The stability problem is studied for hybrid systems with delays in this paper. Based on Lyapunov-Razumikhin approach, a novel theorem is presented for such system with the characteristic of homogeneity so that the system is globally preasymptotically stable. In particular, under the homogeneous assumption, we are able to obtain some rather weak conditions compared with general nonhomogeneous hybrid systems in this paper. Finally, two illustrative numerical examples are presented to demonstrate the applicability and the effectiveness of our theorems.

The essence of biomimetics in human–computer interaction (HCI) is the inspiration derived from natural systems to drive innovations in modern-day technologies. With this in mind, this paper introduces a biomimetic adaptive pure pursuit (A-PP) algorithm tailored for the four-wheel differential drive robot (FWDDR). Drawing inspiration from the intricate natural motions subjected to constraints, the FWDDR’s kinematic model mirrors non-holonomic constraints found in biological entities. Recognizing the limitations of traditional pure pursuit (PP) algorithms, which often mimic a static behavioral approach, our proposed A-PP algorithm infuses adaptive techniques observed in nature. Integrated with a quadratic polynomial, this algorithm introduces adaptability in both lateral and longitudinal dimensions. Experimental validations demonstrate that our biomimetically inspired A-PP approach achieves superior path-following accuracy, mirroring the efficiency and fluidity seen in natural organisms.

This paper studies the problem of the input-to-state stability for homogeneous hybrid systems with bounded time-varying delays. First, some homogeneous concepts and properties are introduced and applied to hybrid systems with bounded time-varying delays. Furthermore, by using Lyapunov-Razumikhin approach, some sufficient conditions are extended to the hybrid systems to analyze the input-to-state stability, and with the homogeneous assumption, some special results can be obtained. Finally, numerical examples are given to illustrate the applicability and the effectiveness of the proposed results.

When deep learning methods are used to detect rail surface defects, the training accuracy declines due to small defects and an insufficient number of samples. This paper investigates the problem of rail surface defect detection by using an improved feature pyramid network (FPN) and the metric learning approach. Firstly, the FPN is improved by adding deformable convolution and convolutional block attention modules to improve the accuracy of detecting defects of different scales, and it is pretrained on the MS COCO dataset. Secondly, a new model is established to extract network features based on the transfer learning model and learned network parameters. Thirdly, a multimodal network structure is constructed, and the distance between each modal representative and the embedded feature vector is calculated to classify the defects. Finally, experiments are carried out on the miniImageNet dataset and the rail surface defect dataset. The results show that the mAP (five-way five-shot) of our method is 73.42% on the miniImageNet dataset and 63.29% on the rail defect dataset. Our experiments show the effectiveness of the proposed method, and the results of the rail surface defect detection are satisfactory. As there are few sample classification studies of rail surface defects, this work provides a different approach and lays a foundation for further research.