Difference between revisions of "Particle steering problem"
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|nx = 2 | |nx = 2 | ||
|nw = 1 | |nw = 1 | ||
| + | |nc = 2 | ||
|nre = 7 | |nre = 7 | ||
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Latest revision as of 09:33, 27 July 2016
| Particle steering problem | |
|---|---|
| State dimension: | 1 |
| Differential states: | 2 |
| Discrete control functions: | 1 |
| Path constraints: | 2 |
| Interior point equalities: | 7 |
The Particle steering problem minimizes "the time taken for a particle, acted upon by a thrust of constant magnitude, to achieve a given altitude and terminal velocity." (Cite and problem taken from the COPS library)
Mathematical formulation
The problem is given by
![\begin{array}{llcl}
\displaystyle \min_{x, u, t_f} & t_f \\[1.5ex]
\mbox{s.t.}
& \ddot{x}_1 & = & a \cos (u), \\
& \ddot{x}_2 & = & a \sin (u), \\
& x(0) &=& (0, 0)^T, \\
& \dot{x}(0) &=& (0, 0)^T, \\
& x_2 (t_f) &=& 5, \\
& \dot{x}(t_f) &=& (45, 0)^T, \\
& u(t) &\in& [-\frac{\pi}{2},\frac{\pi}{2}].
\end{array}](https://mintoc.de/images/math/6/8/0/680aac214a5aba1bf8e9049939671655.png)
where 
is the position of the particle, 
is the control angle and 
is the constant magnitude of thrust.
Source Code
Model descriptions are available in
