The generalized super‐twisting algorithm with adaptive gains

In this article, a novel adaptive generalized super‐twisting algorithm (GSTA) is proposed for a class of systems whose perturbations and uncertain control coefficients may depend on both time and state. The proposed approach uses dynamically adapted control gains, and it is proven that this ensures global finite‐time convergence. A nonsmooth strict Lyapunov function is used to obtain the conditions for global finite‐time stability. A simulation and experimental case study is performed using an articulated intervention autonomous underwater vehicle (AIAUV). It is also shown that the adaptive GSTA causes the tracking errors of the AIAUV to converge to zero in finite time. In the case study, we use the singularity‐robust multiple task‐priority method to create a continuous trajectory for the AIAUV to follow. The simulation and experimental results validate and verify that the proposed approach is well suited for controlling an AIAUV. We also perform a comparison with the super‐twisting algorithm with adaptive gains and the original GSTA to evaluate whether adding adaptive gains to the GSTA actually improves the tracking capabilities by combining the theoretical advantages afforded by the GSTA with the practical advantages afforded by adaptive gains. Based on this comparison, the adaptive GSTA yields the best tracking results overall without increasing the energy consumption, and the simulations and experiments thus indicate that adding adaptive gains to the GSTA does indeed improve the consequent tracking results and capabilities.