01111nas a2200109   4500008004300000245003600043210003600079260001700115520081000132100002300942856003600965       1998                        en_Ud  00aInfinite time regular synthesis0 aInfinite time regular synthesis  bEDP Sciences3 aIn this paper we provide a new sufficiency theorem for regular syntheses. The concept of regular synthesis is discussed in [12], where a sufficiency theorem for finite time syntheses is proved. There are interesting examples of optimal syntheses that are very regular, but whose trajectories have time domains not necessarily bounded. The regularity assumptions of the main theorem in [12] are verified by every piecewise smooth feedback control generating extremal trajectories that reach the target in finite time with a finite number of switchings. In the case of this paper the situation is even more complicate, since we admit both trajectories with finite and infinite time. We use weak differentiability assumptions on the synthesis and weak continuity assumptions on the associated value function.1 aPiccoli, Benedetto  uhttp://hdl.handle.net/1963/3517