Nonlinear optimal vibration control for AUVs with input delay under wave disturbances

Abstract

Nonlinear optimal vibration control (NOVC) for autonomous underwater vehicles (AUVs) with input delay affected by wave disturbances is considered. Firstly, the AUVs model with input delay in vertical plane is obtained, and an exosystem to generate the irregular wave disturbances is constructed. Secondly, through a particular transformation, the original system with input delay is reduced into a delay free system. Then, the coupled two-point boundary value (TPBV) problem for the AUVs system without delay is derived from the optimal control theory. By using a recently developed successive approximation approach to construct sequences, the coupled TPBV problem is transformed into solving two decoupled linear differential sequences in state vectors and adjoint vectors. By iterative solving the two equation sequences, the approximate NOVC law is obtained. Finally, the effectiveness and feasibility of the presented control law is demonstrated by a numerical example of the Remote Environmental Unit (REMUS) AUVs.