Robust adaptive optimal trajectory tracking control for underactuated AUVs with position and velocity constraints in three‐dimensional space

Abstract The safety and optimality of underactuated autonomous underwater vehicles (AUVs) during operations are essential factors to consider. In this context, a three‐dimensional robust adaptive optimal trajectory tracking control method under position and velocity constraints, unknown dynamics, and environmental disturbances is proposed. The main features of the method are: (1) The outputs of an underactuated AUV system are redefined to handle the underactuation problem. (2) The system with position and velocity constraints is transformed into an unconstrained system by a nonlinear state‐dependent transformation. (3) A critic‐identifier architecture is constructed using adaptive dynamic programming and neural networks in a backstepping framework. Specifically, critic networks and weight update laws without requiring initial stability control are designed to solve Hamilton‐Jacobi‐Bellman equations in kinematic and dynamic subsystems, and optimal virtual and actual control laws are obtained. (4) A neural network identifier is developed to estimate unknown dynamics. Disturbances are overcome by improving the cost function and solving for optimal control of the nominal dynamic subsystem. By stability analysis, tracking errors in the AUV closed‐loop system can converge to an arbitrarily small compact set of the origin, and the other signals are uniformly ultimately bounded. Simulation comparisons demonstrate the effectiveness and superiority of the proposed method.