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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

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Abstract The viable maximum of $\int_0
T Lt),u(t?\, dt$ 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


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