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Since autonomous underwater vehicles (AUVs) have highly nonlinear dynamics, the employed controller in these systems must be accurate and robust against noise and uncertainties. Sliding Mode Controller is very robust against both the parameters changing and external disturbance. But, there are some major drawbacks of these controllers such as chattering and high vulnerability against noise. In this paper, by modifying the reaching law and using an adaptive gain in the proposed sliding mode controller, these problems are eliminated from the input signal of the system. In the presented reaching law, a continuous term is used instead of the discrete sign function as well as the velocity term is entered in the reaching law. Since there are external disturbances, noises and uncertainties in the system dynamics and modeling, the states may be separated from the surface. Since the reaching law acts when the states separate from the sliding surface, then the gain of reaching law is adapted according to the uncertainties, states error and velocity. Also, the upper bound of disturbance and uncertainty are estimated. Furthermore, the reaching condition and limitation of the switching variable rate for the proposed controller are investigated. Finally, stability and convergence of the closed-loop system are proven analytically using the Lyapunov stability theorem. Some simulations and comparisons with other methods show efficiency of the presented method.

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Quantum genetic algorithm (QGA) is an optimization algorithm based on the probability that combines the idea of quantum computing and traditional genetic algorithm. In this paper, a new type of control law is developed for an underwater vehicle along with the desired path. The proposed controller is based on sliding mode control (SMC) in which the reaching law is modified to overcome two challenging problems, chattering, and sensitivity against noise. The disturbance is considered as a set of sinus waves with different frequencies which its parameters are estimated by Particle Swarm Optimization (PSO). Since QGA has some advantages such as fast convergence speed, small population size, and strong global search capabilities, we use QGA to determine the gain of the proposed controller. Finally, the Lyapunov theorem is used to prove that trajectory-tracking error converges to zero. Simulation results show that QGA can converge to the optimal response with a population consist of one chromosome.