Difference between revisions of "Particle steering problem"
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FelixMueller (Talk | contribs) (Created page with "{{Dimensions |nd = 1 |nx = 2 |nw = 1 |nre = 7 }}<!-- Do not insert line break here or Dimensions Box moves up in the layout... -->The Particle stee...") |
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|nx = 2 | |nx = 2 | ||
|nw = 1 | |nw = 1 | ||
+ | |nc = 2 | ||
|nre = 7 | |nre = 7 | ||
}}<!-- Do not insert line break here or Dimensions Box moves up in the layout... | }}<!-- Do not insert line break here or Dimensions Box moves up in the layout... | ||
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& \ddot{x}_1 & = & a \cos (u), \\ | & \ddot{x}_1 & = & a \cos (u), \\ | ||
& \ddot{x}_2 & = & a \sin (u), \\ | & \ddot{x}_2 & = & a \sin (u), \\ | ||
− | & x( | + | & x(0) &=& (0, 0)^T, \\ |
& \dot{x}(0) &=& (0, 0)^T, \\ | & \dot{x}(0) &=& (0, 0)^T, \\ | ||
& x_2 (t_f) &=& 5, \\ | & x_2 (t_f) &=& 5, \\ | ||
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</p> | </p> | ||
− | |||
+ | where <math> (x_1, x_2) </math> is the position of the particle, <math> u </math> is the control angle and <math> a </math> is the constant magnitude of thrust. | ||
== Source Code == | == Source Code == | ||
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[[Category:MIOCP]] | [[Category:MIOCP]] | ||
[[Category:ODE model]] | [[Category:ODE model]] | ||
+ | [[Category:Minimum time]] |
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
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