Flatness-based adaptive fuzzy control of an autonomous submarine model

Abstract

The article presents a differential flatness theory-based method for adaptive control of autonomous submarines. A proof is provided about the differential flatness properties of the submarine’s model (having as state variables the vessel’s depth and its pitch angle). This also means that all its state variables and its control inputs can be written as differential functions of the flat output. Making use of its differential flatness features, the submarine’s dynamic model is transformed into the multivariable linear canonical (Brunovsky) form. In the transformed model, the control inputs consist of unknown nonlinear parts, which are identified with the use of neurofuzzy approximators. The learning rate for these estimators is determined by the requirement the first derivative of the closed-loop’s Lyapunov function to be a negative one. Furthermore, with the use of Lyapunov stability analysis it is proven that an H-infinity tracking performance is succeeded for the feedback control loop. This implies enhanced robustness to model uncertainty and to external perturbations. Simulation experiments are carried out to further confirm the efficiency of the proposed adaptive fuzzy control scheme.