Robust Adaptive Dynamic Surface Control for a Class of Nonlinear Dynamical Systems with Unknown Hysteresis

The output tracking problem for a class of uncertain strict-feedback nonlinear systems with unknown Duhem hysteresis input is investigated. In order to handle the undesirable effects caused by unknown hysteresis, the properties in respect to Duhem model are used to decompose it as a nonlinear smooth term and a nonlinear bounded “disturbance-like” term, which makes it possible to deal with the unknown hysteresis without constructing inverse in the controller design. By combining robust control and dynamic surface control technique, an adaptive controller is proposed in this paper to avoid “the explosion complexity” in the standard backstepping design procedure. The negative effects caused by the unknown hysteresis can be mitigated effectively, and the semiglobal uniform ultimate boundedness of all the signals in the closed-loop system is obtained. The effectiveness of the proposed scheme is validated through a simulation example. 1. Introduction With the development of smart materials, some smart materials-based actuators, such as piezoceramic actuators [1], magnetostrictive actuators, and shape memory alloys, are becoming increasingly important in the application areas of aerospace, manufacturing, defense, and civil infrastructure systems [2–5], because of their excellent performance, for example, high precision, fast response, and flexible actuating ability [6–8]. However, a class of nonsmooth nonlinearities, hystereses, with multibranching and nondifferential properties, widely occur in these smart materials-based actuators. When the system is preceded by these actuators, the existence of the hysteresis behaviour in these actuators will degrade the system performance, causing undesirable inaccuracy. The hysteresis nonlinearities are the nature properties of these smart materials, which cannot be cancelled by the improvement of the smart materials. Therefore, how to mitigate the negative effects caused by the hysteresis nonlinearities from control view becomes one important research topic in this area. Due to the nonsmooth nature of hysteresis, most common control approaches developed for nonlinear systems may not be applicable to hysteretic systems directly, which attracted significant attention in the modeling of hysteresis nonlinearities and the hysteretic systems controller design. For the modeling method of the hysteresis, it can be roughly classified as differential equation-based hysteresis models, such as Backlash-like model [9], Bouc-Wen model [10, 11], and Duhem model [10, 12], and operator-based hysteresis models, such as Preisach model,