On the non-recursive dynamic control for uncertain nonlinear systems

This paper presents a non-recursive tracking control for systems under the presence of mismatched disturbances. Firstly, through integrating a series of extended state observers (ESO) for the dynamics at each order, the uncertainties and their corresponding order derivatives can be estimated accurately within finite time. Then through utilizing all the estimations of ESOs and taking advantages of the homogeneous system theory, a non-recursive control works to guarantee the finite-time stability in a concise manner. This kind of non-recursive design framework is conducive to cost-saving and promoting practical implementations, detached from the determination of a series of virtual controllers. Additionally, to employ the time-varying scaling gain for better tracking performance, two kinds of forms, namely the adaptive tuning and implicit-Lyapunov-function (ILF)-based tuning laws, have been proposed to speed up the convergence rate and increase the tracking accuracy. Finally, numerical example results are presented to illustrate the performance of the proposed control scheme.