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Decompositions and bang-bang properties

  • * Corresponding author:Yubiao Zhang

    * Corresponding author:Yubiao Zhang
The first author was partially supported by the National Natural Science Foundation of China under grant 11571264. The second author was partially supported by the National Natural Science Foundation of China under grants 11571264 and 11371285.
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  • We study the bang-bang properties of minimal time and minimal norm control problems (where the target set is the origin of the state space and the controlled system is linear and time-invariant) from a new perspective. More precisely, we study how the bang-bang property of each minimal time (or minimal norm) problem depends on a pair of parameters $(M, y_0)$ (or $(T,y_0)$ ), where $M>0$ is a bound of controls and $y_0$ is the initial state (or $T>0$ is an ending time and $y_0$ is the initial state). The controlled system may have neither the $L^∞$ -null controllability nor the backward uniqueness property.

    Mathematics Subject Classification: Primary: 93B03; Secondary: 93C35.


    \begin{equation} \\ \end{equation}
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  • Figure 1.  The BBP decomposition for $(NP)^{T,y_0}$

    Figure 2.  The BBP decomposition for $(TP)^{M,y_0}$

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