Optimal trajectory-tracking control for underactuated AUV with unknown disturbances via single critic network based adaptive dynamic programming

Tracking control is the one of the basic tasks in motion control for underactuated autonomous underwater vehicle (AUV). The underwater environment exists unknown disturbances and the actuators number of underactuated AUV is less than the number of degrees of freedom (DOF) of underactuated AUV, which adds more difficulties in the process of trajectory-tracking control for underactuated AUV. In order to improve the tracking accuracy and system stability, a single critic network based adaptive dynamic programming (ADP) control scheme is proposed to solve trajectory-tacking control problem. Firstly, a virtual velocity control vector is designed based on the kinematic model of underactuated AUV using backstepping approach, which is taken as a virtual desired velocity of the dynamic model of underactuated AUV with unknown disturbances. Secondly, a tracking error system with unknown disturbances is constructed based on the kinematic model and dynamic model of underactuated AUV. An online policy iteration algorithm is designed and the single critic network is established to approximate the performance index function. The optimal control law is derived. Moreover, the stability of tracking error system is analyzed based on the Lyapunov theory. Finally, the simulation is executed in MATLAB. The simulation results shows that error vector of position and attitude and the error vector of velocity converge to 0 with the proposed control method. The tracking accuracy and convergence velocity are better than the existing methods, such as single critic network based ADP control scheme without backstepping method. © 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.