A local existence result for an optimal control problem modeling the manoeuvring of an underwater vehicle

We prove a local existence result for the manoeuvrability control of a submarine. The problem is formulated as an optimal control problem with a nonlinear and highly coupled system of ODEs for the state law, a Lagrange type cost function, and nonlinear controls which take values on a convex and compact subset of R. Finally, the existence of solution for this problem is obtained by applying a recent general existence result (see [P. Pedregal and J. Tiago, Existence results for optimal control problems with some special non-linear dependence on state and control, SIAM J. Control Opt., 48 n.2 (2009) 415-437]) which, however, requires some modifications to be used in our specific case. keywords Submarine, manoeuvrability control, optimal control problem, relaxation, Young measures, existence theory. AMS 49J15, 49M20, 78M05, 93C15.