We now apply Lemma 4.1 - Pontryagin's maximum principle to Problem ( C x ).
In Section 2, we provide existenceresults and a priori estimates in the form that is required to obtainPontryagin's maximum principle for problem (P).
We apply a direct approach to derive the maximum principle for the problem at hand.
By the classic discuss, we can get the Pontryagain's maximum principle for the problem ( P ) (see [10, 11]).
Motivated by the above works, we construct an appropriate auxiliary function and use the Hopf maximum principle to study problem (1.1 - 1.3 1.1 - 1.3
A design scheme for solving the maximum principle boundary-value problem for arbitrary turning conditions and inertial characteristics of the spacecraft is given.
When the control domain U is convex, the local maximum principle for this problem was studied in (Dokuchaev and Zhou 1999, Ji and Zhou 2006, Peng 1993, Shi and Wu 2006, Wu 1998, Xu 1995) see also the references therein.
We state Pontryagin's maximum principle for optimal control problems.
The earliest results on the extension of Pontryagin's maximum principle to stochastic control problems are obtained in [16 19].
In this section, we give an application of the theorem to the stochastic maximum principle in optimal control problems through an example of the linear quadratic case.
