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

In this note, new necessary and sufficient conditions are derived for actuator failure compensation for linear time-invariant systems with actuator failures characterized by unknown input signals stuck at some unknown fixed values at unknown time instants, for state tracking with state feedback. It is shown that the number of fully functional actuators is crucial in determining the actuation range, which specifies the compensation design conditions in terms of system actuation structure. 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 dynamics parameters and actuator failure parameters including failure values, times, and patterns. Simulation results are presented to verify the desired system performance with failure compensation.