Composite practical fixed-time distributed formation tracking control of deferred constrained multiple quadrotor UAVs under external disturbance

Considering deferred time-varying tracking error constraint and external disturbance, a disturbance observer based-practical fixed-time formation tracking controller is designed for multiple quadrotor UAVs(QUAVs). To begin with, a shifting function is proposed to ensure that the tracking error of a class of MIMO nonlinear systems can quickly return to the constraint from the outside of constraint. At the same time, the shifting function sets the initial value to an arbitrarily small constant, which can avoid the singular problem. Then, nonlinear transformation is established to transfer the constrained problem into an unconstrained problem. Furthermore, an adaptive gain fixed-time disturbance observer (AGFXDO) is proposed to tackle the external disturbance with relaxed assumption condition. The fixed-time stability of the estimate error is proven. Based on those, a practical fixed-time distributed formation tracking control strategy is designed for the multiple QUAVs. The practical fixed-time stability of the transformed error is rigorously proven and the tracking error is guaranteed to yield the constraint and converges to an arbitrarily small vicinity of zero after prespecified time for arbitrarily given bounded initial values. At the end, the effectiveness of the developed control scheme is illustrated by the compared simulations. Through the comparative analysis of metrics integral of absolute magnitude of error (TAE), integral of time-multiplied absolute magnitude of the error (ITAE), integral of square value of controller signal (ISV), the tracking errors enter the constraint boundaries within 3 seconds and rapidly achieve convergence. Compared with the existing FXDO-based method, the proposed AGFXDO based control approach reduces 21.7% of TAE and 76.9% of ITAE, simultaneously, it maintains lower controller value as reflected in ISV.