The generalized super-twisting algorithm with adaptive gains

In this paper a novel adaptive generalized super-twisting algorithm is proposed for a class of systems whose perturbations and uncertain control coefficients are time- and state-dependent. The proposed approach uses dynamically adapted control gains, and it is proven that this ensures global finite-time convergence. A non-smooth strict Lyapunov function is used to obtain the conditions for the global finite-time stability. As a case study, it is also shown that the tracking errors of an articulated intervention AUV converge asymptotically to zero when the proposed adaptive generalized super-twisting algorithm is applied. A simulation study is performed that shows the effectiveness of the proposed algorithm.