About the Bang-Bang Principle for piecewise affine systems
Résumé
We show that for piecewise affine controlled systems, the Bang-Bang Principle does not hold even when the dynamics is continuous with respect to the state variable. However, we show that there exist minimal time trajectories with extreme controls at the loci where the dynamics is differentiable. We give two examples which exhibit singular arcs exactly at the loci of non-differentiability.
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