Buckling column

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Flow* buckling_column.model

Model description

The buckling column model is studied in [1], its dynamics is given by

    \[ \left\{ \begin{array}{lcl} \dot{x} & = & y \\ \dot{y} & = & 2 \cdot x - x^3 - 0.2 \cdot y + 0.1 \end{array} \right. \]

Reachability setting

The initial set under our consideration is x\in [-0.5,-0.4], y\in [-0.5,-0.4] .

Results

The following figure shows an overapproximation computed by Flow* for the time horizon [0,10] :

buckling_column

References

[1] F. Zhao. Automatic Analysis and Synthesis of Controllers for Dynamical Systems Based on Phase-Space Knowledge. PhD thesis, Massachusetts Institute of Technology, 1992.