Non-smooth Predictive Control for Wiener Systems with Backlash-Like Hysteresis

Abstract

In this paper, a nonsmooth predictive control method for Wiener systems with backlash-like hysteresis is proposed. In this type of system, the backlash-like hysteresis is connected in series with a preceded linear dynamic subsystem. A backlash-like hysteresis is modeled as a nonsmooth function with multivalued mapping; the corresponding objective function of the control system is also defined as being nonsmooth. In this case, the implementation of conventional model predictive control for such systems will encounter a challenge, since the gradients of the control criterion function with respect to control variables do not exist at nonsmooth points. In order to solve this problem, a nonsmooth receding horizon strategy based on Clarke subgradients is proposed. Moreover, the robust stability of the predictive control of such nonsmooth Wiener systems is analyzed. Finally, a numerical example and a simulation study on a mechanical transmission system are implemented to validate the proposed method.