Finite-Time Adaptive Dynamic Surface Control of a Quadrotor with Input Delay

Abstract
This paper presents finite-time adaptive multi-dimensional Taylor network (MTN)-based dynamic surface control (DSC) for attitude and position control of a quadrotor subjected to input delay, parametric uncertainties, and external disturbances. The input delay is compensated using the Pade approximation approach. Due to the simple structure, low computation, and excellent approximation capability of the MTN, it is employed to approximate the uncertain nonlinearities of the quadrotor system. The MTN is updated using a single parameter instead of a vector of many weights to simplify it further. An improved DSC strategy is employed to achieve the attitude and position tracking of the quadrotor in finite time. Different from the traditional first-order filter of the DSC, a modified first-order filter is proposed such that it not only prevents the “explosion of complexity” problem associated with the conventional backstepping approach but also utilizes extra terms to guarantee finite-time convergence and estimates and compensates the problem of boundary layer error. Thus, the assumption that the maximum bound of the derivative of the virtual control law is known is no longer required. The gains of the DSC are updated online so that proper gains are adapted in response to the change in the reference trajectories to improve the tracking accuracy. Lyapunov candidate function is used to prove the finite-time convergence of the closed-loop system to a compact set. Finally, numerical simulations have been provided to demonstrate the advantages of the improved DSC scheme.