A Zonotopic Disturbance Observer and Fully Actuated System Framework for Fault-Tolerant Control of Discrete-Time Uncertain Nonlinear Systems

This article presents a fault-Tolerant control (FTC) strategy for discrete-Time uncertain nonlinear systems by integrating a set-based observer with the fully actuated system (FAS) framework. Traditional approaches often estimate unknown actuator faults as deterministic point values, which overlook the effects of bounded noises and disturbances inherent in physical systems. To address this, we propose a zonotopic disturbance observer (ZDOB) that provides a more realistic fault estimation. The ZDOB simultaneously computes a point estimate and a tight geometric enclosure of the fault regarding the uncertainty boundary, capturing its uncertainty without the restrictive coordinate transformations required by prior interval-observer designs. Then, we develop a unified FTC law that leverages both the fault point and set information within the FAS structure, which dynamically adjusts the FTC gain bounds, allowing for a less conservative controller design that robustly compensates for the fault. We prove that the resulting closed-loop system is uniformly ultimately bounded, and the effectiveness of the proposed method is validated through comparative simulations on a dual-rotor helicopter system.