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

$\begin{array}{llclr} \displaystyle \min_{z, u, t_f} & t_f \\[1.5ex] \mbox{s.t.} & \dot{z}_1 & = & z_2, \\ & \dot{z}_2 & = & u, \\[1.5ex] & z(0) &=& (0,0)^T, \\ & z(t_f) &=& (300,0)^T, \\[1.5ex] & z_1(t) & \in & [0,33],\\ & z_2(t) & \in & [0,330],\\ & u(t) & \in & [-2,1].\\ \end{array}$

where $z = (z_1, z_2)^T$.

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