*(x.at(0)/r)))+(p*calp*dTx/m);
a2=(3.0*mu*x.at(0)/(r4)*(x.at(1)/r))+(p*calp*dTy/m);
b1=(3.0*mu*x.at(1)/(r4)*(x.at(0)/r))+(p*salp*dTx/m);
b2=(-mu/r3)+((3.0*mu*x.at(1)/(r4)*(x.at(1)/r)))+(p*salp*dTy/m);
c1=(-p*dTx/g0Isp);c2=(-p*dTy/g0Isp);
dxdt.at(5)=-x.at(7)*a1-x.at(8)*b1-x.at(9)*c1;
dxdt.at(6)=-x.at(7)*a2-x.at(8)*b2-x.at(9)*c1;
dxdt.at(7)=-x.at(5);
dxdt.at(8)=-x.at(6);
dxdt.at(9)=-p*T*costsqrt/msq;
};
std::vector<state_type> x;
double a,rad,v,x0,y0,vx0,vy0;
a=re*params.rpfac/(1.0-params.ecc);
rad=a*(1.0-sqr(params.ecc))/(1.0+params.ecc*cos(params.nu*pi/180));
x0=rad*cos(params.nu*pi/180);
y0=rad*sin(params.nu*pi/180);
v=sqrt(mu*((2.0/rad)-(1.0/a)));
double gamma=atan2(params.ecc*sin(params.nu*pi/180.0),1.0+params.ecc*cos(params.nu*pi/180.0));
vx0=v*cos(0.5*pi-gamma+params.nu*pi/180.0);vy0=v*sin(0.5*pi-gamma+params.nu*pi/180.0);
x.push_back(x0);///X COORDINATE
x.push_back(y0);///Y COORDINATE
x.push_back(vx0);///X VELOCITY
x.push_back(vy0);///Y VELOCITY
x.push_back(mi);///INIT MASS
for(unsigned int i=0;i<5;i++){
x.push_back(vals.at(i));
}
double endtime=86400.0*vals.at(5);
integrate_adaptive(controlled_stepper,rhs,x,0.0,endtime,0.1,write_cout);
cost_val=(abs(-1.0+((sqr(x.at(0))+sqr(x.at(1)))/sqr(rm))));///achieve position
cost_val+=(abs(-1.0+((sqr(x.at(2))+sqr(x.at(3)))/sqr(vm))));///achieve velocity
cost_val+=(abs(-1.0+(sqr(abs(x.at(0)*x.at(3)-x.at(1)*x.at(2))/(rm*vm)))));///achieve angular momentum
massfrac=(mi-x.at(4))/mi;
break;
}
case 20:{
/**< 2D CONTINUOUS THRUST TANGENTIAL */
using namespace boost::numeric::odeint;
typedef Agent_datatype state_type;
typedef runge_kutta_fehlberg78<std::vector<state_type>> stepper_type;
typedef controlled_runge_kutta<stepper_type> controlled_stepper_type;
static const double mu=params.mu;
static const double g0=params.g0;
static const double Isp=params.Isp;
static const double g0Isp=g0*Isp;
static double mi=params.mi;
const double pi=acos(-1.0);
double r,alph,T;
double m;
double p,calp,salp;
state_type abs_err=1.0e-16,rel_err=1.0e-16,a_x=1.0,a_dxdt=1.0;
controlled_stepper_type controlled_stepper(default_error_checker<state_type,
range_algebra,default_operations>(abs_err,rel_err,a_x,a_dxdt));
auto rhs=[&](const std::vector<state_type> x, std::vector<state_type> &dxdt, const state_type){
r=sqrt(sqr(x.at(0))+sqr(x.at(1)));///RADIUS
T=params.kfactor*sqr(params.rinit/r);
m=x.at(4);
///condition to prevent bad stuff
if(m<0.1*mi){
T=0.0;
}
alph=atan2(x.at(3),x.at(2));
calp=cos(alph);salp=sin(alph);
p=1.0;
///STATE EQUATIONS
dxdt.at(0)=x.at(2);
dxdt.at(1)=x.at(3);
dxdt.at(2)=(-mu*x.at(0)/cube(r))-(p*T*calp/m);
dxdt.at(3)=(-mu*x.at(1)/cube(r))-(p*T*salp/m);
dxdt.at(4)=-p*T/(g0Isp);
};
const double re=params.rinit;
double a,rad,v,x0,y0,vx0,vy0;
a=re*params.rpfac/(1.0-params.ecc);
rad=a*(1.0-sqr(params.ecc))/(1.0+params.ecc*cos(params.nu*pi/180));
x0=rad*cos(params.nu*pi/180);
y0=rad*sin(params.nu*pi/180);
v=sqrt(mu*((2.0/rad)-(1.0/a)));
double gamma=atan2(params.ecc*sin(params.nu*pi/180.0),1.0+params.ecc*cos(params.nu*pi/180.0));
vx0=v*cos(0.5*pi-gamma+params.nu*pi/180.0);vy0=v*sin(0.5*pi-gamma+params.nu*pi/180.0);
std::vector<Agent_data> x;
x.push_back(x0);///X COORDINATE
x.push_back(y0);///Y COORDINATE
x.push_back(vx0);///X VELOCITY
x.push_back(vy0);///Y VELOCITY
x.push_back(mi);///INIT MASS
for(unsigned int i=0;i<5;i++){
x.push_back(vals.at(i));
}
double endtime=86400.0*vals.at(5);
integrate_adaptive(controlled_stepper,rhs,x,0.0,endtime,endtime/1000.0);
double rm=params.rf_fac*params.rinit;
cost_val=(abs(-1.0+((sqr(x.at(0))+sqr(x.at(1)))/sqr(rm))));///achieve position
if(x.at(4)<0.1*mi){
cost_val+=1e5;
}
massfrac=(mi-x.at(4))/mi;
break;
}
case 21:{
/**< 2D CONTINUOUS THRUST MIN effort */
/**< ax, ay FORMULATION WITH THRUST LIMIT */
using namespace boost::numeric::odeint;
typedef Agent_datatype state_type;
typedef runge_kutta_fehlberg78<std::vector<state_type>> stepper_type;
// typedef controlled_runge_kutta<stepper_type> controlled_stepper_type;
static const double mu=params.mu;
static const double g0=params.g0;
static const double Isp=params.Isp;
static const double g0Isp=g0*Isp;
static double mi=params.mi;
double ri=params.rinit;
// double ve=sqrt(mu/re);
double rm=params.rf_fac*params.rinit;
double vm=sqrt(mu/rm);
static const double pi=acos(-1.0);
double r,T,accl;
double r4,r3,m;
double l,costsqrt;
double ax,ay;
double a1,a2,b1,b2;
auto controlled_stepper=make_controlled(params.integ_tol,params.integ_tol,params.maxstep*86400.0,stepper_type());
auto rhs=[&](const std::vector<state_type> x, std::vector<state_type> &dxdt, const state_type){
r=sqrt(sqr(x.at(0))+sqr(x.at(1)));///RADIUS
r4=sqr(sqr(r));r3=cube(r);
m=x.at(4);
if(params.NEP==1){
///NEP
T=params.kfactor;
}
else{
///SEP INVERSE SQR LAW
T=params.kfactor*sqr(ri/r);
///COVERSTONE CARROLL
// T=(params.kfactor)*((0.7119713 + 0.4089753/(r/ri) + -0.0783905/(sqr(r/ri)))/(1.0+-0.0201896*(r/ri)+0.0623406*sqr(r/ri)))/(sqr(r/ri));
}
costsqrt=sqrt(sqr(x.at(7))+sqr(x.at(8)));
l=(costsqrt/m)-(x.at(9)/(g0Isp));
if(l>=0.0){
ax=-x.at(7)*T/(costsqrt*m);
ay=-x.at(8)*T/(costsqrt*m);
}
else{
ax=0.0;ay=0.0;
}
accl=sqrt(sqr(ax)+sqr(ay));
if(m<0.025*mi){
ax=0.0;ay=0.0;accl=0.0;
}
///STATE EQUATIONS
dxdt.at(0)=x.at(2);
dxdt.at(1)=x.at(3);
dxdt.at(2)=(-mu*x.at(0)/cube(r))+(ax);
dxdt.at(3)=(-mu*x.at(1)/cube(r))+(ay);
dxdt.at(4)=-x.at(4)*accl/(g0Isp);
///COSTATE EQUATIONS
a1=(-mu/r3)+((3.0*mu*x.at(0)/(r4)*(x.at(0)/r)));
a2=(3.0*mu*x.at(0)/(r4)*(x.at(1)/r));
b1=(3.0*mu*x.at(1)/(r4)*(x.at(0)/r));
b2=(-mu/r3)+((3.0*mu*x.at(1)/(r4)*(x.at(1)/r)));
dxdt.at(5)=-x.at(7)*a1-x.at(8)*b1;
dxdt.at(6)=-x.at(7)*a2-x.at(8)*b2;
dxdt.at(7)=-x.at(5);
dxdt.at(8)=-x.at(6);
dxdt.at(9)=+x.at(9)*accl/g0Isp;
};
std::vector<state_type> x;
double a,rad,v,x0,y0,vx0,vy0;
a=ri*params.rpfac/(1.0-params.ecc);
rad=a*(1.0-sqr(params.ecc))/(1.0+params.ecc*cos(params.nu*pi/180));
x0=rad*cos(params.nu*pi/180);
y0=rad*sin(params.nu*pi/180);
v=sqrt(mu*((2.0/rad)-(1.0/a)));
double gamma=atan2(params.ecc*sin(params.nu*pi/180.0),1.0+params.ecc*cos(params.nu*pi/180.0));
vx0=v*cos(0.5*pi-gamma+params.nu*pi/180.0);vy0=v*sin(0.5*pi-gamma+params.nu*pi/180.0);
x.push_back(x0);///X COORDINATE
x.push_back(y0);///Y COORDINATE
x.push_back(vx0);///X VELOCITY
x.push_back(vy0);///Y VELOCITY
x.push_back(mi);///INIT MASS
for(unsigned int i=0;i<5;i++){
x.push_back(vals.at(i));
}
double endtime=86400.0*vals.at(5);
integrate_adaptive(controlled_stepper,rhs,x,0.0,endtime,endtime/1000.0,write_cout);
cost_val=sqr(abs(-1.0+((sqr(x.at(0))+sqr(x.at(1)))/sqr(rm))));///achieve position
cost_val+=sqr(abs(-1.0+((sqr(x.at(2))+sqr(x.at(3)))/sqr(vm))));///achieve velocity
cost_val+=sqr(abs(-1.0+sqr(abs(x.at(0)*x.at(3)-x.at(1)*x.at(2))/(rm*vm))));///achieve angular momentum
cost_val+=sqr(x.at(9)/1e4);
// cost_val+=(abs(mi-x.at(4))/mi);
if(x.at(4)<0.1*mi){
cost_val+=1e5;
}
break;
}
case 22:{
/**< 3D MIN FUEL OPTIMAL CONTROL FOR SPACECRAFT */
using namespace boost::numeric::odeint;
typedef Agent_datatype state_type;
typedef runge_kutta_fehlberg78<std::vector<state_type>> stepper_type;
// typedef controlled_runge_kutta<stepper_type> controlled_stepper_type;
/// ///////////////////////////////////////////////////////////////////////////////
auto controlled_stepper=make_controlled(1.0e-16,1.0e-16,10*86400.0,stepper_type());
/// ///////////////////////////////////////////////////////////////////////////////
const double pi=acos(-1.0);
const double mu=params.mu;
const double g0Isp=params.g0*params.Isp;
const double mi=params.mi;
double T=params.kfactor;
const double ri=params.rinit;
// const double rf=ri*params.rf_fac;
// const double ecc=params.ecc;
// const double nu=params.nu;
double r,alpha,beta,m,r2,r3,r4,msq,p,l1,l2;
double costsqrt,dTx,dTy,dTz,rx,ry,rz,ca,sa,cb,sb;
double a1,a2,a3,b1,b2,b3,c1,c2,c3,d1,d2,d3;
///RHS FOR OF ODE SYSTEM
auto rhs=[&](const std::vector<state_type> x, std::vector<state_type> &dxdt, const state_type t){
r=sqrt(sqr(x.at(0))+sqr(x.at(1))+sqr(x.at(2)));
r2=sqr(r);r3=cube(r);r4=sqr(r2);
m=x.at(6);msq=sqr(m);
costsqrt=sqrt(sqr(x.at(10))+sqr(x.at(11))+sqr(x.at(12)));
///MAX AVAILABLE THRUST DETERMINATION
if(params.NEP==1){
///NEP
T=params.kfactor;
dTx=0.0;dTy=0.0;dTz=0.0;
}
else{
///SEP INVERSE SQR LAW
T=params.kfactor*sqr(ri/r);
if(r<0.25*ri){///SATURATE THRUST
T=params.kfactor*sqr(1.0/0.25);
}
dTx=-2.0*T*x.at(0)/r2;dTy=-2.0*T*x.at(1)/r2;dTz=-2.0*T*x.at(2)/r2;
}
///CONTROL LAW
l1=-T*((costsqrt/m)+(x.at(13)/g0Isp));
l2=-l1-sqr(T);
alpha=pi+atan2(x.at(11),x.at(10));
beta=pi+0.0*atan2(x.at(12),-sqrt(sqr(x.at(10))+sqr(x.at(11))));
p=1.0;
if(l1>=0){
p=0.0;
}
if(l2>=0){
p=1.0;
}
if(l1<0&&l2<0){
p=-l1/sqr(T);
}
///MINIMUM FINAL MASS
if(m<0.10*mi){
p=0.0;
}
ca=cos(alpha);sa=sin(alpha);cb=cos(beta);sb=sin(beta);
///STATE EQUATIONS
dxdt.at(0)=x.at(3);
dxdt.at(1)=x.at(4);
dxdt.at(2)=x.at(5);
dxdt.at(3)=(-mu*x.at(0)/r3)+(p*T*ca*cb/m);
dxdt.at(4)=(-mu*x.at(1)/r3)+(p*T*sa*cb/m);
dxdt.at(5)=(-mu*x.at(2)/r3)+(p*T*sb/m);
dxdt.at(6)=(-p*T/g0Isp);
///COSTATE EQUATIONS
rx=x.at(0)/r;ry=x.at(1)/r;rz=x.at(2)/r;
a1=(-mu/r3)+(3.0*mu*x.at(0)*rx/r4)+(p*ca*cb*dTx/m);
a2=(3.0*mu*x.at(0)*ry/r4)+(p*ca*cb*dTy/m);
a3=(3.0*mu*x.at(0)*rz/r4)+(p*ca*cb*dTz/m);
b1=(3.0*mu*x.at(1)*rx/r4)+(p*sa*cb*dTx/m);
b2=(-mu/r3)+(3.0*mu*x.at(1)*ry/r4)+(p*sa*cb*dTy/m);
b3=(3.0*mu*x.at(1)*rz/r4)+(p*sa*cb*dTz/m);
c1=(3.0*mu*x.at(1)*rx/r4)+(p*sb*dTx/m);
c2=(3.0*mu*x.at(1)*ry/r4)+(p*sb*dTy/m);
c3=(-mu/r3)+(3.0*mu*x.at(1)*rz/r4)+(p*sb*dTz/m);
d1=(-p*dTx/g0Isp);d2=(-p*dTy/g0Isp);d3=(-p*dTz/g0Isp);
dxdt.at(7)=-x.at(10)*a1-x.at(11)*b1-x.at(12)*c1-x.at(13)*d1;
dxdt.at(8)=-x.at(10)*a2-x.at(11)*b2-x.at(12)*c2-x.at(13)*d2;
dxdt.at(9)=-x.at(10)*a3-x.at(11)*b3-x.at(12)*c3-x.at(13)*d3;
dxdt.at(10)=-x.at(7);
dxdt.at(11)=-x.at(8);
dxdt.at(12)=-x.at(9);
dxdt.at(13)=-p*(costsqrt)/msq;
};
///INITIAL CONDITIONS
const double re=params.rinit;
// const double ve=sqrt(mu/re);
const double rm=params.rf_fac*params.rinit;
const double vm=sqrt(mu/rm);
double a,rad,v,x0,y0,vx0,vy0;
a=re*params.rpfac/(1.0-params.ecc);
rad=a*(1.0-sqr(params.ecc))/(1.0+params.ecc*cos(params.nu*pi/180));
x0=rad*cos(params.nu*pi/180);
y0=rad*sin(params.nu*pi/180);
v=sqrt(mu*((2.0/rad)-(1.0/a)));
double gamma=atan2(params.ecc*sin(params.nu*pi/180.0),1.0+params.ecc*cos(params.nu*pi/180.0));
vx0=v*cos(0.5*pi-gamma+params.nu*pi/180.0);vy0=v*sin(0.5*pi-gamma+params.nu*pi/180.0);
std::vector<Agent_data> x;
x.push_back(x0);///X COORDINATE
x.push_back(y0);///Y COORDINATE
x.push_back(0.0);///Z COORDINATE
x.push_back(vx0);///X VELOCITY
x.push_back(vy0);///Y VELOCITY
x.push_back(0.0);///Z VELOCITY
x.push_back(mi);///INIT MASS
for(unsigned int i=0;i<7;i++){
x.push_back(vals.at(i));
}
double endtime=86400.0*vals.at(7);
/// ///////////////////////////////////////////////////////////////////////////////
integrate_adaptive(controlled_stepper,rhs,x,0.0,endtime,1.0,write_cout);
/// ///////////////////////////////////////////////////////////////////////////////
cost_val=1.5*(abs(-1.0+((sqr(x.at(0))+sqr(x.at(1))+sqr(x.at(2)))/sqr(rm))));///achieve position
cost_val+=1.0*(abs(-1.0+((sqr(x.at(3))+sqr(x.at(4))+sqr(x.at(5)))/sqr(vm))));///achieve velocity
cost_val+=0.25*tanh(abs(x.at(2)/rm)+abs(x.at(5)/vm));///out of plane motion
cost_val+=1.0*(abs(-1.0+sqr(abs(x.at(0)*x.at(4)-x.at(1)*x.at(3))/(rm*vm))));///achieve angular momentum
cost_val*=(cost_val<=1e-2)?(0.15*(mi-x.at(6))/mi):1.0;
// cost_val+=(abs(x.at(1)*x.at(5)-x.at(2)*x.at(4))/(rm*vm));///ang momentum
// cost_val+=(abs(x.at(2)*x.at(3)-x.at(0)*x.at(5))/(rm*vm));///ang momentum
break;
}
case 23:{
/**< 2D MIN FUEL OPTIMAL CONTROL FOR SPACECRAFT */
/**< NO INTERMEDIATE STATE */
using namespace boost::numeric::odeint;
typedef Agent_datatype state_type;
typedef runge_kutta_fehlberg78<std::vector<state_type>> stepper_type;
/// ///////////////////////////////////////////////////////////////////////////////
auto controlled_stepper=make_controlled(1.0e-16,1.0e-16,1.0*86400.0,stepper_type());
/// ///////////////////////////////////////////////////////////////////////////////
const double pi=acos(-1.0);
const double mu=params.mu;
const double g0Isp=params.g0*params.Isp;
const double mi=params.mi;
double T=params.kfactor;
const double ri=params.rinit;
double r,alpha,m,r2,r3,r4,msq,p,l1;
double costsqrt,dTx,dTy,rx,ry,ca,sa;
double a1,a2,b1,b2,c1,c2;
///RHS FOR OF ODE SYSTEM
auto rhs=[&](const std::vector<state_type> x, std::vector<state_type> &dxdt, const state_type t){
r=sqrt(sqr(x.at(0))+sqr(x.at(1)));
r2=sqr(r);r3=cube(r);r4=sqr(r2);
m=x.at(4);msq=sqr(m);
costsqrt=sqrt(sqr(x.at(7))+sqr(x.at(8)));
///MAX AVAILABLE THRUST DETERMINATION
if(params.NEP==1){
///NEP
T=params.kfactor;
dTx=0.0;dTy=0.0;
}
else{
///SEP INVERSE SQR LAW
T=params.kfactor*sqr(ri/r);
if(r<0.25*ri){///SATURATE THRUST
T=params.kfactor*sqr(1.0/0.25);
}
dTx=-2.0*T*x.at(0)/r2;dTy=-2.0*T*x.at(1)/r2;
}
///CONTROL LAW
l1=T*((costsqrt/m)+((x.at(9)-1.0)/g0Isp));
alpha=pi+atan2(x.at(8),x.at(7));
if(l1>=0){
p=1.0;
}
else{
p=0.0;
}
///MINIMUM FINAL MASS
if(m<0.025*mi){
p=0.0;
}
ca=cos(alpha);sa=sin(alpha);
///STATE EQUATIONS
dxdt.at(0)=x.at(2);
dxdt.at(1)=x.at(3);
dxdt.at(2)=(-mu*x.at(0)/r3)+(p*T*ca/m);
dxdt.at(3)=(-mu*x.at(1)/r3)+(p*T*sa/m);
dxdt.at(4)=(-p*T/g0Isp);
///COSTATE EQUATIONS
rx=x.at(0)/r;ry=x.at(1)/r;
a1=(-mu/r3)+(3.0*mu*x.at(0)*rx/r4)+(p*ca*dTx/m);
a2=(3.0*mu*x.at(0)*ry/r4)+(p*ca*dTy/m);
b1=(3.0*mu*x.at(1)*rx/r4)+(p*sa*dTx/m);
b2=(-mu/r3)+(3.0*mu*x.at(1)*ry/r4)+(p*sa*dTy/m);
c1=(-p*dTx/g0Isp);c2=(-p*dTy/g0Isp);
dxdt.at(5)=-x.at(7)*a1-x.at(8)*b1-x.at(9)*c1;
dxdt.at(6)=-x.at(7)*a2-x.at(8)*b2-x.at(9)*c2;
dxdt.at(7)=-x.at(5);
dxdt.at(8)=-x.at(6);
dxdt.at(9)=-p*T*(costsqrt)/msq;
};
///INITIAL CONDITIONS
const double re=params.rinit;
const double rm=params.rf_fac*params.rinit;
const double vm=sqrt(mu/rm);
double a,rad,v,x0,y0,vx0,vy0;
a=re*params.rpfac/(1.0-params.ecc);
rad=a*(1.0-sqr(params.ecc))/(1.0+params.ecc*cos(params.nu*pi/180));
x0=rad*cos(params.nu*pi/180);
y0=rad*sin(params.nu*pi/180);
v=sqrt(mu*((2.0/rad)-(1.0/a)));
double gamma=atan2(params.ecc*sin(params.nu*pi/180.0),1.0+params.ecc*cos(params.nu*pi/180.0));
vx0=v*cos(0.5*pi-gamma+params.nu*pi/180.0);vy0=v*sin(0.5*pi-gamma+params.nu*pi/180.0);
std::vector<Agent_data> x;
x.push_back(x0);///X COORDINATE
x.push_back(y0);///Y COORDINATE
x.push_back(vx0);///X VELOCITY
x.push_back(vy0);///Y VELOCITY
x.push_back(mi);///INIT MASS
for(unsigned int i=0;i<5;i++){
x.push_back(vals.at(i));
}
double endtime=86400.0*vals.at(5);
/// ///////////////////////////////////////////////////////////////////////////////
integrate_adaptive(controlled_stepper,rhs,x,0.0,endtime,0.001,write_cout);
/// ///////////////////////////////////////////////////////////////////////////////
cost_val=(abs(-1.0+((sqr(x.at(0))+sqr(x.at(1)))/sqr(rm))));///achieve position
cost_val+=(abs(-1.0+((sqr(x.at(2))+sqr(x.at(3)))/sqr(vm))));///achieve velocity
cost_val+=(abs(-1.0+(sqr(abs(x.at(0)*x.at(3)-x.at(1)*x.at(2))/(rm*vm)))));///achieve angular momentum
massfrac=(mi-x.at(4))/mi;
break;
}
case 24:{
/**< 2D MIN FUEL OPTIMAL CONTROL FOR SPACECRAFT */
/**< INTEGRATION TERMINATION BASED ON RADIUS */
/**< OUTWARD PROPAGATING */
/**< NO INTERMEDIATE STATE */
using namespace boost::numeric::odeint;
typedef Agent_datatype state_type;
typedef runge_kutta_fehlberg78<std::vector<state_type>> stepper_type;
/// ///////////////////////////////////////////////////////////////////////////////
auto controlled_stepper=make_controlled(params.integ_tol,params.integ_tol,params.maxstep*86400.0,stepper_type());
/// ///////////////////////////////////////////////////////////////////////////////
const double pi=acos(-1.0);
const double mu=params.mu;
const double g0Isp=params.g0*params.Isp;
const double mi=params.mi;
double T=params.kfactor;
const double ri=params.rinit;
double r,alpha,m,r2,r3,r4,msq,p,l1;
double costsqrt,dTx,dTy,rx,ry,ca,sa;
double a1,a2,b1,b2,c1,c2;
///RHS FOR OF ODE SYSTEM
auto rhs=[&](const std::vector<state_type> x, std::vector<state_type> &dxdt, const state_type t){
r=sqrt(sqr(x.at(0))+sqr(x.at(1)));
r2=sqr(r);r3=cube(r);r4=sqr(r2);
m=x.at(4);msq=sqr(m);
costsqrt=sqrt(sqr(x.at(7))+sqr(x.at(8)));
///MAX AVAILABLE THRUST DETERMINATION
if(params.NEP==1){
///NEP
T=params.kfactor;
dTx=0.0;dTy=0.0;
}
else{
///SEP INVERSE SQR LAW
T=params.kfactor*sqr(ri/r);
if(r<0.25*ri){///SATURATE THRUST
T=params.kfactor*sqr(1.0/0.25);
}
dTx=-2.0*T*x.at(0)/r2;dTy=-2.0*T*x.at(1)/r2;
}
///CONTROL LAW
l1=T*((costsqrt/m)+((x.at(9)-1.0)/g0Isp));
alpha=pi+atan2(x.at(8),x.at(7));
if(l1>=0){
p=1.0;
}
else{
p=0.0;
}
///MINIMUM FINAL MASS
if(m<0.025*mi){
p=0.0;
}
ca=cos(alpha);sa=sin(alpha);
///STATE EQUATIONS
dxdt.at(0)=x.at(2);
dxdt.at(1)=x.at(3);
dxdt.at(2)=(-mu*x.at(0)/r3)+(p*T*ca/m);
dxdt.at(3)=(-mu*x.at(1)/r3)+(p*T*sa/m);
dxdt.at(4)=(-p*T/g0Isp);
///COSTATE EQUATIONS
rx=x.at(0)/r;ry=x.at(1)/r;
a1=(-mu/r3)+(3.0*mu*x.at(0)*rx/r4)+(p*ca*dTx/m);
a2=(3.0*mu*x.at(0)*ry/r4)+(p*ca*dTy/m);
b1=(3.0*mu*x.at(1)*rx/r4)+(p*sa*dTx/m);
b2=(-mu/r3)+(3.0*mu*x.at(1)*ry/r4)+(p*sa*dTy/m);
c1=(-p*dTx/g0Isp);c2=(-p*dTy/g0Isp);
dxdt.at(5)=-x.at(7)*a1-x.at(8)*b1-x.at(9)*c1;
dxdt.at(6)=-x.at(7)*a2-x.at(8)*b2-x.at(9)*c2;
dxdt.at(7)=-x.at(5);
dxdt.at(8)=-x.at(6);
dxdt.at(9)=-p*T*(costsqrt)/msq;
};
///INITIAL CONDITIONS
const double re=params.rinit;
double a,rad,v,x0,y0,vx0,vy0;
a=re*params.rpfac/(1.0-params.ecc);
rad=a*(1.0-sqr(params.ecc))/(1.0+params.ecc*cos(params.nu*pi/180));
x0=rad*cos(params.nu*pi/180);
y0=rad*sin(params.nu*pi/180);
v=sqrt(mu*((2.0/rad)-(1.0/a)));
double gamma=atan2(params.ecc*sin(params.nu*pi/180.0),1.0+params.ecc*cos(params.nu*pi/180.0));
vx0=v*cos(0.5*pi-gamma+params.nu*pi/180.0);vy0=v*sin(0.5*pi-gamma+params.nu*pi/180.0);
std::vector<Agent_data> x;
x.push_back(x0);///X COORDINATE
x.push_back(y0);///Y COORDINATE
x.push_back(vx0);///X VELOCITY
x.push_back(vy0);///Y VELOCITY
x.push_back(mi);///INIT MASS
for(unsigned int i=0;i<5;i++){
x.push_back(vals.at(i));
}
/// ///////////////////////////////////////////////////////////////////////////////
double rac,rprev;
double t,dt,tprev,dtprev;
std::vector<double> xprev;
t=0.0;dt=1e-3;
rac=sqrt(sqr(x.at(0))+sqr(x.at(1)));
/// ///////////////////////////////////////
double rp=params.rf_fac*params.rinit;
double vp=sqrt(mu*(1.0+params.eccf)/rp);
double rfinal=(rp/(1.0-params.eccf));
/// ///////////////////////////////////////
while(1){
tprev=t;dtprev=dt;xprev=x;
rprev=rac;
controlled_stepper.try_step(rhs,x,t,dt);
rac=sqrt(sqr(x.at(0))+sqr(x.at(1)));
dt=(dt>1.0*86400)?(1.0*86400):dt;
if(rac>rfinal){
t=tprev;
x=xprev;
rac=rprev;
dt=0.5*(dtprev);
}
else{
write_cout(x,t);
}
if(abs(rac-rfinal)/abs(rfinal)<params.a_tol||t>86400.0*params.maxtime){
break;
}
}
/// ///////////////////////////////////////////////////////////////////////////////
double nu_c=atan2(x.at(1),x.at(0))-params.omegaf*pi/180.0;
double ra=rp*(1.0+params.eccf)/(1.0+params.eccf*cos(nu_c));
double va=sqrt(mu*((2.0/ra)-((1.0-params.eccf)/rp)));
double Ha=rp*vp;
double rc=sqrt(sqr(x.at(0))+sqr(x.at(1)));
double vc=sqrt(sqr(x.at(2))+sqr(x.at(3)));
double Hc=((x.at(0)*x.at(3)-x.at(1)*x.at(2)));
double ex=(Hc*x.at(3)/mu)-x.at(0)/rc;
double ey=(-Hc*x.at(2)/mu)-x.at(1)/rc;
double ac=1.0/((2.0/rc)-sqr(vc)/mu);
double eccf=sqrt(sqr(ex)+sqr(ey));
cost_val=(abs(-1.0+sqr(rc/ra)));///achieve position
cost_val+=(abs(-1.0+sqr(vc/va)));///achieve velocity
cost_val+=(sqr(-1.0+(Hc/Ha)));///achieve angular momentum
cost_val+=sqr(ex-params.eccf*cos(params.omegaf*pi/180.0));
cost_val+=sqr(ey-params.eccf*sin(params.omegaf*pi/180.0));
massfrac=(mi-x.at(4))/mi;
cost_val*=(cost_val<1e-2)?massfrac:1.0;
break;
}
case 25:{
/**< 3D MIN FUEL OPTIMAL CONTROL FOR SPACECRAFT */
/**< NO INTERMEDIATE THROTTLE */
using namespace boost::numeric::odeint;
typedef Agent_datatype state_type;
typedef runge_kutta_fehlberg78<std::vector<state_type>> stepper_type;
/// ///////////////////////////////////////////////////////////////////////////////
auto controlled_stepper=make_controlled(params.integ_tol,params.integ_tol,params.maxstep*86400.0,stepper_type());
/// ///////////////////////////////////////////////////////////////////////////////
const double pi=3.1415926535897932384626433832795028;
const double mu=params.mu;
double g0Isp=params.g0*params.Isp;
const double mi=params.mi;
double T=params.kfactor;
const double ri=params.rinit;
double r,m,r2,r3,r4,msq,l,rf;
double costsqrt,rx,ry,rz;
double ax,ay,az,accl;
///RHS FOR OF ODE SYSTEM
auto rhs=[&](const std::vector<state_type> x, std::vector<state_type> &dxdt, const state_type t){
r=sqrt(sqr(x.at(0))+sqr(x.at(1))+sqr(x.at(2)));
r2=sqr(r);r3=cube(r);r4=sqr(r2);
m=x.at(6);msq=sqr(m);
costsqrt=sqrt(sqr(x.at(10))+sqr(x.at(11))+sqr(x.at(12)));
///MAX AVAILABLE THRUST DETERMINATION
if(params.NEP==1){
///NEP
T=params.kfactor;
}
else{
///SEP INVERSE SQR LAW
T=params.kfactor*sqr(ri/r);
// T=(T>0.236)?0.236:T;
// T=(T<0.040)?0.040:T;
// g0Isp=1900.0+(T-0.017)*10456.0;g0Isp*=9.806;
// if(r<0.25*ri){///SATURATE THRUST
// T=params.kfactor*sqr(1.0/0.25);
// }
}
///CONTROL LAW
l=(costsqrt/m)-(x.at(13)/g0Isp);
rf=-(T/m)/costsqrt;
if(l>=0.0){
ax=rf*x.at(10);ay=rf*x.at(11);az=rf*x.at(12);
}
else{
ax=0.0;ay=0.0;az=0.0;
}
accl=sqrt(sqr(ax)+sqr(ay)+sqr(az));
///MINIMUM FINAL MASS
if(m<0.025*mi){
accl=0.0;ax=0.0;ay=0.0;az=0.0;
}
///STATE EQUATIONS