A Finite-Time Disturbance Observer-Based Control for Constrained Second-Order Dynamical Systems and Its Application to the Attitude Tracking of a UAV

As second-order dynamical systems are omnipresent, solving the control problem for such a class of systems has attracted worldwide attention. Among many techniques, the backstepping control method is well-known for its straightforward design and efficacy, yet it suffers from the inherent issue of complexity explosion. This work aims to leverage the backstepping method in a finite-time-converging control scheme. First, to address the presence of external disturbances, a nonlinear, unknown-input observer is introduced, which provides a disturbance estimate with finite-time convergence. Second, a fast-converging finite-time filter is used to estimate the derivative of virtual control inputs in the backstepping framework. Next, the outputs of the disturbance observer and the filter are used to formulate a finite-time, backstepping control law. Additionally, the closed-loop system is proven to be finite-time stable through a rigorous stability analysis. Finally, the proposed algorithm is applied to an unmanned aerial vehicle (UAV) system and validated through simulations and experiments under actual flight conditions. The experimental results demonstrate the feasibility of the implementation and the practical efficacy of the proposed approach.