# Time optimal car problem (TACO)

This page contains a model of the Time optimal car problem in AMPL format, making use of the TACO toolkit for AMPL control optimization extensions. The model 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*

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Note that you will need to include a generic AMPL/TACO support file, OptimalControl.mod.
To solve this model, you require an optimal control or NLP code that uses the TACO toolkit to support the AMPL optimal control extensions.

### AMPL

This is the source file tocar1_taco.mod

# ---------------------------------------------------------------- # Time optimal car problem using AMPL and TACO # (c) Christian Kirches, Sven Leyffer # # Source: Cuthrell/Biegler'87, Logsdon/Biegler'92 # ---------------------------------------------------------------- include OptimalControl.mod; var t; var tf := 20, >= 5, <= 50; var s := 0, >= 0, <= 330; var v := 0, >= 0, <= 30; var gas := 0.0, >= -2.0, <= 1.0; let gas.type := "u0"; var p := 0.05, >= 0, <= 0.1; minimize EndTime: eval(t,tf); let EndTime.scale := 10.0; subject to ODE_s: diff(s,t) = v; ODE_v: diff(v,t) = gas - p; IVC_s: eval(s,0) = 0; IVC_v: eval(v,0) = 0; TC_s: eval(s,tf) = 300.0; let TC_s.scale := 100.0; TC_v: eval(v,tf) = 0; let TC_v.scale := 10.0; let IVC_s.type := "dpc"; let IVC_v.type := "dpc"; option solver ...; solve;

## Other Descriptions

Other descriptions of this problem are available in

- Mathematical notation at Time optimal car problem

## 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 |