Synchronization Control for AUVs via Optimal-Sliding-Mode Adaptive Dynamic Programming with Actuator Saturation and Performance Constraints in Dynamic Recovery

This paper proposes an optimal-sliding-mode-based adaptive dynamic programming (ADP) master–slave synchronous control strategy for the actuator saturation and performance constraints that AUVs face in dynamic recovery. First, by introducing the sliding-mode function into the value function to optimize the state error and its derivative simultaneously, the convergence speed is significantly improved. Second, by designing the performance constraint function to directly map the sliding-mode function, the evolution trajectory of the sliding-mode function is constrained, ensuring the steady-state and transient characteristics. In addition, the hyperbolic tangent function (tanh) is introduced into the value function to project the control inputs into an unconstrained policy domain, thereby eliminating the phase lag inherent in conventional saturation compensation schemes. Finally, the requirement for initial stability is relaxed by constructing a single-critic network to approximate the optimal control policy. The simulation results show that the proposed method has significant advantages in terms of the position and attitude synchronization error convergence rate, steady-state accuracy, and control signal continuity compared with the conventional ADP method.