Underwater robotic vehicles have become an important tool for various underwater tasks because they háve greater speed, endurance, depth capability, and safety than human divers. The problem of controlling a remotely operated underwater vehicle in 6 degrees of freedom (DOF) is addressed in this paper, as an example of a system containing severe non-linearities. Neural networks are been used in a closed-loop to approximate the nonlinear vehicle dynamics. No prior off-line training phase and no explicit knowledge of the structure of the vehicle are required, and the proposed scheme exploits the advantages of both neural network control and adaptive control. A control law and a stable on-line adaptive law are derived using the Lyapunov theory, and the convergence of the tracking error to zero and the bounded-ness of signals are guaranteed by applying Barbalaťs Lyapunov-like lemma. In this páper, a neural network architecture based on radial basis functions has been ušed to evaluate the performance of the proposed adaptive controller for the motion of the Norwegian Experimental Remotely Operated Vehicle (NEROV).
We present a result on the stability of moving invariant manifolds of nonlinear uncertain impulsive differential-difference equations. The result is obtained by means of piecewise continuous Lyapunov functions and a comparison principle.