Adaptive nonlinear control of systems containing a deadzone

The authors present an adaptive nonlinear controller for a plant containing a nonsmooth nonlinearity with unknown parameters in the span of the control (specifically, a deadzone). They develop a Lyapunov-based adaptation scheme which updates the parameters of the specific region of the deadzone in which the system is operating. They then employ some switching logic to turn on and off the adaptation as the state of the system proceeds from one region of the deadzone to another. A significant feature of the adaptive controller is the presence of set uncertainty. Thus, conceptually, adaptation is not only for unknown parameters, but also for the regions of the piecewise smooth nonlinearity