Robust Fault-tolerant H∞ Control with Adaptive Compensation

This paper is concerned with the robust fault-tolerant H∞ control problem of linear time-invariant systems with an adaptive mechanism for the general actuator fault and perturbation compensations. A novel dynamic output feedback controller is constructed by stabilizing controller gains and adaptive control gain functions. Based on the mode-dependent Lyapunov functions method, less conservative linear matrix inequalities (LMIs) are developed to find the stabilizing controller gains such that the H∞ performance is optimized. Besides, direct adaptive control schemes are proposed to adjust the control gain functions online in order to compensate for actuator faults and perturbations. Based on a notion of an adaptive H∞ performance index, the designed controller can guarantee the stability and adaptive H∞ performances of the resulting closed-loop systems. Moreover, a challenging problem of how much performance will be degraded by applying adaptive mechanism for fault compensations is also demonstrated. A numerical example of a linearized dynamic aircraft system and its simulation results are given.