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Minimal controllability time for finite-dimensional control systems under state constraints

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Figure 1: Limit trajectories for the 2D Brunovsky system ˙ y 1 = y 2 , ˙ y 2 = u, with initial point y 0 = ( 0, − 1 ) ⊺ and target y 1 = ( 0, 1 ) ⊺ .
Figure 2: We take M = 10. The zones ( P 0,M ) and ( P M,0 ) are delimited by the red lines
Figure 3: Relations between the state trajectory with and without the state constraint and under the control constraint ∣ v (⋅)∣ ⩽ M .
Figure 6: State constraint set considered in Example 5.2, the forbidden zones are in grey.
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