Noncertainty-Equivalent Adaptive Control for Submarines Using SDU Decomposition: A FAS Approach

A fully actuated system (FAS) model of the submarine, whose input matrix has nonzero leading principal minors, is obtained. A noncertainty-equivalent adaptive (NCEA) controller based on the FAS model is developed for the submarine with parameter uncertainties to achieve precise asymptotic tracking of the desired trajectories. Unlike conventional adaptive control within the FAS framework, the adaptation law, together with a properly selected nonlinear function, composes full estimations of unknown parameters, boosting the convergence of the parameter estimates and improving the overall tracking performance. Thanks to the characteristic of the input matrix, a mathematical matrix factorization technique coined SDU decomposition is introduced to circumvent the singularity of the control law caused by estimations of unknown parameters in the input matrix. A Lyapunov-based analysis ensures the stability of the closed-loop error system. The numerical simulation of a submarine is provided to illustrate the effectiveness of the proposed approach.