| Abstract: |
| In this talk, we extend previous results, obtained by the authors, on the determination of the \emph{admissible set}, namely the subset of the state space where the \emph{mixed multidimensional constraints}, i.e. constraints involving both the state and input vectors, can be satisfied for all times. We prove that the boundary of this admissible set may be divided in two parts, one of them being called \emph{barrier}, a semipermeable surface that must satisfy a minimum-like principle involving the Karush-K\"{u}hn-Tucker multipliers associated to the constraints and endpoint conditions describing the geometric way this barrier ends when touching the constraint boundary. The proof uses a similar argument, in the context of mixed constraints and without optimality requirements, as in the Pontryagin-Boltyansky-Gamkrelidze-Mischenko construction of extremals by needle perturbations, without restricting the extremal integral curves to remain on a constraint boundary and without restriction on the regularity of the extremal control vectors. We then give a quick outline of some applications and open questions. |
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