In this paper, the event-triggered control problem is investigated using backstepping techniques for nonlinear systems with dead-zone input. The external disturbance and unknown parameters are also considered in the controller’s design. It is well known that errors in input signal measurements are inevitable. In event-triggered control, such errors will directly affect whether the control signal is updated. This measurement error can be seen in the form of interference to the threshold. Therefore, unlike traditional event-triggered control, the existence of threshold disturbance is considered in the controller’s design. The proposed controller can not only compensate for the uncertainties caused by external disturbance and unknown parameters but can also suppress the unknown effects caused by threshold interference. In addition, to obtain a continuous controller, a smooth function is constructed to approximate the discontinuous sign function. In this way, Zeno behavior is successfully avoided. The boundedness of all signals and the tracking performance of the system can be guaranteed by the proposed control scheme. Numerical simulation and actual system simulation demonstrate the effectiveness of the proposed control scheme. The comparative simulation results also verify this event-triggered controller’s advantages, including better tracking performance and fewer trigger times.

A prescribed performance neuro-adaptive control scheme is proposed for a single-link flexible-joint robotic manipulator with unknown deadzone and actuator faults. A new smooth deadzone inverse model is constructed to offset the adverse effect caused by the input deadzone in the actuator of flexible-joint manipulators. The control law is developed by coordinating prescribed performance control with a backstepping technique to ensure transient/steady-state performance, while adaptive neural networks are employed for uncertainty approximation. The tracking error is always restricted within the prescribed bound during the control process, and it ultimately converges to the small neighborhood of origin. All signals in the closed-loop flexible-joint robotic manipulator system are proved to be uniformly bounded. Simulation results are provided to demonstrate the efficiency of the prescribed performance adaptive neural network backstepping control scheme.

With the development of power electronics technology, permanent magnet brushless DC motors have developed rapidly and are now widely used in electric vehicles, flywheel energy storage, rail transit, and other applications. The stator slot structure is one of the main factors affecting the performance of the motor. A low-power permanent magnet brushless DC motor was selected as the research object, and the finite element analysis method was used to study the effects of different slot and pole combinations and stator slot types on the cogging torque, reluctance torque, and back electromotive force of the permanent magnet brushless DC motor. The influence of the stator slot structure of the motor on the performance of the motor was analyzed, and the optimal slot-pole combination and stator slot type were determined. The results showed that the cogging torque of the 2-stage 24-slot motor was 14 mN·m, and the reluctance torque was 75 mN·m. The cogging torque and reluctance torque were the smallest, and the back electromotive force waveform was similar to a trapezoidal wave. The motor cogging torque of the pear-shaped round slot was the smallest, with a value of 460 mN·m, and the motor reluctance torque of the pear-shaped trapezoidal slot was the smallest, with a value of 1.2 N·m. The back electromotive force waveforms of the motors with four different stator slot types were similar.

The chemical composition of vegetable cooking oils is a key parameter in determining the quality of their products. Antioxidants are widely used in these products to extend their shelf life. In this study, the concentration of butylated hydroxytoluene (BHT) in edible oil was quantitatively determined by Raman spectroscopy combined with chemometrics. Initially, Raman spectra of edible oil samples with varying concentrations of BHT were obtained. Subsequently, three variable selection methods were applied to the pre-processed spectra. Optimised characteristic wavelengths were then used to establish a Radial Basis Function (RBF) neural network and partial least squares (PLS) models. The impact of variable selection on feature wavelengths was evaluated for both models in both independent and combined cases. The results demonstrate that the features identified through multiple variable selection methods correlate highly with the BHT content and can be utilised to develop high-precision detection models. The findings indicate that the PLS model, optimised using competitive adaptive reweighting (CARS), achieved the best prediction performance, with an average $R_P^2$ of 0.9687, and RMSEP of 3.1211. These results demonstrate the feasibility of using Raman spectroscopy combined with chemometrics for the rapid screening of BHT in edible oils. While the current study focuses on a broad concentration range to validate the method’s linearity, further optimisation is required for trace-level detection to meet strict regulatory limits.

This paper considers remote state estimation in cyber-physical systems (CPSs) with multiple sensors, where measurements of each sensor are transmitted to the corresponding remote estimator over a shared communication network with interdependent security. A stochastic non-cooperative game framework with asymmetric information is provided, in which each sensor is in pursuit of minimizing the security investment cost on the first stage associated with the expected error covariance as small as possible at the corresponding remote estimator on the second stage. The asymmetry of information among sensors poses a challenge to characterize or compute the Nash equilibria (NE). To overcome the challenge, based on the common information among sensors, the game with asymmetric information is transformed into another game with symmetric information such that a subclass of NE refer to common information based Markov perfect equilibria of the original game can be achieved by using a backward induction algorithm. Finally, a numerical example is presented to verify the obtained results.