Adaptive control with nearest-neighbor previous instant compensation for discrete-time nonlinear strict-feedback systems

Many nonlinear systems can be modeled by or converted to strict-feedback forms, whose stabilization problem without modeling uncertainties has been extensively discussed in the literature. However, in practice, inevitable modeling uncertainties, especially co-existence of parametric uncertainties and nonparametric uncertainties, will make it very difficult and challenging to achieve desirable control performance. In this background, we consider a challenging adaptive control problem, aiming at asymptotic tracking to any bounded reference signal, in the presence of periodic uncertainties of both parametric and nonparametric types, i.e., periodic time-varying parameters and periodic unknown time-delays in the uncertain nonlinearities, for a class of strict-feedback discrete-time nonlinear systems due to the lack of related research and the increasing demand of digital control in current epoch. To deal with the co-existing various uncertainties, which bring highly-nonlinear coupled effects to the closed-loop system, a novel nearest-neighbor previous instant compensation technique, combined with the lifting approach and the future states prediction, is introduced in this paper to asymptotically fully compensate the effects of uncertainties. With such elaborately constructed adaptive estimation mechanism, the developed discrete-time backstepping adaptive controller can guarantee the closed-loop stability as well as asymptotic output tracking, which have been rigorously established and testified by extensive simulations.