Reverse-Order Multi-Objective Evolution Algorithm for Multi-Objective Observer-Based Fault-Tolerant Control of T-S Fuzzy Systems

In this study, a multi-objective
$H_{2}/H_{\infty }$
observer-based fault-tolerant control (FTC) design with reverse-order multi-objective evolution algorithm (MOEA) is proposed to deal with the FTC problem of Takagi-Sugeno (T-S) fuzzy systems. To achieve the optimal robust FTC design for the T-S fuzzy systems under the sensor and actuator faults, as well as external disturbance and measurement noise, the multi-objective
$H_{2} /H_{\infty }$
observer-based FTC scheme is proposed to efficiently estimate the system state and the fault signals based on a proposed smoothed fault signal model. Then, multi-objective
$H_{2}/H_{\infty }$
FTC performance can be achieved by an estimated state and fault signal feedback scheme to efficiently compensate the effect of fault signals and attenuate the effect of external disturbance. By using the proposed indirect method, the multi-objective
$H_{2}/H_{\infty }$
observer-based FTC design problem is transformed into linear matrix inequalities (LMIs)-constrained multi-objective optimization problem (MOP). Besides, to overcome the difficulties in searching large fuzzy parameters of observer-based FTC design for solving the LMIs-constrained MOP, a reverse-order MOEA is proposed to overcome the bottleneck to efficiently solve the MOP for multi-objective
$H_{2}/H_{\infty }$
observer-based FTC of T-S fuzzy system by searching feasible objective vectors in the objective space instead of searching fuzzy design parameters in the parametric space. Two practical examples are considered for the performance validation with (i)
$H_{2}/H_{\infty }$
observer-based FTC design for the missile guidance system with the actuator and sensor fault signals due to the sudden cheating side-step maneuvering and the hostile jamming interference and (ii)
$H_{2}/H_{\infty }$
observer-based FTC design for inverted pendulum system which effected by the constant actuator fault.