A fuzzy singular perturbation model with additive faults on control inputs and external disturbances, a fuzzy $H_\infty$ fault detector (FHFD), and a fuzzy $H_\infty$ fault-tolerant controller (FHFTC) are constructed for nonlinear singularly perturbed systems (NSPSs) with actuator faults and external disturbances, respectively. The sufficient conditions for FHFD and FHFTC existence are derived respectively, which are described by a set of $\sigma$ -independent linear matrix inequalities (LMIs), such that it can avoid the ill-conditioned problems caused by the tiny parameter $\sigma$ . An application to a CE150 helicopter with abrupt and intermittent faults is provided to verify the above approaches. The innovation of the paper lies in the following points: i) The FD and FTC for NSPSs are handled under the united model, which can avoid the incomplete decoupling problem caused by decomposing NSPSs as the slow and fast subsystems. ii) The estimate values for actuator faults are regarded as a state vector of the FHFD, and the output feedback control law is introduced into FHFD, which make the FHFD not only can accurately detect faults but also can stabilize the closed loop system. iii) A new method to transform the nonlinear matrix inequalities into the LMIs is proposed. iv) The presented FHFTC can avoid the problems of missing or inaccurate status information caused by the sensor faults because it adopts the state feedback of the FHFD.

Iron ladles play a significant role in the industrial intelligence upgrade of steel plants. Accurate recognition and tracking for moving iron ladles can provide the location, speed, and operations information of iron ladles, which are essential for making scheduling plans for steel production. YOLOv8 detection and state-of-the-art (SOTA) tracking algorithms for iron ladles are presented in this paper. The Video data sets with or without shelters are constructed by collecting the actual iron ladles working data. Some own image and video datasets are added to the above datasets by using Segment Anything (SAM) and DarkLabel due to lack of iron ladles data. The YOLOv8 detection model is applied to detect the iron ladles, and three trackers, which are the StrongSORT, OC-SORT, and BOT-SORT, are applied to achieve real-time position information of iron ladles, respectively. In order to improve the identification and tracking accuracy for iron ladles, a genetic algorithm is used to optimize the parameter of the above three trackers. The training and testing results of the above model show that the BOT-SORT tracking model with genetic optimization achieves the highest accuracy that HOTA score is 97.49, both MOTA and IDF1 are 100.

Fuzzy singularly perturbed modelling and sensor fault detection for nonlinear singularly perturbed systems (NSPSs) are investigated. A continuous-time fuzzy singularly perturbed model with superimposed faults on state variables and external disturbances are established to describe NSPSs with sensor faults. Based on the model, a novelty $H_{\mathrm{\infty }}$ fuzzy fault detector (FFD) is designed, and the sufficient conditions for $H_{\mathrm{\infty }}$ performance are derived. The above approaches are applied to a CE150 helicopter with abrupt and intermittent faults on sensors. The innovations of this paper are as follows: (i) The nonlinear and slow–fast time-scales are described by a united continuous-time fuzzy singularly perturbed model, and based-it a FFD is designed, which can avoid the incomplete decoupling problem caused by decomposition methods; (ii) The sensor faults are expressed by the superimposed faults on state variables when the continuous-time fuzzy singularly perturbed model is constructed, which is less conservative than existing methods; (iii) In the FFD design, the first-order derivative model of the estimate function for sensor faults is established, and it is combined with a fuzzy observer, which can improve the detection accuracy of the FFD; (iv) $H_{\mathrm{\infty }}$ control technology is introduced into the FFD design process to suppress external disturbances.