Dual closed-loop robust adaptive fast integral terminal sliding mode formation finite-time control for multi-underactuated AUV system in three dimensional space

Abstract This paper addresses a dual closed-loop fast integral terminal sliding mode control method of a multi-underactuated AUV formation system with uncertain model parameters and environmental disturbances. Different from the traditional sliding mode control method, this technique can not only keep the formation stable, but also significantly overcomes the problem that the formation tracking errors of the traditional method may not converge to zero in finite time. Then, an adaptive radial basis function (RBF) neural network controller is incorporated with a conditional integrator to deal with the uncertain model parameters, approximation errors and environmental disturbances in practical multi-AUV systems. And also the proposed controller is continuous with the property of chattering restraining. A virtual leader is adopted on the basis of the leader-following strategy to improve the robustness of the formation system and prevent the problem of formation collapse caused by the failure of the leader AUV. Moreover, the rigorous stability analysis based on Lyapunov method and numerical simulations demonstrate tracking errors converge to 0 in finite time. Finally, simulation results demonstrate the effectiveness of the proposed formation controller: the AUV formation can track the desired trajectory accurately with ± 10% model parameter perturbation.