Hamilton-Jacobi inequality based reliable H∞ control for nonlinear systems

In this paper, the problem of reliable H^∞ control for affine systems is addressed. First, the normal state, partial failure and outage of an actuator are simultaneously considered by introducing a new actuator model, then, two reliable H^∞ controllers are proposed for two cases: one has only one faulty actuator in the set of all actuators, and the other has a certain number of faulty actuators in a pre-specified subset of all the actuators. The conditions for the existence of reliable H^∞ controllers are presented. The analyses show that the resulting closed-loop control system is asymptotically stable and has certain disturbance attenuation ability.