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

$\begin{array}{ll}\underset{z,u,t_f}{\min }& t_f\\ \text{s.t.}& {\dot{z}}_1& =& z_2,\\ & {\dot{z}}_2& =& u,\\ & z(0)& =& (0,0{)}^T,\\ & z(t_f)& =& (300,0{)}^T,\\ & z_1(t)& \in & [0,33],\\ & z_2(t)& \in & [0,330],\\ & u(t)& \in & [-2,1].\\ \end{array}$

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

Source Code

Model descriptions are available in

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