Quick reachability and proper extension for problems with unbounded controls

Maria Soledad Aronna (1, 2, 3) , Monica Motta (4) , Franco Rampazzo (4)

1 Commands - Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems
2 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
3 IMPA - Instituto Nacional de Matemática Pura e Aplicada
4 Dipartimento di Matematica Pura e Applicata [Padova]

For a CONTROL SYSTEM of the form _ x = f (x; u; v) + Σm =1 g (x)u_ ; on [0;T]; (x; u)(0) = ( x; u); with x : [0;T] ! IRn; u : [0;T] ! U IRm; v : [0;T] ! V IRl ; we rely on the notion of LIMIT SOLUTION, and we investigate whether minimum problems with L1controls are PROPER EXTENSIONS of regular problems with more regular controls (AC or BV). Motivation: optimality conditions, numerical methods, etc.

Domaines: Optimisation et contrôle [math.OC]

Maria Soledad Aronna, Monica Motta, Franco Rampazzo. Quick reachability and proper extension for problems with unbounded controls. NETCO 2014, 2014, Tours, France. ⟨hal-01024111⟩