Time optimal car problem

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

$\begin{array}{llclr} \min_{z, u, t_{f}} & t_{f} \\ s.t. & {\dot{z}}_{1} & = & z_{2}, \\ {\dot{z}}_{2} & = & u, \\ z (0) & = & (0, 0)^{T}, \\ z (t_{f}) & = & (300, 0)^{T}, \\ z_{1} (t) & \in & [0, 33], \\ z_{2} (t) & \in & [0, 330], \\ u (t) & \in & [- 2, 1] . \end{array}$

where $z = (z_{1}, z_{2})^{T}$ .

Source Code

Model descriptions are available in

AMPL/TACO code at Time optimal car problem (TACO)

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