Dissipativity-Based Integrated Fault Estimation and Fault Tolerant Control for IT2 Polynomial Fuzzy Systems With Sensor and Actuator Faults

Abstract

The integrated fault estimation and fault-tolerant control scheme is developed in this paper for a series of interval type-2 polynomial fuzzy systems with both sensor faults and actuator faults, where the bi-directional influence between fault estimation unit and fault-tolerant control unit is investigated. Considering the existence of sensor faults, unmeasurable premise variables are investigated for more general situations and Class III state/fault estimation observers are established for the final fault estimation and fault-tolerant control purposes. To increase design flexibility and reduce physical implementation complexity, the proposed method allows the observer and original system to share asynchronous membership functions and a different number of fuzzy rules. <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$(\mathcal{Q,S,R}) \,-\, \alpha$</tex-math></inline-formula> dissipative performance index is also introduced to fulfill a wider vary of perfor-mance requirements. Membership-function-dependent stability constraints are given in the format of bi-linear polynomial matrix inequalities to obtain less conservative results, which are computed by a two-step path-following method. Superiority and validity are demonstrated by an inverted pendulum example in terms of estimation errors, fault-tolerant control performance and control inputs.