Numerous practical systems refered in this book, such as aircraft and spacecraft flight control systems, process control systems, and power systems that have actuator nonlinearities present at the input or nonlinearities sandwiched in between two dynamic blocks, are also prone to actuator failures. Adaptive control of such systems in presence of nonlinearities as well as failures, presents a new challenging problem. This research topic is practically important as many of these systems are critical and actuator failures and non-linearities if not compensated, may lead to disasters, for instance, aircraft accidents have been caused by actuator failures. The compensation of actuator nonlinearities is equally important as they limit both static and dynamic performance of control systems. These nonlinearities are typically nonsmooth nonlinearities such as dead-zone, hysteresis and backlash.