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ode_def.cpp
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/* ============================================================================
File : ode_def.cpp
Author : Sylvie Putot, Ecole Polytechnique (France)
Part of the RINO package for Inner and Outer Reachability Analysis.
The place to define initial conditions and parameters the systems of ODEs or DDEs on which to perform reachability
============================================================================ */
#include <assert.h>
#include <math.h>
#include <cstring>
#include <gsl/gsl_math.h>
#include <gsl/gsl_sf_gamma.h>
#include "filib_interval.h"
#include "tadiff.h"
#include "fadiff.h"
#include "fadbad_aa.h"
#include "ode_def.h"
#include "matrix.h"
using namespace std;
double t_end; // ending time of integration
double t_begin; // starting time of initialization
double tau; // integration time step (fixed step for now)
double control_period = 0.0;
int Taylor_order;
double delay; // = 1; // delay in DDE
int nb_subdiv_delay; // = 10; // number of Taylor models on [0,delay]
// parameters of the system of the ODEs
vector<interval> params; // constant params of the ODE
vector<AAF> params_aff; // constant params of the ODE (don't appear in the Jacobian) - same as params but aff form
vector<AAF> nncontrol;
vector<vector<AAF>> Jac_params; // (\partial u) / (partial x)
vector<vector<AAF>> Jac_params_order2; // (\partial u) / (partial x)
vector<interval> initial_values; // initial values
vector<AAF> initial_values_aff; // same as initial_values_int but in affine forms
vector<interval> center_initial_values;
vector<AAF> center_initial_values_aff;
vector<interval> inputs; // uncertain inputs and parameters
vector<AAF> inputs_aff; // uncertain inputs and parameters
vector<interval> fullinputs; // uncertain inputs and parameters
vector<AAF> fullinputs_aff; // uncertain inputs and parameters
vector<int> nb_inputs; // piecewise constant input changes value every t_end/nb_inputs[i] seconds
vector<interval> center_fullinputs;
vector<AAF> center_fullinputs_aff;
vector<int> index_param;
vector<int> index_param_inv;
// to save initial_values and fullinputs when subdivisions
vector<interval> initial_values_save;
vector<interval> fullinputs_save;
vector<interval> eps;
vector<vector<interval>> Jac_param_inputs; // for inputs defined as g(x1,...xn): we give the jacobian
//vector<F<AAF>> nn_outputs; // result of NN evaluation
// define the dimensions of your system (ODE or DDE) and if we want initial subdivisions
void define_system_dim()
{
/*************************************************************************** ODE ************************************************************/
paramsdim = 0;
inputsdim = 0;
nncontroldim = 0;
nb_subdiv_init = 1; // nb of initial subdivisions of the input range
if (systype == 0) // ODE
{
if (syschoice == 12345)
{
sysdim = 7;
}
else if (syschoice == 1) // running example
{
sysdim = 1;
paramsdim = 1;
}
else if (syschoice == 2) // Brusselator
{
sysdim = 2;
paramsdim = 2;
}
else if (syschoice == 3) // ballistic
{
sysdim = 4;
}
else if (syschoice == 4) // ballistic linearise + masse incertaine
{
sysdim = 4;
inputsdim = 1;
}
else if (syschoice == 5) // self-driving car
{
sysdim = 2;
paramsdim = 2;
}
else if (syschoice == 6) // self-driving car
{
sysdim = 2;
inputsdim = 2;
// paramsdim = 2;
}
else if (syschoice == 7) // self-driving car with time-varying parameters
{
sysdim = 4;
paramsdim = 2;
}
else if (syschoice == 8)
{
sysdim = 1;
}
else if (syschoice == 9) // Acrobatic quadcopter
{
sysdim = 6;
inputsdim = 2;
}
else if (syschoice == 99) // Acrobatic quadcopter with m et Iyy as disturbances
{
sysdim = 6;
inputsdim = 4;
}
else if (syschoice == 10) // 10-D near-hover quadrotor
{
sysdim = 10;
inputsdim = 6;
}
else if (syschoice == 11) // Dubbins vehicle
{
sysdim = 3;
inputsdim = 4;
}
else if (syschoice == 12) // academic example to investigate time-varying parameters
{
sysdim = 2;
}
else if (syschoice == 13) // Laub-Loomis Benchmark [Arch 2019]
{
sysdim = 7;
paramsdim = 1;
}
else if (syschoice == 14) // Van der Pol oscillator [Arch 2019]
{
sysdim = 2;
}
else if (syschoice == 15) // Van der Pol oscillator [Arch 2018 and Sparse Polynomial zonotopes]
{
sysdim = 2;
}
else if(syschoice == 17) // quadrotor model [Arch 2019]
{
sysdim = 12;
}
else if (syschoice == 18) // HSCC 2019 paper crazyflie example
{
sysdim = 14;
// paramsdim = 3;
// 0 for sysdim params
}
else if (syschoice == 181) // HSCC 2019 paper crazyflie example with neural network controller
{
sysdim = 14;
inputsdim = 3;
// 0 for sysdim params
}
else if (syschoice == 182) // HSCC 2019 paper crazyflie example with neural network controller and agressive altitude PID
{
sysdim = 14;
inputsdim = 3;
// 0 for sysdim params
}
else if (syschoice == 183) // HSCC 2019 paper crazyflie example with neural network controller and agressive altitude PID
{
sysdim = 14;
inputsdim = 3;
// 0 for sysdim params
}
else if (syschoice == 19) { // academic example, time-varying (piecewise constant) parameters
sysdim = 2;
inputsdim = 1;
}
else if (syschoice == 21) { // academic example, time-varying (piecewise constant) parameters
sysdim = 2;
inputsdim = 1;
}
else if (syschoice == 22) { // academic example, time-varying (piecewise constant) parameters
sysdim = 2;
inputsdim = 1;
}
else if (syschoice == 23) { // pursuer-evader example Mitchell
sysdim = 3;
inputsdim = 2;
}
else if (syschoice == 24) { // [Franzle et al.]
sysdim = 2;
inputsdim = 1;
}
else if (syschoice == 25) { // [Franzle et al.] reversed time van der pol oscillator with uncertainty
sysdim = 2;
inputsdim = 1;
}
else if (syschoice == 26) { // [Franzle et al.] 7-d biological system
sysdim = 7;
inputsdim = 1;
}
else if (syschoice == 27) { // [Franzle et al.] 7-d biological system but with sharing
sysdim = 7;
inputsdim = 1;
}
else if (syschoice == 28) { // [Franzle et al.] 7-d biological system but with sharing
sysdim = 7;
inputsdim = 0;
}
else if (syschoice == 29) { // EX_10 Reachability for Neural Feedback Systems using Regressive Polynomial Rule Inference
sysdim = 4;
inputsdim = 2;
}
else if (syschoice == 30) { // EX_1 Reachability for Neural Feedback Systems using Regressive Polynomial Rule Inference
sysdim = 2;
inputsdim = 1;
}
else if (syschoice == 301) { // EX_1 Reachability for Neural Feedback Systems using Regressive Polynomial Rule Inference
sysdim = 2;
inputsdim = 0;
}
else if (syschoice == 31) { // Quadcopter Mikhail Bessa
sysdim = 14;
inputsdim = 3;
}
else if (syschoice == 311) { // Quadcopter Mikhail Bessa avec 3 composantes en plus
sysdim = 11;
inputsdim = 3;
}
else if (syschoice == 32) { // EX_2 Reachability for Neural Feedback Systems using Regressive Polynomial Rule Inference
sysdim = 2;
inputsdim = 1;
}
else if (syschoice == 33) { // EX_3 Reachability for Neural Feedback Systems using Regressive Polynomial Rule Inference
sysdim = 2;
inputsdim = 1;
}
else if (syschoice == 34) { // EX_4 Reachability for Neural Feedback Systems using Regressive Polynomial Rule Inference
sysdim = 3;
inputsdim = 1;
}
else if (syschoice == 35) { // EX_5 Reachability for Neural Feedback Systems using Regressive Polynomial Rule Inference
sysdim = 3;
inputsdim = 1;
}
else if (syschoice == 36) { // EX_6 Reachability for Neural Feedback Systems using Regressive Polynomial Rule Inference
sysdim = 3;
inputsdim = 1;
}
else if (syschoice == 37) { // EX_7 Reachability for Neural Feedback Systems using Regressive Polynomial Rule Inference
sysdim = 3;
inputsdim = 1;
}
else if (syschoice == 38) { // EX_8 Reachability for Neural Feedback Systems using Regressive Polynomial Rule Inference
sysdim = 4;
inputsdim = 1;
}
else if (syschoice == 381) { // EX_8 Reachability for Neural Feedback Systems using Regressive Polynomial Rule Inference
sysdim = 4;
inputsdim = 0;
paramsdim = 1;
}
else if (syschoice == 382) {
sysdim = 2;
inputsdim = 0;
paramsdim = 1;
}
else if (syschoice == 383) { // EX_2 Reachability for Neural Feedback Systems using Regressive Polynomial Rule Inference
sysdim = 2; // EX13 sherlock/systems_with_networks
paramsdim = 1;
}
else if (syschoice == 384) { // EX_3 Reachability for Neural Feedback Systems using Regressive Polynomial Rule Inference
sysdim = 2; // EX14 sherlock/systems_with_networks
paramsdim = 1; // EX15 sherlock/systems_with_networks
}
else if (syschoice == 385) { // EX_4 Reachability for Neural Feedback Systems using Regressive Polynomial Rule Inference
sysdim = 3;
paramsdim = 1;
}
else if (syschoice == 386) { // EX_5 Reachability for Neural Feedback Systems using Regressive Polynomial Rule Inference
sysdim = 3;
paramsdim = 1;
}
else if (syschoice == 387) { // EX_6 Reachability for Neural Feedback Systems using Regressive Polynomial Rule Inference
sysdim = 3;
paramsdim = 1;
}
else if (syschoice == 388) { // EX_7 Reachability for Neural Feedback Systems using Regressive Polynomial Rule Inference
sysdim = 3;
paramsdim = 1;
}
else if (syschoice == 39) { // EX_9 Reachability for Neural Feedback Systems using Regressive Polynomial Rule Inference
sysdim = 4;
inputsdim = 1;
}
else if (syschoice == 40) { // EX_10 Reachability for Neural Feedback Systems using Regressive Polynomial Rule Inference
sysdim = 4;
inputsdim = 2;
}
else if (syschoice == 41) { // essai
sysdim = 2;
inputsdim = 1;
}
else if (syschoice == 42) // HSCC 2019 paper crazyflie example+aerodynamical effects
{
sysdim = 14;
// paramsdim = 3;
// 0 for sysdim params
}
else if (syschoice == 43) // HSCC 2019 paper crazyflie example - new PID, no aerodynamical effects
{
sysdim = 14;
// paramsdim = 3;
// 0 for sysdim params
}
else if (syschoice == 44) // HSCC 2019 paper crazyflie example+ new PID, with aerodynamical effects
{
sysdim = 14;
// paramsdim = 3;
// 0 for sysdim params
}
else if (syschoice == 45) { // Mountain car Verisig
sysdim = 2;
inputsdim = 0;
}
else if (syschoice == 451) { // Mountain car Verisig
sysdim = 2;
inputsdim = 0;
nncontroldim = 1;
}
else if (syschoice == 46) { // Tora Heterogeneous ARCH-COMP 2020 - NNV (avec RNN format sfx obtenu a partir du .mat),
sysdim = 4;
inputsdim = 0;
}
else if (syschoice == 461) { // Tora Heterogeneous ARCH-COMP 2020 - NNV (avec RNN format sfx obtenu a partir du .mat),
sysdim = 4;
inputsdim = 0;
nncontroldim = 1;
}
else if (syschoice == 471) { // // Ex 1 ReachNNstar (avec RNN format sfx obtenu a partir du .txt),
sysdim = 2;
inputsdim = 0;
nncontroldim = 1;
}
else if (syschoice == 1111) { // toy example
sysdim = 2;
inputsdim = 0;
nncontroldim = 1;
}
else if (syschoice == 1113) { // toy example
sysdim = 2;
inputsdim = 0;
paramsdim = 0;
}
else if (syschoice == 481) { // // Ex 2 ReachNNstar (avec RNN format sfx obtenu a partir du .txt),
sysdim = 2;
inputsdim = 0;
nncontroldim = 1;
}
else if (syschoice == 482) { // // Ex 3 ReachNNstar (avec RNN format sfx obtenu a partir du .txt),
sysdim = 2;
inputsdim = 0;
nncontroldim = 1;
}
else if (syschoice == 483) { // // Ex 4 ReachNNstar (avec RNN format sfx obtenu a partir du .txt),
sysdim = 3;
inputsdim = 0;
nncontroldim = 1;
}
else if (syschoice == 484) { // // Ex 5 ReachNNstar (avec RNN format sfx obtenu a partir du .txt),
sysdim = 3;
inputsdim = 0;
nncontroldim = 1;
}
else if (syschoice == 491) // Ex ACC de Verisig (avec nn obtenu a partir du yaml)
{
sysdim = 6;
inputsdim = 0;
nncontroldim = 1;
}
else if (syschoice == 493) // Ex QMPC de Verisig (avec nn obtenu a partir du yaml)
{
sysdim = 6;
inputsdim = 0;
nncontroldim = 3;
}
else if (syschoice == 50) // Ex mixed monotonicity
{
sysdim = 3;
inputsdim = 2;
}
else if (syschoice == 51) //
{
sysdim = 2;
inputsdim = 0;
}
else if (syschoice == 52) //
{
sysdim = 1;
inputsdim = 0;
}
else if (syschoice == 53) //
{
sysdim = 2;
inputsdim = 0;
}
else if (syschoice == 54) //
{
sysdim = 3;
}
else if (syschoice == 55) // simple Dubbins for quantifier alternation
{
sysdim = 3;
inputsdim = 2;
}
}
/*************************************************************************** DDE ************************************************************/
else if (systype == 1) // DDE
{
if (syschoice == 1) // running example
{
sysdim = 1;
// nb_subdiv_init = 2;
// nb_subdiv_init = 10;
// recovering = 0.1; // recovering between 2 subdivisions when subdividing initial parameters
}
if (syschoice == 2) //
{
sysdim = 2;
}
else if (syschoice == 3) // Xue 2017 (Ex 3)
{
sysdim = 7;
}
else if (syschoice == 4) // Szczelina 1 and 2 2014
{
sysdim = 1;
}
else if (syschoice == 5) // Szczelina 2 2014
{
sysdim = 1;
}
else if (syschoice == 6) // self-driving car
{
sysdim = 2;
paramsdim = 2;
}
else if (syschoice == 8) // self-driving car but with coeff in interv
{
sysdim = 2;
inputsdim = 2;
}
else if (syschoice == 9)
{
sysdim = 1;
}
else if (syschoice == 10) // platoon of 5 vehicles
{
sysdim = 9;
}
else if (syschoice == 11) // platoon of 7 vehicles
{
sysdim = 19;
}
}
// if (params_filename) // called with configuration file: we overwrite the initialization of init_system
// readfromfile_nbsubdiv(params_filename, nb_subdiv_init);
}
// d0 and t_begin are for DDEs only, rest are common to ODE and DDE
void read_parameters(const char * params_filename)
{
const int LINESZ = 2048;
char buff[LINESZ];
char initialcondition[LINESZ];
const char space[2] = " ";
double a, b;
int c;
cout << "****** Reading system parameter from file " << params_filename << " ******" << endl;
FILE *params_file = fopen(params_filename,"r");
if (params_file == NULL)
cout << "Error reading " << params_filename << ": file not found" << endl;
while (fgets(buff,LINESZ,params_file)) {
// sscanf(buff, "system = %s\n", sys_name);
// sscanf(buff, "initially = %[^\n]\n", initial_condition); // tell separator is newline, otherwise by default it is white space
sscanf(buff, "time-horizon = %lf\n", &t_end);
sscanf(buff, "integration-step = %lf\n", &tau);
sscanf(buff, "control-step = %lf\n", &control_period);
// sscanf(buff, "output-variables = %[^\n]\n", output_variables);
sscanf(buff, "delay = %lf\n", &delay); // for DDEs
sscanf(buff, "starting-time = %lf\n", &t_begin); // for DDEs
sscanf(buff, "nb-time-subdivisions = %d\n", &nb_subdiv_delay); // for DDEs : subdiv of time interval delay : tau is deduced
sscanf(buff, "order = %d\n", &Taylor_order);
sscanf(buff, "interactive-visualization = %d\n", &interactive_visualization);
sscanf(buff, "refined-mean-value = %d\n", &refined_mean_value);
if (sscanf(buff, "variables-to-display = %s\n", initialcondition) == 1)
{
for (int i=0; i< sysdim; i++)
variables_to_display[i] = false;
char *token = strtok(buff,space);
token = strtok(NULL,space);
token = strtok(NULL,space);
int i;
while( token != NULL ) {
sscanf(token,"%d",&i);
variables_to_display[i-1] = true;
// cout <<"input="<<inputs[i].convert_int()<<endl;
token = strtok(NULL,space);
}
}
if (sscanf(buff, "initial-values = %s\n", initialcondition) == 1)
{
char *token = strtok(buff,space);
token = strtok(NULL,space);
token = strtok(NULL,space);
int i = 0;
nb_subdiv_init = 1;
component_to_subdiv = -1;
component_to_subdiv2 = -1;
// only one component can be subdivided for now (we keep the last if several...)
while( token != NULL ) {
if (sscanf(token,"([%lf,%lf],%d)",&a,&b,&c) == 3) {
if (component_to_subdiv > -1) // we already have one component to subdivide
{
component_to_subdiv2 = i;
cout << "component "<< i << " should also be subdivided " << endl;
}
else
{
nb_subdiv_init = c;
component_to_subdiv = i;
cout << "component "<< i << " should be dubdivided " << c << "times" << endl;
}
}
else
sscanf(token,"[%lf,%lf]",&a,&b);
initial_values[i] = interval(a,b);
cout <<"initial_value="<<interval(a,b)<<endl;
i++;
token = strtok(NULL,space);
}
}
if (sscanf(buff, "inputs = %s\n", initialcondition) == 1)
{
char *token = strtok(buff,space);
token = strtok(NULL,space);
token = strtok(NULL,space);
int i = 0;
while( token != NULL ) {
if (sscanf(token,"([%lf,%lf],%d)",&a,&b,&c) == 3)
nb_inputs[i] = c;
else {
nb_inputs[i] = 1;
sscanf(token,"[%lf,%lf]",&a,&b);
}
inputs[i] = interval(a,b);
// cout <<"input="<<interval(a,b)<<endl;
// cout <<"nb_inputs["<<i<<"]="<<nb_inputs[i]<<endl;
i++;
token = strtok(NULL,space);
}
}
if (sscanf(buff, "params = %s\n", initialcondition) == 1)
{
char *token = strtok(buff,space);
token = strtok(NULL,space);
token = strtok(NULL,space);
int i = 0;
while( token != NULL ) {
sscanf(token,"[%lf,%lf]",&a,&b);
params[i] = interval(a,b);
params_aff[i] = params[i];
i++;
token = strtok(NULL,space);
}
}
if (sscanf(buff, "uncontrolled = %s\n", initialcondition) == 1)
{
for (int i=0 ; i<inputsdim; i++)
is_uncontrolled[i] = false;
char *token = strtok(buff,space);
token = strtok(NULL,space);
token = strtok(NULL,space);
int i;
while( token != NULL ) {
sscanf(token,"%d",&i);
is_uncontrolled[i-1] = true;
// cout <<"is_uncontrolled="<<i<<endl;
token = strtok(NULL,space);
}
}
}
fclose(params_file);
// cout << "system name = " << sys_name << endl;
cout << "****** End parameter reading ******" << endl << endl;
}
// the main function to define the system
// for ODEs and DDEs: define bounds for parameters and inputs, value of delay d0 if any, and parameters of integration (timestep, order of TM)
void init_system()
{
// inputs
cout << "inputsdim=" << inputsdim << "sysdim=" << sysdim << endl;
inputs_aff = vector<AAF>(inputsdim);
inputs = vector<interval>(inputsdim); // bounds
nb_inputs = vector<int>(inputsdim); // number of instances for each input
for (int i=0; i<inputsdim; i++)
nb_inputs[i] = 1;
uncontrolled = 0;
controlled = 0;
is_uncontrolled = vector<bool>(inputsdim);
for (int i=0 ; i<inputsdim; i++)
is_uncontrolled[i] = false; // controlled input or parameter
target_set = vector<interval>(sysdim);
unsafe_set = vector<interval>(sysdim);
// initial values
initial_values_aff = vector<AAF>(sysdim);
initial_values = vector<interval>(sysdim);
// parameters not part of the jacobian
if (paramsdim > 0) {
params = vector<interval>(paramsdim);
params_aff = vector<AAF>(paramsdim);
}
if (nncontroldim > 0) {
nncontrol = vector<AAF>(nncontroldim);
Jac_params = vector<vector<AAF>>(sysdim, vector<AAF>(sysdim+inputsdim)); // should probably be sysdim \times jacdim but jacdim not yet defined ?
Jac_params_order2 = vector<vector<AAF>>(sysdim, vector<AAF>(sysdim+inputsdim)); // should probably be sysdim \times jacdim but jacdim not yet defined ?
}
refined_mean_value = false;
if (systype == 0) // ODE
{
t_begin = 0;
if (syschoice == 1) // running example
{
tau = 0.01;
t_end = 2.;
Taylor_order = 3;
initial_values[0] = interval(0.9,1);
params[0] = 1.0;
// nb_subdiv_init = 2;
// component_to_subdiv = 0;
}
else if (syschoice == 2) // Brusselator
{
tau = 0.05;
t_end = 10.;
Taylor_order = 4;
initial_values[0] = interval(0.9,1);
initial_values[1] = interval(0,0.1);
params[0] = 1;
params[1] = 1.5;
}
else if (syschoice == 3) // ballistic
{
tau = 0.1;
t_end = 4.;
Taylor_order = 3;
initial_values[0] = interval(181.,185.); // velocity // interval(175.0,190.0); pour Eric
// ix[1] = 3.14159/180*interval(2.5,3.5); // angle // interval(0,5) pour Eric
// ix[1] = mid(3.14159/180*interval(2.5,3.5)) + interval(-0.00872664, -0.00497644); // almost fault trajectories
initial_values[1] = interval(0.0436,0.0611); // 3.14159/180*interval(2.5,3.5); // mid(3.14159/180*interval(2.5,3.5)) + interval( -0.00497644,0.00872664); // complement = safe trajectories
initial_values[2] = interval(0.0,0.01);
initial_values[3] = interval(0.0,0.01);
}
else if (syschoice == 4) // ballistic linearise
{
tau = 0.1;
t_end = 1.4;
Taylor_order = 3;
initial_values[0] = interval(181.,185.); // velocity // interval(175.0,190.0); pour Eric
// ix[1] = 3.14159/180*interval(2.5,3.5); // angle // interval(0,5) pour Eric
// ix[1] = mid(3.14159/180*interval(2.5,3.5)) + interval(-0.00872664, -0.00497644); // almost fault trajectories
initial_values[1] = interval(0.0436,0.0611); // 3.14159/180*interval(2.5,3.5); // mid(3.14159/180*interval(2.5,3.5)); // + interval( -0.00497644,0.00872664); // complement = safe trajectories
initial_values[2] = interval(0.0,0.01);
initial_values[3] = interval(0.0,0.25); // interval(0.0,0.01);
inputs[0]= interval(11.,15.); // 14.... la masse (incontrollable)
is_uncontrolled[0] = true;
nb_subdiv_init = 1;
component_to_subdiv = 3;
component_to_subdiv2 = 4;
}
else if (syschoice == 5) // self-driving car; sysdim = 2, jacdim = 2
{
tau = 0.05;
t_end = 5.;
Taylor_order = 3; // order of Taylor Models
// initial condition
initial_values[0] = interval(-0.1,0.1);
initial_values[1] = interval(0,0.1);
// uncertain parameter
params[0] = interval(1.9,2.1); // Kp
params[1] = interval(2.9,3.1); // Kd
}
else if (syschoice == 6) // self-driving car with piecewise constant parameters; sysdim = 4, jacdim = 4
{
tau = 0.02;
t_end = 5.;
Taylor_order = 3; // order of Taylor Models
// uncertain parameter occurring in initial condition
initial_values[0] = interval(-0.1,0.1);
initial_values[1] = interval(0,0.1);
inputs[0] = interval(1.9,2.1); // Kp
inputs[1] = interval(2.9,3.1); // Kd
is_uncontrolled[1] = true; // Kd uncontrolled
// is_uncontrolled[2] = true; // Kp uncontrolled
}
// REFLECHIR COMMENT GERER CA DIFFEREMMENT
else if (syschoice == 7) // self-driving car with time varying parameters; sysdim = 4, jacdim = 4
{
tau = 0.02;
t_end = 5.;
Taylor_order = 3; // order of Taylor Models
// uncertain parameter occurring in initial condition
initial_values[0] = interval(-0.1,0.1);
initial_values[1] = interval(0,0.1);
initial_values[2] = interval(1.9,2.1); // Kp
initial_values[3] = interval(2.9,3.1); // Kd
params[0] = interval(-2,2);
params[1] = interval(-2,2);
// is_uncontrolled[3] = true; // Kd uncontrolled
// is_uncontrolled[2] = true; // Kp uncontrolled
}
else if (syschoice == 8)
{
tau = 0.01;
t_end = 5.;
Taylor_order = 3;
initial_values[0] = interval(0.4,0.5);
}
else if (syschoice == 9) // acrobatic quadrotor
{
tau = 0.01;
t_end = 0.5;
Taylor_order = 4;
initial_values[0] = interval(-1.,1.); // px
initial_values[1] = interval(-0.1,0.1); // vx
initial_values[2] = interval(-1.,1.); // py
initial_values[3] = interval(-0.1,0.1); // vy
initial_values[4] = interval(-0.1,0.1); // phi
initial_values[4] = interval(-0.1,0.1); // omega
inputs[0] = interval(9,9.5125); // interval(0,18.39375); // T1
inputs[1] = interval(9,9.5125); // interval(0,18.39375); // T2
}
else if (syschoice == 99) // acrobatic quadrotor with m et Iyy as disturbances
{
tau = 0.01;
t_end = 0.5;
Taylor_order = 4;
initial_values[0] = interval(-1.,1.); // px
initial_values[1] = interval(-0.1,0.1); // vx
initial_values[2] = interval(-1.,1.); // py
initial_values[3] = interval(-0.1,0.1); // vy
initial_values[4] = interval(-0.1,0.1); // phi
initial_values[4] = interval(-0.1,0.1); // omega
inputs[0] = interval(9,9.5125); // interval(0,18.39375); // T1
inputs[1] = interval(9,9.5125); // interval(0,18.39375); // T2
inputs[2] = interval(1.25,1.25); // m
is_uncontrolled[2] = true;
inputs[3] = interval(0.03,0.03); // Iyy
is_uncontrolled[3] = true;
}
else if (syschoice == 10) // 10-D near-hover quadrotor
{
tau = 0.01;
t_end = 0.3;
Taylor_order = 3;
initial_values[0] = interval(-1.,1.); // px
initial_values[1] = interval(-0.1,0.1); // vx
initial_values[2] = interval(-0.1,0.1); // thetax
initial_values[3] = interval(-0.1,0.1); // omegax
initial_values[4] = interval(-1.,1.); // py
initial_values[5] = interval(-0.1,0.1); // vy
initial_values[6] = interval(-0.1,0.1); // thetay
initial_values[7] = interval(-0.1,0.1); // omegay
initial_values[8] = interval(-2.5,2.5); // pz
initial_values[9] = interval(-0.1,0.1); // vz
inputs[0] = interval(-0.5,0.5); is_uncontrolled[0] = true; // disturbance dx
inputs[1] = interval(-0.5,0.5); is_uncontrolled[1] = true; // disturbance dy
inputs[1] = interval(-0.5,0.5); is_uncontrolled[2] = true; // disturbance dz
inputs[3] = interval(-0.17453,0.17453); // control input Sx - desired pitch angle (+/-Pi/18)
inputs[4] = interval(-0.17453,0.17453); // control input Sy - desired roll angle
inputs[5] = interval(0,19.62); // control input Sz - vertical thrust <= 2g
}
else if (syschoice == 11) // Dubbins vehicle
{
tau = 0.01;
t_end = 1.;
Taylor_order = 3;
initial_values[0] = interval(-0.5,0.5); // px
initial_values[1] = interval(-0.5,0.5); // py
initial_values[2] = interval(-0.1,0.1); // theta
inputs[0] = interval(-1,1); is_uncontrolled[0] = true; // disturbance b1
inputs[1] = interval(-1,1); is_uncontrolled[1] = true; // disturbance b2
inputs[1] = interval(-5,5); is_uncontrolled[2] = true; // disturbance b3
inputs[3] = interval(-1,1); // control a
}
else if (syschoice == 12)
{
tau = 1.;
t_end = 2.;
Taylor_order = 4;
initial_values[0] = 1;
initial_values[1] = 0;
inputs[0] = interval(0,0.1);
inputs[1] = interval(0,0.1);
}
else if (syschoice == 13) // Laub-Loomis Benchmark [Arch 2019]
{
tau = 0.1;
t_end = 20.;
Taylor_order = 3;
interval W = interval(-0.05,0.05);
// to express that it is the same interval: use params[0] = interval(-0.1,0.1) and inputs[0] = 1.2 + params[0]; etc
initial_values[0] = 1.2 + W;
initial_values[1] = 1.05 + W;
initial_values[2] = 1.5 + W;
initial_values[3] = 2.4 + W;
initial_values[4] = 1. + W;
initial_values[5] = 0.1 + W;
initial_values[6] = 0.45 + W;
}
else if (syschoice == 14) // Van der Pol oscillator [Arch 2019]
{
tau = 0.01;
t_end = 6.;
Taylor_order = 10;
// for mu = 1
initial_values[0] = interval(1.25,1.55);
initial_values[1] = interval(2.35,2.45);
// for mu = 2
// inputs[0] = interval(1.55,1.85);
// inputs[1] = interval(2.35,2.45);
}
else if (syschoice == 15) // Van der Pol oscillator [Arch 2018 and Sparse Polynomial zonotopes]
{
tau = 0.005;
t_end = 3.15;
Taylor_order = 10;
// for mu = 1
initial_values[0] = interval(1.23,1.57);
initial_values[1] = interval(2.34,2.46);
// for mu = 2
// inputs[0] = interval(1.55,1.85);
// inputs[1] = interval(2.35,2.45);
}
else if(syschoice == 17) // quadrotor model [Arch 2019]
{
tau = 0.1;
t_end = 5;
Taylor_order = 3;
for (int j=0 ; j<sysdim; j++)
initial_values[j] = 0;
// positions
initial_values[0] = interval(-0.4,0.4);
initial_values[1] = interval(-0.4,0.4);
initial_values[2] = interval(-0.4,0.4);
// velocities
initial_values[3] = interval(-0.4,0.4);
initial_values[4] = interval(-0.4,0.4);
initial_values[5] = interval(-0.4,0.4);
}
else if (syschoice == 18) // crazyflie HSCC 2019 paper
{ // do not forget to initialize the setpoints in the ode_def.h file...
tau = 0.01;
t_end = 5.;
Taylor_order = 3;
for (int j=0 ; j<sysdim; j++)
initial_values[j] = 0;
initial_values[3] = interval(-0.01,0.01); // = interval(-0.5,0.5) * M_PI/180.0; // p ?
initial_values[4] = interval(-0.01,0.01); //interval(-0.5,0.5) * M_PI/180.0; // q ?
initial_values[5] = interval(-0.01,0.01); //interval(-0.5,0.5) * M_PI/180.0; // q ?
initial_values[12] = interval(-0.05,0.05); // * M_PI/180.0; // z ?
// initial_values[3] = //interval(-0.00872,0.00872); // = interval(-0.5,0.5) * M_PI/180.0; // p ?
// initial_values[4] = //interval(-0.00872,0.00872); //interval(-0.5,0.5) * M_PI/180.0; // q ?
// initial_values[12] = //interval(-0.2,0.2); // * M_PI/180.0; // z ?
// roll yaw pitch (degree) inputs value (here we consider input as initial)
// inputs[0] = interval(3.0 , 5.0) * M_PI/180.0;
// inputs[1] = interval(3.0 , 5.0) * M_PI/180.0;
// inputs[2] = 0.0 * M_PI/180.0;
// p , q , r in rad/s -> the value here is an upper bound of the gyro noise of crazyflie
// inputs[3] = interval(-0.05,0.05);
// inputs[4] = interval(-0.05,0.05);
// inputs[5] = interval(-0.01,0.01);;
// err_p , err_q , err_r
initial_values[6] = 0.0;
initial_values[7] = 0.0;
initial_values[8] = 0.0;
// body speed u , v and w -> for embedded verif we instead use world speed
initial_values[9] = 0.0;
initial_values[10] = 0.0;
initial_values[11] = 0.0;
// Z and err_Vz
// inputs[12] = interval(-0.1 , 0.1);
initial_values[13] = 0.0;
}
else if (syschoice == 181) // crazyflie HSCC 2019 paper with neural network controoller
{ // do not forget to initialize the setpoints in the ode_def.h file...
tau = 0.02;
t_end = 2.;
Taylor_order = 3;
for (int j=0 ; j<sysdim; j++)
initial_values[j] = 0;
// initial_values[3] = 0; // interval(-0.00872,0.00872); // = interval(-0.5,0.5) * M_PI/180.0; // p ?
// initial_values[4] = 0; //interval(-0.00872,0.00872); //interval(-0.5,0.5) * M_PI/180.0; // q ?
// initial_values[12] = interval(-0.001,0.001); // interval(-0.2,0.2); // * M_PI/180.0; // z ?
initial_values[3] = interval(-0.001,0.001); // = interval(-0.5,0.5) * M_PI/180.0; // p ?
initial_values[4] = interval(-0.001,0.001); //interval(-0.5,0.5) * M_PI/180.0; // q ?
initial_values[12] = interval(-0.01,0.01); // * M_PI/180.0; // z ?
// initial_values[3] = interval(-0.00872,0.00872); // = interval(-0.5,0.5) * M_PI/180.0; // p ?
// initial_values[4] = interval(-0.00872,0.00872); //interval(-0.5,0.5) * M_PI/180.0; // q ?
// initial_values[12] = interval(-0.2,0.2); // * M_PI/180.0; // z ?
// roll yaw pitch (degree) inputs value (here we consider input as initial)
// inputs[0] = interval(3.0 , 5.0) * M_PI/180.0;
// inputs[1] = interval(3.0 , 5.0) * M_PI/180.0;
// inputs[2] = 0.0 * M_PI/180.0;
// p , q , r in rad/s -> the value here is an upper bound of the gyro noise of crazyflie
// inputs[3] = interval(-0.05,0.05);
// inputs[4] = interval(-0.05,0.05);
// inputs[5] = interval(-0.01,0.01);;
// err_p , err_q , err_r
initial_values[6] = 0.0;
initial_values[7] = 0.0;
initial_values[8] = 0.0;
// body speed u , v and w -> for embedded verif we instead use world speed
initial_values[9] = 0.0;
initial_values[10] = 0.0;
initial_values[11] = 0.0;