A Local Existence Result for an Optimal Control Problem Modeling the Manoeuvring of an Underwater Vehicle

Nonlinear Analysis-Real World Applications, 11(4) (2010), 2573-2583
http://dx.doi.org/10.1016/j.nonrwa.2009.09.002

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(3). 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 Optim. 48 (2) (2009) 415-437]) which, however, requires some modifications in order to be applicable in our specific case. (C) 2009 Elsevier Ltd. All rights reserved.