Adaptive compensation for infinite number of actuator failures based on tuning function approach

In controlling nonlinear uncertain systems, compensating for infinite number of actuator failures/faults based on the well-known tuning function approach is an important, yet challenging problem in the field of adaptive control. In fact, it has been illustrated through simulation examples that instability is observed when an existing tuning function based scheme designed for compensating finite number of actuator failures is applied to an infinite number case. So far, there is still no solution to this problem. In this paper, we address this issue by proposing a novel adaptive scheme. Technically, our scheme is developed from a new piecewise Lyapunov function analysis, the parameter projection and a modified tuning function method. It is proved that all closed-loop signals are ensured bounded by the control scheme even there is a possibility that the actuator failures take place infinitely, provided that the minimum time interval between two successive failures is bounded below by any positive scalar. Moreover, the ultimate bound of tracking error can be reduced arbitrarily small even for relatively frequent failures. In addition, a guideline for improving transient performance in terms of L2-norm of tracking error is also established. Perfect asymptotic tracking is obtained when the total number of actuator failures becomes finite.