Polynomial Fuzzy Observer-Based Integrated Fault Estimation and Fault-Tolerant Control With Uncertainty and Disturbance

This article studies the integrated fault-tolerant control (FTC) and fault estimation (FE) problem using polynomial fuzzy model (PFM) based on the sum of squares (SOS) approach. The integrated approach not only considers the bidirectional interaction between fault diagnosis and control units but also ensures an optimal response. The transient management in the fault occurrence situation and the alleviation of bidirectional interaction between FE and FTC are the motivational challenges. However, the integrated approach increases the complexity and problem's dimension. In this situation, PFM can reduce the problem's dimensions and increase modeling accuracy. The additive actuator faults, input disturbance, and structured uncertainty are considered to bring the problem closer to practical applications. A polynomial fuzzy observer with unknown input is designed to estimate the time-varying faults that is used to remove the effects of faults on the control input. Thus, the proposed approach benefits from PFM in FE and FTC synthesis to reduce the design dimensions, have a more precise model, and make the synthesis less conservative. Moreover, the PFM is more robust against intense model uncertainties and faults. To evaluate the proposed approach, the FTC of an inverted-pendulum system is simulated. The fault-tolerant and fault estimation performances of the proposed approach are compared with those of the linear matrix inequality (LMI) approach. The simulated results show that the proposed SOS approach outperforms the LMI approach.