Discrete indirect adaptive sliding mode control for uncertain Hammerstein nonlinear systems

The robustness issue of uncertain nonlinear systems’ control has attracted the attention of numerous researchers. In this paper, we propose three techniques to deal with the uncertain Hammerstein nonlinear model. First, a discrete sliding mode control (SMC) is developed, which is based on converting the original nonlinear system into a linearized one in the vicinity of the operating region using Taylor series expansion. However, the presence of relatively high nonlinearities and parameter variations leads to the deterioration of the desired performances. In order to overcome these problems and to improve the performance of classical SMC, we propose two solutions. The first one is based on the synthesis of a discrete SMC, taking into account the presence of nonlinearity. The second solution is a new discrete adaptive SMC for input–output Hammerstein model. In order to show the effectiveness of the proposed controllers, a detailed robustness analysis is clearly developed. Simulation examples are reported at the end of the paper.