@article {2005, title = {Hybrid necessary principle}, journal = {SIAM J. Control Optim. 43 (2005) 1867-1887}, number = {SISSA;71/2002/M}, year = {2005}, note = {Proceedings of IFAC Conference on Analysis and Design of Hybrid Systems, Saint Malo, France}, publisher = {SIAM}, abstract = {We consider a hybrid control system and general optimal control problems for this system. We suppose that the switching strategy imposes restrictions on control sets and we provide necessary conditions for an optimal hybrid trajectory, stating a hybrid necessary principle (HNP). Our result generalizes various necessary principles available in the literature.}, doi = {10.1137/S0363012903416219}, url = {http://hdl.handle.net/1963/1641}, author = {Mauro Garavello and Benedetto Piccoli} }