Adaptive Integral Sliding Mode Control with Gaussian Processes for AUVs

This paper proposes a novel adaptive integral sliding mode control (ISMC) scheme for robust trajectory tracking of autonomous underwater vehicles (AUVs) utilizing Gaussian process (GP) regression. By incorporating GPs into the ISMC framework, the proposed control strategy exhibits robustness against significant system uncertainties and aggressive desired trajectories. The GP posterior means offer high-probability uncertainty compensation, while the posterior variances enable adaptive tuning of controller gains and learning rates. A novel adaptive gain law is introduced to prevent excessive gain growth and nonsmooth control actions near the sliding manifold. Lyapunov stability analysis guarantees that the tracking errors of the proposed scheme converge to an arbitrarily small bound within a specific probability. Simulation results demonstrate the superior transient tracking performance of the proposed method compared to both the standard GP-ISMC without gain adaptation and the adaptive GP-ISMC using standard monotonically increasing adaptive laws.