Finite Time Adaptive Multi-Dimensional Taylor Network Control of a Quadrotor with Input Delay

This study introduces an innovative finite-time adaptive control strategy for trajectory tracking of a quadrotor, accounting for input delay, model uncertainty, and external disturbances. This strategy includes an advanced Dynamic Surface Control (DSC) technique with a Multi-Dimensional Taylor Network (MTN) for approximating the unknown nonlinearities. To alleviate the adverse impacts of control input delay, a Padebased approximation is utilized for the delay compensation. The existing DSC schemes use a linear filter to prevent the 'explosion of complexity' characteristic of conventional backstepping designs. However, they introduce boundary-layer errors and can only guarantee asymptotic stability, which can affect tracking accuracy. As such, a new nonlinear filter with an adaptive gain is constructed for the DSC so that it can mitigate boundarylayer error online and prevent the 'explosion of complexity' with guaranteed finite-time stability. The MTN substitutes traditional neural networks with a concise polynomial-based approximator, thereby reducing computational cost. Moreover, the MTN is adjusted by employing a lone adaptive parameter rather than a whole weight vector as in neural networks. Numerical simulations and comparisons with a traditional adaptive DSC (ADSC) and a disturbance-observer-based backstepping (DOB) controller are performed considering ± 30% parametric uncertainty, timevarying disturbances, and an input delay of 0.03 seconds. The results show that the proposed controller has the fastest convergence, low overshoot, and more accurate steady-state.