# Active Compensation Fault-Tolerant Control for Uncertain Systems with Both Actuator and Sensor Faults

## TL;DR

This paper introduces a new control method that can handle both sensor and actuator faults in uncertain systems, ensuring stability and performance.

## Contribution

A novel fault reconstruction method and FTC scheme that simultaneously handles sensor and actuator faults using a combination of observers.

## Key findings

- The proposed method decouples sensor faults using an output transformation and a reduced-order observer.
- An interval observer achieves asymptotic convergence for fault reconstruction.
- The FTC scheme ensures asymptotic stability even with simultaneous sensor and actuator faults.

## Abstract

This paper develops a novel fault reconstruction (FR) method and an FR-based fault-tolerant control (FTC) scheme for systems suffering from both sensor and actuator faults based on the combination of a Luenberger-like reduced-order observer and an interval observer. Firstly, by introducing an output transformation, an auxiliary output that is able to decouple the sensor fault is obtained. Secondly, for addressing the external disturbance and actuator fault, a multiple unknown input (MUI) is formed, and a reduced-order observer that is able to decouple the MUI is constructed. Consequently, asymptotic convergence estimations of the state and the sensor fault can be accomplished. Thirdly, in order to obtain the asymptotic convergence actual FR (AFR), an interval observer is designed. After this, an algebraic connection of the MUI and the state error estimation is given, and, based on the algebraic relationship, an algebraic MUI reconstruction (MUIR) method is proposed. Finally, an FTC scheme is developed by using the state estimation and MUIR. Under the FTC, the closed-loop system is asymptotically stable even if it suffers from sensor and actuator faults simultaneously. Theoretical analysis demonstrates that the observer-based FTC mechanism satisfies the separation principle. At last, two simulation examples are given to verify the effectiveness of the proposed methods.