FAT-based approximate feedback linearization of rate-dependent nonlinear dynamics

A rate-dependent nonlinearity presents different dynamics in response to variations of the input signal frequency. Both the Jacobian linearization and feedback linearization strategies cannot give proper performance for systems with these nonlinearities. In this paper, a new linearization algorithm is proposed for rate-dependent nonlinearities where a function approximator is designed to cover the effect of the nonlinearity such that a desired proportionality between the input and output signals can be realized. The proposed strategy is so general that the nonlinearity is allowed to be uncertain. The error between the system and the desired linear dynamics is verified by the Lyapunov method to be uniformly ultimately bounded. Linearization of a rate-dependent hysteresis with simulation justifications is presented to show the efficacy of the proposed design.