On matching conditions for adaptive state tracking control of systems with actuator failures

New necessary and sufficient conditions are derived for state tracking with state feedback for linear time-invariant systems with actuator failures. The actuator failures are characterized by unknown input signals stuck at some unknown fixed values at unknown time instants. It is shown that the number of non-failed actuators is crucial in determining the actuation range which specifies the compensation design conditions. Such conditions are required for both a nominal design using system knowledge and an adaptive design without system knowledge. An adaptive actuator failure compensation control scheme based on relaxed system actuation conditions is developed for systems with unknown parameters and unknown actuator failure values, times and patterns. Simulation results are presented to verify the desired system performance with failure compensation