Adaptive control of systems with nonsmooth input and output nonlinearities

We develop adaptive control schemes for plants with unknown nonsmooth nonlinearities such as dead-zone, backlash and hysteresis at both the input and output of a linear dynamics. We employ new controller parametrizations with nonlinearity inverses for parametrized nonlinearities. When implemented with true parameters and properly initialized, the inverse controller ensures closed-loop-signal boundedness and output tracking. When implemented with parameter estimates, the inverse controller leads to linearly parametrized error models suitable for adaptation. We design adaptive laws to update the parameter estimates to design adaptive inverse controllers for unknown nonlinearities in two cases: the linear part known and the linear part unknown, which ensure closed-loop signal boundedness.