Design and experimental realization of a backstepping nonlinear H∞ control for an autonomous underwater vehicle using a nonlinear matrix inequality approach

Abstract

This paper focuses on the development of a nonlinear [Formula: see text] control (NHC) algorithm for an autonomous underwater vehicle (AUV) in the vertical plane. A three-degree-of-freedom AUV depth model is developed in terms of a nonlinear affine form which is used to design the control algorithm. The depth is controlled using a backstepping technique which generates a desired pitch angle for the NHC algorithm. The nonlinear control is designed using the [Formula: see text]-gain analysis which is transformed into a Hamilton–Jacobi–Isaacs (HJI) inequality. Further, the HJI inequality is presented in terms of a nonlinear matrix inequality structure in order to find a solution for the NHC problem using the concept of convex optimization. Hence, we desire to test the convex property of the nonlinear system before the realization of the control algorithm. The robust behaviour of the NHC algorithm is realized by ensuring the performance of the proposed control algorithm in the face of model and parameter uncertainties. A comparison between the NHC algorithm and the state-dependent Riccati equation is made in order to show the efficacy of the developed control algorithm. Furthermore, an experimental study of the proposed control scheme has been pursued to analyse the effectiveness of the developed control algorithm.