caa a22 4500 397558759 CHVBK 20180308164810.0 cr unu---uuuuu 161202e199612 xx s 000 0 eng 10.1093/imamci/13.4.403 doi (NATIONALLICENCE)oxford-10.1093/imamci/13.4.403 The Pontryagin maximum principle: the constancy of the Hamiltonian [Elektronische Daten] [G. LITTLE, E. R. PINCH] The maximum principle was proved by Pontryagin using the assumption that the controls involved were measurable and bounded functions of time. However in many applications the optimal control is piecewise continuous and bounded. Thus it is natural to try to consturct a proof assuming that the admissible controls lie in the class of piecewise continuous bounded functions of t. This turns out to involve some subtle difficulties, and several of the proofs currently in the literature are defective. Here we address one of these difficulties: that of showing that, for an optimal control, the Hamiltonian is constant for all values of t. This result is a crucial one for anyone wishing to solve problems of optimal control. It is by no means a simple corollary of the maximum property. What a number of books actually establish is that the Hamiltonian is piecewise constant, taking a fixed value between the discontinuities of the optimal control. We supply a continuity argument which resolves this difficulty. © Oxford University Press Articles nationallicence LITTLE G. Mathematics Department, Manchester University aut PINCH E. R. Mathematics Department, Manchester University aut IMA Journal of Mathematical Control and Information Oxford University Press 13/4(1996-12), 403-408 0265-0754 13:4<403 1996 13 imamci https://doi.org/10.1093/imamci/13.4.403 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1093/imamci/13.4.403 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- LITTLE G. Mathematics Department, Manchester University aut NATIONALLICENCE 700 1- PINCH E. R. Mathematics Department, Manchester University aut NATIONALLICENCE 773 0- IMA Journal of Mathematical Control and Information Oxford University Press 13/4(1996-12), 403-408 0265-0754 13:4<403 1996 13 imamci Metadata rights reserved CC BY-NC-4.0 http://creativecommons.org/licenses/by-nc/4.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-oxford