Discrete-time adaptive control of systems with multi-segment piecewise-linear nonlinearities

Inverse schemes are constructed for multi-segment 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. Simulation results show that the proposed adaptive inverse controllers achieve the desired tracking performance despite the presence of the unknown nonlinearity