Nonlinear matrix inequality approach based heading control for an autonomous underwater vehicle with experimental realization

Abstract

A nonlinear ℋ∞ control algorithm has been developed for heading control of an autonomous underwater vehicle (AUV). A state feedback approach is used to design the nonlinear control using nonlinear matrix inequality (NLMI) approach. The control law is derived using ℒ∞ gain analysis, which is then transformed into Hamilton–Jacobi–Isaacs (HJI) inequality by formulating it as a nonlinear matrix inequality. The nonlinear control law is obtained by solving the NLMI using the convex optimization technique. The convex property of the nonlinear system is verified before the realization of the control algorithm. The robustness study of the proposed control algorithm for the control of AUV in heading plane is carried out in presence of model uncertainties. The effectiveness of the control algorithm is studied first by pursuing the simulation using MATLAB/Simulink and then by performing experimentation on a prototype AUV developed in the laboratory of our institute.