Particle steering problem - Revision history

FelixMueller at 08:33, 27 July 2016

2016-07-27T08:33:24Z

← Older revision		Revision as of 08:33, 27 July 2016
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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...

FelixMueller at 22:11, 27 June 2016

2016-06-27T22:11:55Z

← Older revision		Revision as of 22:11, 27 June 2016
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	[[Category:MIOCP]]		[[Category:MIOCP]]
	[[Category:ODE model]]		[[Category:ODE model]]
			[[Category:Minimum time]]

FelixMueller: /* Mathematical formulation */

2016-05-05T18:18:11Z

Mathematical formulation

← Older revision		Revision as of 18:18, 5 May 2016
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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(~~t_0~~) &=& (0, 0)^T, \\		& 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, \\

FelixMueller: /* Mathematical formulation */

2016-05-05T18:17:55Z

Mathematical formulation

← Older revision		Revision as of 18:17, 5 May 2016
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	</math>		</math>
	</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.		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 ==

FelixMueller: Created page with "{{Dimensions |nd = 1 |nx = 2 |nw = 1 |nre = 7 }}The Particle stee..."

2016-05-05T18:17:48Z

Created page with "{{Dimensions |nd = 1 |nx = 2 |nw = 1 |nre = 7 }}The Particle stee..."

New page

{{Dimensions
|nd = 1
|nx = 2
|nw = 1
|nre = 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 [http://www.mcs.anl.gov/~more/cops/ COPS library])

== Mathematical formulation ==

The problem is given by

<p>
<math>
\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(t_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}
</math>
</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 ==

Model descriptions are available in

* [[:Category:AMPL/TACO | AMPL/TACO code]] at [[Particle steering problem (TACO)]]


[[Category:MIOCP]]
[[Category:ODE model]]