Approximate Dynamic Inversion for Nonaffine Nonlinear Systems With High-Order Mismatched Disturbances and Actuator Saturation

Abstract

In this paper, a novel disturbance-observer-based approximate dynamic inversion (ADI) approach is developed for pure-feedback nonaffine-in-control nonlinear systems (PFNNSs) in the presence of both high-order mismatched disturbances and actuator saturation. Finite-time disturbance observers (FTDOs) are utilized to estimate the disturbances and their derivatives. Then, we rebuild the system with the outputs of FTDOs. Thereafter, ADI is employed to derive the desired virtual and actual control of the nominal system, where no disturbances and saturation are presented. Furthermore, an augmented intermediate subsystem is constructed for the reduced slow subsystem to compensate for the difference between inputs with and without saturation by approximating its inversion. The stability of the closed-loop system is studied using Tikhonov's theorem. The proposed method is applied to a numerical example and a one-link robotic system with a brush DC motor. The simulation results demonstrate the validity of the presented approach. INDEX TERMS High-order mismatched disturbances, actuator saturation, finite-time disturbance observer, approximate dynamic inversion, singular perturbation theory.

A note on a performance recovery method for a class of nonaffine‐in‐control nonlinear systems with input saturation

“…It is worth noting that Assumption 1 is standard context in the relevant literature. [11][12][13][14] It is reasonable for the controllability of the plant and can be satisfied in practical engineering to design high-performance controllers. 15,16 Remark 3.…”

“…In Reference 11, the high‐amplitude phenomenon of approximate dynamic inversion was studied, and the idea of an intermediate subsystem was addressed to restrict the amplitude of control input. In Reference 12, the authors combined this method with the finite‐time disturbance observer for output tracking in spite of mismatched disturbance and input constraint. Nevertheless, in the past literature, 11,12 the stability is mainly concerned, while the recovery of the transient performance of the nominal system has not been taken into account.…”

“…In Reference 12, the authors combined this method with the finite‐time disturbance observer for output tracking in spite of mismatched disturbance and input constraint. Nevertheless, in the past literature, 11,12 the stability is mainly concerned, while the recovery of the transient performance of the nominal system has not been taken into account. Meanwhile, the anti‐windup controllers in References 11 and 12 are developed through back‐stepping procedure.…”

“…Nevertheless, in the past literature, 11,12 the stability is mainly concerned, while the recovery of the transient performance of the nominal system has not been taken into account. Meanwhile, the anti‐windup controllers in References 11 and 12 are developed through back‐stepping procedure. Hence, the systems have to be in or can be transformed into the strict/pure‐feedback form.…”

Control Design for the Autonomous Horizontal Takeoff Phase of the Reusable Launch Vehicles

“…Common methods to solve this problem are to design interval state estimator and sliding mode disturbance observer [30][31][32][33][34][35]. The method used here is to observe the uncertainty factor in real time and modify the MPC.…”