Flatness-Based Adaptive Fuzzy Control of Autonomous Submarines

Abstract

The paper proposes adaptive fuzzy control based on differential flatness theory for autonomous submarines. It is proven that the dynamic model of the submarine, having as state variables the vessel’s depth and its pitch angle, is a differentially flat one. This means that all its state variables and its control inputs can be written as differential functions of the flat output and its derivatives. By exploiting differential flatness properties the system’s dynamic model is written in the multivariable linear canonical (Brunovsky) form, for which the design of a state feedback controller becomes possible. After this transformation, the new control inputs of the system contain unknown nonlinear parts, which are identified with the use of neurofuzzy approximators. The learning procedure for these estimators is determined by the requirement the first derivative of the closed-loop’s Lyapunov function to be a negative one. Moreover, the Lyapunov stability analysis shows that H-infinity tracking performance is succeeded for the feedback control loop and this assures improved robustness to the aforementioned model uncertainty as well as to external perturbations. The efficiency of the proposed adaptive fuzzy control scheme is confirmed through simulation experiments.