Category:C

From Mintoc

Jump to: navigation, search

This category lists all problems on mintoc.de that have a description of differential equations in C format. Herein, the standard form is related to MUSCOD-format. For a standard MIOC written as

\begin{array}{llcl} \displaystyle \min_{x(\cdot), u(\cdot), v(\cdot), q, \rho} & \phi(x(t_f), q, \rho) \\[1.5ex] \mbox{s.t.} & \dot{x}(t) & = & f(x(t), u(t), v(t), q, \rho), \\ & 0 &\le& c(x(t),u(t),v(t), q, \rho), \\[1.5ex] & 0 &=& r^{\text{eq}}(x(t_0),x(t_1), \dots, x(t_m), q, \rho), \\ & 0 &\le& r^{\text{ieq}}(x(t_0),x(t_1), \dots, x(t_m), q, \rho), \\[1.5ex] & v(t) &\in& \Omega := \{v^1, v^2, \dots, v^{n_\omega} \},\\ & \rho &\in& \Rho := \{\rho^1, \rho^2, \dots, \rho^{n_\Rho} \}, \end{array}

the format looks, e.g., something like this: 

rhs[0] =   xd[0] - xd[0]*xd[1] - p[0]*u[0]*xd[0];
rhs[1] = - xd[1] + xd[0]*xd[1] - p[1]*u[0]*xd[1];

for the special case

\begin{array}{llcl} & \dot{x}_0(t) & = & x_0(t) - x_0(t) x_1(t) - \; c_0 x_0(t) \; w(t), \\ & \dot{x}_1(t) & = & - x_1(t) + x_0(t) x_1(t) - \; c_1 x_1(t) \; w(t). \end{array}

Here the vector entries rhs[i] contain the values of the right hand side function f_i(\cdot). The vector entries xd[i] contains the differential variables xi(t), u[i] the control variables ui(t) or vi(t), and p[i] contains the model parameters por control differential variables qi(t) resp. ρi(t).

Retrieved from "http://www.mintoc.de/index.php/Category:C"
Personal tools