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/*
* MIT No Attribution
*
* Copyright (C) 2010-2023 Joel Andersson, Joris Gillis, Moritz Diehl, KU Leuven.
*
* Permission is hereby granted, free of charge, to any person obtaining a copy of this
* software and associated documentation files (the "Software"), to deal in the Software
* without restriction, including without limitation the rights to use, copy, modify,
* merge, publish, distribute, sublicense, and/or sell copies of the Software, and to
* permit persons to whom the Software is furnished to do so.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED,
* INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A
* PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
* HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
* OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
*
*/
#include <iostream>
#include <casadi/casadi.hpp>
using namespace casadi;
// Declare solvers to be loaded manually
extern "C" void casadi_load_integrator_cvodes();
extern "C" void casadi_load_integrator_idas();
extern "C" void casadi_load_integrator_rk();
extern "C" void casadi_load_nlpsol_ipopt();
extern "C" void casadi_load_nlpsol_scpgen();
bool sundials_integrator = true;
bool explicit_integrator = false;
bool lifted_newton = false;
int main(){
// Load integrators manually
casadi_load_integrator_cvodes();
casadi_load_integrator_idas();
casadi_load_integrator_rk();
casadi_load_nlpsol_ipopt();
casadi_load_nlpsol_scpgen();
// Time length
double T = 10.0;
// Shooting length
int nu = 20; // Number of control segments
// Time horizon for integrator
double t0 = 0;
double tf = T/nu;
// Initial position
std::vector<double> X0(3);
X0[0] = 0; // initial position
X0[1] = 0; // initial speed
X0[2] = 1; // initial mass
// Time
SX t = SX::sym("t");
// Differential states
SX s = SX::sym("s"), v = SX::sym("v"), m = SX::sym("m");
SX x = SX::vertcat({s, v, m});
// Control
SX u = SX::sym("u");
SX alpha = 0.05; // friction
SX beta = 0.1; // fuel consumption rate
// Differential equation
SX rhs = SX::vertcat({v, (u-alpha*v*v)/m, -beta*u*u});
// Initial conditions
std::vector<double> x0 = {0, 0, 1};
// DAE
SXDict dae = {{"x", x}, {"p", u}, {"t", t}, {"ode", rhs}};
// Integrator options
std::string plugin;
Dict opts;
if(sundials_integrator){
if(explicit_integrator){
// Explicit integrator (CVODES)
plugin = "cvodes";
// opts["exact_jacobian"] = true;
// opts["linear_multistep_method"] = "bdf"; // adams or bdf
// opts["nonlinear_solver_iteration"] = "newton"; // newton or functional
} else {
// Implicit integrator (IDAS)
plugin = "idas";
opts["calc_ic"] = false;
}
opts["fsens_err_con"] = true;
opts["quad_err_con"] = true;
opts["abstol"] = 1e-6;
opts["reltol"] = 1e-6;
opts["stop_at_end"] = false;
// opts["fsens_all_at_once"] = false;
opts["steps_per_checkpoint"] = 100; // BUG: Too low number causes segfaults
} else {
// An explicit Euler integrator
plugin = "rk";
opts["expand_f"] = true;
opts["interpolation_order"] = 1;
opts["number_of_finite_elements"] = 1000;
}
// Create integrator
Function F = integrator("integrator", plugin, dae, t0, tf, opts);
// control for all segments
MX U = MX::sym("U",nu);
// Integrate over all intervals
MX X=X0;
for(int k=0; k<nu; ++k){
// Integrate
X = F(MXDict{{"x0", X}, {"p", U(k)}}).at("xf");
// Lift X
if(lifted_newton){
X = lift(X, X);
}
}
// Objective function
MX J = dot(U,U);
// Terminal constraints
MX G = vertcat(X(0),X(1));
// Create the NLP
MXDict nlp = {{"x", U}, {"f", J}, {"g", G}};
// NLP solver options
Dict solver_opts;
std::string solver_name;
if(lifted_newton){
solver_name = "scpgen";
solver_opts["verbose"] = true;
solver_opts["regularize"] = false;
solver_opts["max_iter_ls"] = 1;
solver_opts["max_iter"] = 100;
solver_opts["qpsol"] = "nlp"; // Use IPOPT as QP solver
Dict ipopt_options;
ipopt_options["tol"] = 1e-12;
ipopt_options["print_level"] = 0;
ipopt_options["print_time"] = false;
solver_opts["qpsol_options"] =
Dict{{"nlpsol_options", Dict{{"nlpsol", "ipopt"}}}};
} else {
solver_name = "ipopt";
solver_opts["ipopt.tol"] = 1e-10;
solver_opts["ipopt.hessian_approximation"] = "limited-memory";
}
// Create NLP solver
Function solver = nlpsol("nlpsol", solver_name, nlp, solver_opts);
// Bounds on u and initial condition
std::vector<double> umin(nu, -10), umax(nu, 10), u0(nu, 0.4);
// Bounds on g
std::vector<double> gmin = {10, 0}, gmax = {10, 0};
// Solve NLP
std::vector<double> Usol;
solver({{"lbx", umin}, {"ubx", umax}, {"x0", u0}, {"lbg", gmin}, {"ubg", gmax}},
{{"x", &Usol}});
std::cout << "optimal solution: " << Usol << std::endl;
return 0;
}
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