Fast finite-time backstepping controller for a quadrotor UAV under state constraints

Quadrotors have gained popularity in a wide range of applications. In this paper, a new approach for solving the tracking control problem of quadrotors with full-state constraints is presented. The proposed method involves a backstepping control scheme integrated with a fast finite-time filter. First, necessary state transformations are performed to support the design of the finite-time filter and controller. Next, the controller is formulated based on the backstepping technique. All the state constraints are taken into consideration in the controller. However, it is well-known that the backstepping control design can lead to the “explosion of complexity” when calculating time derivatives of certain nonlinear functions. Therefore, the proposed filter comes to provide a solution for estimating the time derivatives with the estimation errors converging to zero in finite time. The closed-loop system's finite-time stability is rigorously proved using the Lyapunov theory, despite the state constraints. Simulation results demonstrate the feasibility and efficacy of the proposed method.