Contents I. Introduction
During the last decades, analysis and control of hysteresis systems have received considerable attention because hysteresis nonlinearities exist in many physical systems, devices, and materials. Nondifferentiable hysteresis nonlinearities significantly limit system performances by causing undesired inaccuracies or oscillations that may result in instability [1], [2]. System control with hysteresis nonlinearity is an important and frequently difficult topic in control system research [3]. To address such a difficult problem, a mathematical model that can represent the nonlinear hysteresis behavior and be used for control design is critical [4]. As a result, several mathematical models for hysteresis dynamics have been proposed, such as the Duhen model [1], the Preisach model [2], the Krasnosel’skii-Pokrovkii model [3], the Prandtl-Ishlinskii hysteresis operator [1], the Bouc-Wen differential model [5], [6], and the lines-segment hysteresis model [7]. The Bouc-Wen model has several sub-models, including the classical Bouc-Wen model [8], [9], [10], the generalized Bouc-Wen model [11], [12], and other extensions. The Bouc-Wen model is one of the most commonly recognized phenomenological models in mechanics. The characteristics of the Bouc-Wen model allow it to capture a wide range of hysteretic cycles analytically. However, only a few works have been explored based on controlling systems utilizing Bouc-Wen hysteresis, for example, see [8], [9], [10], [11], [12], [13].
