Discrete-time adaptive control of systems with multisegment piecewise-linear nonlinearities

Inverse schemes are constructed for multisegment piecewise-linear nonlinearities. Adaptive laws are proposed to update the inverse to cancel the effect of the unknown characteristic of such a nonlinearity which appears at the input of a linear part. Two adaptive control schemes using an adaptive inverse and a linear controller structure are developed: one for the linear part known and the other for the linear part unknown. Different adaptive designs are given based on different a priori nonlinearity knowledge necessary for the construction of an adaptive inverse. The adaptive inverse controllers ensure closed-loop signal boundedness and lead to significant improvements of system tracking performance.