From the text: We address some open problems in adaptive control of systems with unknown actuator failures. We present a solution to a class of such problems, i.e., direct adaptive-state feedback control for state trajectory tracking in the presence of unknown actuator failures that are constant, or parametrizable time-varying, or nonparametrizable time-varying. We derive necessary and sufficient conditions for the existence of such an adaptive actuator failure compensation and develop the controller structures, parametrizations, error models, and adaptive laws for such systems. We analyze the stability and tracking performance of the adaptive laws and demonstrate them by simulation results. The adaptive designs and analyzes presented can be extended to the case where the state reference model system has multiple inputs that characterize more freedom in the desired system behavior. The adaptive designs presented ensure stability and tracking in the presence of actuator failures that occur at uncertain instants of time and are uncertain in value and pattern, and in the presence of parametric uncertainties in the plant dynamics.
Other problems in adaptive control of systems in the presence of actuator failures that are currently under investigation include output tracking with relaxed plant-model matching conditions using state feedback, output tracking using output feedback, and extensions to nonlinear systems.