Viabilizability of Control Signals under Control Authority Degradation

In this work, we solve the problem of mitigating control authority degradation in real time. In particular, we focus on controlled nonlinear affine-in-control evolution equations with finite control input and finite- or infinite-dimensional state. We consider control input degradation parameterized by Lipschitz continuous maps. These degradation modes are encountered in practice due to actuator wear and tear, hard locks on actuator ranges due to over-excitation, as well as more general changes in the control allocation dynamics. In previous work, we have derived sufficient conditions for real-time identifiability of control authority degradation. In this work, we build on these results by introducing the concept of viabilizability, which deals with the existence of a viabilizing map. Viabilizing maps remap commanded control signals to viabilized signals that produce a minimally disturbed approximation of the commanded control signal after control authority degradation. We develop sufficient conditions on viabilizability for a class of control degradation modes, as well as error bounds on approximate viabilizing maps and methods for viabilizing fixed gain controllers.