  In this work, we solve the problem of quantifying and mitigating control
authority degradation in real time. Here, our target systems are controlled
nonlinear affine-in-control evolution equations with finite control input and
finite- or infinite-dimensional state. We consider two cases of control input
degradation: finitely many affine maps acting on unknown disjoint subsets of
the inputs and general 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. We derive sufficient conditions for identifiability of
control authority degradation, and propose a novel real-time algorithm for
identifying or approximating control degradation modes. We demonstrate our
method on a nonlinear distributed parameter system, namely a one-dimensional
heat equation with a velocity-controlled moveable heat source, motivated by
autonomous energy-based surgery.
