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# ISC-PIF Publications

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 User bonneuil title Maximum under continuous-discrete-time dynamic with target and viability constraints Authors Noël Bonneuil Source Optimisation 61(8) August 2012 901-913 Year 2012 Type Journal Type of publication Other

## Optional Infos

 Abstract The viable maximum of $\int_0T Lt),u(t?\, dt$ of a continuous function $L\in {\mathcal L}1(I\hspace{-1.2mm}R{2m+1}, I\hspace{-1.2mm}R+)$ under a dynamic $x'(t)\in Ft?$ under constraint $x(t)\in K$ where $K$ is closed is obtained on the boundary of the capture-viability kernel in direction of high $y$ of the target $K\times\{0\}$ viable in $K\times I\hspace{-1.2mm}R^+$ under the extended dynamic $(x'(t),y'(t))\in (Ft?,-Lt),u(t?)$. The result holds true with discrete-continuous-time measurable controls. Example and application to an hybrid dynamics under viability constraints and target are given. Created Tuesday 11 December, 2012 12:01:40