• Korean Journal of Mathematics
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• v.14 no.1
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• pp.79-83
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• 2006

In this paper, we apply Zermelo's problem of navigation on Riemannian manifolds to Hermitian manifolds. Using a similar technique with which we define a Randers metric in a Finsler manifold by perturbing Riemannian metric with a vector field, we construct an $(a,b,f)$-metric in a Rizza manifold from a Hermitian metric and a given vector field.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.17 no.1
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• pp.117-126
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• 2013

A ship is intended to reach a specified target point in the minimum-time when it travels with a constant speed through a region of strong currents and its heading angle is the control variable. This is called the Zermelo's navigation problem. Its approximate solution for the minimum-time control may be found using the calculus of variation. However, the accuracy of its approximate solution is not high since the solution is based on a table form of inverse relations for some complicated nonlinear equations. To enhance the accuracy, this paper employs the neural network to represent the inverse relation of the complicated nonlinear equations. The accurate minimum-time control is possible with the interpolation property of the neural network. Through the computer simulation study we have found that the proposed method is superior to the conventional ones.