## 1 Introduction  
Dielectric electro-active polymer (DEAP) materials are a promising actuation technology due to the merits of lightweight, large strain, high energy density, low-noise, and fast response [1, 2]. DEAP materials, as a kind of soft electroactive material, are composed of a polymer film sandwiched between two silver metal soft electrodes layers [3]. The working principle of DEAP materials is shown in Figure 1. It can be simply divided into three steps [3]: (1) a large driving voltage is applied to the silver metal soft electrodes layers to produce a high electric field; (2) the silver metal soft electrodes layers can be regarded as a flat capacitor, a Maxwell stress will be produced by electrostatic forces; (3) the polymer film is extruded under the Maxwell stress to result in actuation. Based on this basic working principle, DEAP materials have been widely applied in high-precision trajectory tracking control as actuators and achieved great potential for applications in bioinspired soft robots filed, including an arm wrestling robot [4], a flying robot [5], and a swimming robot [6]. However, like other smart materials such as shape memory alloys (SMA), piezoelectrics and magnetostriectives, the inherent asymmetric rate-dependent hysteresis nonlinearity is ubiquitous in DEAP actuators [7], which causes tracking inaccuracy, leads to a decrease in the performance of the closed-loop system, or may even result in oscillations. Therefore, the asymmetric rate-dependent hysteresis modeling and tracking control of such DEAP actuators have been important issues. The asymmetric rate-dependent hysteresis models of the smart materials can be roughly classified into three categories. The first category is physics-based hysteresis models. For instance, [PERSON]. [8] presented a dynamic Jiles-Atherton model to describe the asymmetric rate-dependent hysteresis of giant magnetostrictive actuators (GMAs). The second category is phenomenological hysteresis models. For example, [PERSON]. [9] proposed an MPI model to characterize the asymmetric rate-dependent hysteresis of dielectric elastomer actuators (DEAs), where dynamical envelope functions were used to describe the rate-dependent hysteresis, and polynomial operators were introduced to characterize the asymmetric. [PERSON]. [10] proposed an MPI model to describe the asymmetric rate-dependent hysteresis of magnetostrictive actuators, in which a rate-dependent PI model was utilized to describe the rate-dependent hysteresis, and dead-zone operators were introduced to characterize the asymmetric. The third category is the intelligent methods-based hysteresis models. [PERSON]. [11] developed a nonlinear ARX recurrent neural network hysteresis model to characterize the asymmetric rate-dependent hysteresis of SMA actuators. [PERSON]. [7; 12] developed a Preisach-type dynamic nonlinear ARX fuzzy hysteresis model to describe the asymmetric rate-dependent hysteresis of DEAP actuators. It should be pointed out that the unmodeled hysteresis nonlinearity, residual dynamics, parameter uncertainties and external disturbances will reduce the trajectory tracking accuracy. Therefore, it is necessary to design a robust controller to deal with the nonlinear disturbances. Various control strategies have been developed for trajectory tracking control of DEAP actuators such as PID control [7; 13], internal model control [14] and adaptive sliding mode control (SMC) [15]. Among those control strategies, SMC scheme has been widely used to control the hysteresis nonlinearity systems, because SMC scheme can guarantee the global robustness of the systems, and can simply and effectively cope with parameters variation and external disturbances [16]. However, the conventional SMC scheme can only make the system states converge to the equilibrium point asymptotically with infinite settling time. To overcome the shortcoming, terminal sliding mode controller (TSMC) scheme was proposed [17], in which a nonlinear switching surface was employed to achieve finite time convergence [18].