Practical Finite-Time Command-Filtered Adaptive Backstepping With Its Applications to Quadrotor Hovers

In this article, a practical finite-time command-filtered adaptive backstepping (PFTCFAB) control method is presented for a class of uncertain nonlinear systems with nonparametric unknown nonlinearities and external disturbances. Unlike PFTCFAB control techniques that use neural networks (NNs) or fuzzy-logic systems (FLSs) to deal with system uncertainties, the proposed method is capable of handling such uncertainties without the need for NNs or FLSs, thus reducing complexity and increasing reliability. In the proposed approach, novel function adaptive laws are designed to directly estimate unknown nonparametric nonlinearities and external disturbances by means of command filter techniques, and a type of practical finite-time command filters is proposed to obtain such laws. Moreover, the PFTCFAB controllers and finite-time command filters are designed with practical finite-time Lyapunov stability, which ensures finite-time stability of system tracking and filter estimation errors. Experimental results with a quadrotor hover system are presented and discussed to demonstrate the advantages and effectiveness of the proposed control strategy.

I. Introduction

In recent years, command-filtered backstepping and command-filtered adaptive backstepping control techniques have been widely applied in many practical systems, because their computation complexity is lower than that of standard backstepping techniques. In [1] and [2], command-filtered backstepping and command-filtered adaptive backstepping were introduced to overcome the “explosion of complexity” problem caused by calculating the time derivatives of virtual control functions in backstepping. In [2], compensation signals are designed to eliminate the influence of filter errors. Subsequently, many command-filtered backstepping- or adaptive backstepping-based systems have been developed. For example, speed regulation for diesel generator systems with parametric uncertainties is addressed in [3] using a command-filtered backstepping control technique. In [4], trajectory tracking control for quadrotor unmanned aerial vehicles is implemented using command-filtered backstepping and disturbance observers, considering disturbances and input saturation. Wang et al. [5] investigated the command-filtered adaptive backstepping synchronization control problem for a servo system-driven system with torque disturbances, unmodeled dynamics, and motor parameter uncertainties. A new command-filtered adaptive backstepping technique was developed in [6] for autonomous underwater vehicles with model uncertainties and input saturation. From the aforementioned results, it can be concluded that stabilization and tracking control problems can be well solved via command-filtered adaptive backstepping, provided the nonlinear system only contains parameter uncertainties. However, if completely unknown nonparametric nonlinearities exist, control problems for nonlinear systems are intractable by only using command-filtered adaptive backstepping without resorting to other techniques.