## 1 Introduction  
More severe environmental pollution and energy crisis problems are forcing the development of clean, efficient vehicles with low emissions. Hybrid electric vehicles (HEVs) with artistic multi-power-source designs possess the merits of high efficiency, a negligible driving range limitation and easy braking energy regeneration, representing a promising development direction in the automobile industry [1, 2, 3]. To reduce fuel consumption and emissions, HEVs can operate in a suitable mode for different traffic conditions [4, 5, 6, 7]. However, the frequent mode transitions will lead to the deterioration in the performance of HEVs due to the clutch-torque-induced disturbance and differences in dynamic characteristics between the engine and motor. A noticeable jerk occurs especially during the clutch slipping process, which may shock the powertrain [8, 9]. Hence, the quality of the mode transition should be considered when designing the control strategy for HEVs. Recently, lots of control strategies have been investigated and presented that deal with the mode transition problem for HEVs. [PERSON] et al. presented a coordinated control strategy for parallel HEV based on hybrid control theory [10]. Hybrid controllers were designed for several switched hybrid dynamical systems, and results demonstrate that a seamless transition can be achieved using the proposed controllers. In [11], during mode transitions, the model reference control (MRC) method was applied in a series-parallel HEV to coordinate the clutch torque, motor torque and engine torque. Compared to the conventional method, the MRC method could reduce torque interruption and achieved less vehicle jerk. In [12], taking various unmodeled dynamics and parameter uncertainties into consideration, engine-side and motor-side controllers were devised separately by using feed-forward and robust feedback control strategies. The simulation results demonstrate that the drivability performance for a parallel HEV was improved significantly. Additionally, [PERSON] et al. utilized disturbance observers to devise a four-phase control algorithm for parallel HEVs with a clutch during mode transitions [13]. [PERSON] et al. proposed a hierarchical control system based on the robust \(H_{\infty}\) control strategy to realize a smooth and fast mode transition for a plug-in HEV [14]. Based on the available research, it can be deduced that the essence of these control algorithms is the coordinated control for the engine and motor during mode transitions. The expected vehicle drivability and smoothness can be guaranteed by suppressing fluctuations in coupling torque on the driveshaft while satisfying the torque requirements of the vehicle [15]. However, the influence of clutch torque is not considered in the existing coordinated control strategies. The speed fluctuations on both sides of the clutch, as well as the variation in the friction coefficient with the temperature of the friction plate, will results in a significant nonlinear characteristic of the torque transferred by the clutch [16; 17; 18; 19]. The torque ripple generated by the engine at the side of driving plate can also have an adverse effect during the process of clutch engagement. Despite the short duration of the slipping phase, the nonlinear variation in torque will intensify the mismatching torque in the vehicle powertrain, leading to an obvious unpleasant driving sensation [20; 21; 22; 23]. Hence, further improvement in the drivability and smoothness of HEVs during mode transition remains a challenge. Focusing on the mode transition process from the electric mode to the hybrid driving mode, this paper proposes a novel coordinated strategy to deal with deterioration issues in the drivability and smoothness for parallel HEVs. First, a novel sliding mode control (SMC) strategy based on the group-preserving (GP) scheme was devised to control the motor.