Continuous–Discrete Observation-Based Robust Tracking Control of Underwater Vehicles: Design, Stability Analysis, and Experiments

This study addresses the tracking control problem of underwater vehicles using a new robust observation-based control scheme. The advantages of the robust integral of the sign of the error (RISE) control, as well as the saturation function and well-known super-twisting algorithm, have been exploited to design a saturated super-twisting RISE (S+RISE) control scheme. However, the proposed S+RISE method requires continuous state measurements. To resolve this issue, a continuous–discrete time observer (CDO) is proposed, which works in tandem with the proposed controller. The resulting control scheme is known as CDO-S+RISE. In addition to estimating disturbances, the proposed CDO solves the problem of multiple sampling rates of the sensors. To demonstrate the asymptotic stability of the resulting nonobservation-based closed-loop dynamics with the proposed S+RISE control scheme, Lyapunov arguments are proposed. Then, the exponential stability of the unperturbed closed loop with the proposed CDO, as well as with the proposed S+RISE controller, is studied based on the Lyapunov–Krasovskii concept. To verify the performance recovery of the overall observation-based closed-loop system CDO-S+RISE (controlled by the proposed S+RISE control scheme), an invariant set
$\mathcal {A}_{\mathbb {R}}$
is determined using a composite Lyapunov–Krasovskii functional, which guarantees the convergence of the tracking errors to the origin. Several real-time experimental scenarios were conducted on the Leonard underwater vehicle prototype to validate the efficiency and robustness of the proposed CDO-S+RISE scheme.