# Time optimal car problem

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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