Difference between revisions of "Time optimal car problem"
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* [[:Category:AMPL/TACO | AMPL/TACO code]] at [[Time optimal car problem (TACO)]] | * [[:Category:AMPL/TACO | AMPL/TACO code]] at [[Time optimal car problem (TACO)]] | ||
| − | + | * [[:Category:Gekko | GEKKO Python code]] at [[Time optimal car problem (GEKKO)]] | |
== References == | == References == | ||
Latest revision as of 21:30, 13 March 2019
| Time optimal car problem | |
|---|---|
| State dimension: | 1 |
| Differential states: | 2 |
| Continuous control functions: | 1 |
| Path constraints: | 6 |
| Interior point equalities: | 4 |
The Time optimal car problem "consists of starting and stopping a car in minimum for a fixed distance (300 units)" and can be found e.g. in [Cuthrell1987]The entry doesn't exist yet. and [Logsdon1992]Author: Logsdon, J.S.; L.T. Biegler
Journal: Chemical Engineering Science
Number: 4
Pages: 851--864
Title: Decomposition strategies for large-scale dynamic optimization problems
Volume: 47
Year: 1992
.
Mathematical formulation
![\begin{array}{llclr}
\displaystyle \min_{z, u, t_f} & t_f \\[1.5ex]
\mbox{s.t.}
& \dot{z}_1 & = & z_2, \\
& \dot{z}_2 & = & u, \\[1.5ex]
& z(0) &=& (0,0)^T, \\
& z(t_f) &=& (300,0)^T, \\[1.5ex]
& z_1(t) & \in & [0,33],\\
& z_2(t) & \in & [0,330],\\
& u(t) & \in & [-2,1].\\
\end{array}](https://mintoc.de/images/math/b/c/5/bc5dfa7775c0adeffc5c872fbc729259.png)
where 
.
Source Code
Model descriptions are available in
- AMPL/TACO code at Time optimal car problem (TACO)
- GEKKO Python code at Time optimal car problem (GEKKO)
References
| [Cuthrell1987] | The entry doesn't exist yet. | |
| [Logsdon1992] | Logsdon, J.S.; L.T. Biegler (1992): Decomposition strategies for large-scale dynamic optimization problems. Chemical Engineering Science, 47, 851--864 | |
