Performance criterion

As a performance criterion, the minimum distance between two points has chosen to transfer the system from a point to another. The optimal control will try to minimize this measure. For this performance, only position of the UUV is of interest. When missions of underwater vehicles are considered, mostly, the positioning of the underwater vehicle is carried out. Thus, the performance criterion describing the minimum distance between two points in 3-D space can be written as a terminal-error function:

Jc = (xf (t) - xd)2 + (yf (t) - yd)2 + (zf (t) - zd)2 . (12)

Jc represents the deviation of the actual path of the system from its desired path. The components of the final position vector, xo, yd, and zd, are chosen as constant. For the calculation of the functions, Xf(t), y/t), and z(t), which give the actual position of the vehicle, the relation (1) is used.

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