Adaptive Control for Nonlinear System with Unknown Hysteresis

An adaptive control and an adaptive robust control (ARC) algorithm were developed for a class of nonlinear system with unknown input backlash-like hysteresis. The existing robust adaptive control methods mainly focus on using various linearly parameterized models with on-line parameter adaptation for an approximate inversion of the unknown backlash-like nonlinearity. Due to the inherent dynamic nonlinear nature of the unknown backlash-like nonlinearity, existing robust adaptive control methods mainly focus on using approximate inversion by on-line parameter adaptation. Unlike many existing control schemes, the backlash-like hysteresis inverse wasn't constructed in this paper. The proposed adaptive control law ensured asymptotic tracking stability of the closed-loop system. But the violent chatting limited its application in practice. The adaptive robust control ensured that all signals of the closed-loop system were bounded and the tracking within a desired precision. The theoretical analysis and simulation results show the validity of the proposed controllers.