The twin parametric-margin support vector machine (TPMSVM) is an excellent kernel-based nonparallel classifier. However, TPMSVM was originally designed for binary classification, which is unsuitable for real-world multiclass applications. Therefore, this paper extends TPMSVM for multiclass classification and proposes a novel K multiclass nonparallel parametric-margin support vector machine (MNP-KSVC). Specifically, our MNP-KSVC enjoys the following characteristics. (1) Under the “one-versus-one-versus-rest” multiclass framework, MNP-KSVC encodes the complicated multiclass learning task into a series of subproblems with the ternary output $\{-1,0,+1\}$. In contrast to the “one-versus-one” or “one-versus-rest” strategy, each subproblem not only focuses on separating the two selected class instances but also considers the side information of the remaining class instances. (2) MNP-KSVC aims to find a pair of nonparallel parametric-margin hyperplanes for each subproblem. As a result, these hyperplanes are closer to their corresponding class and at least one distance away from the other class. At the same time, they attempt to bound the remaining class instances into an insensitive region. (3) MNP-KSVC utilizes a hybrid classification and regression loss joined with the regularization to formulate its optimization model. Then, the optimal solutions are derived from the corresponding dual problems. Finally, we conduct numerical experiments to compare the proposed method with four state-of-the-art multiclass models: Multi-SVM, MBSVM, MTPMSVM, and Twin-KSVC. Experimental results demonstrate the feasibility and effectiveness of MNP-KSVC in terms of multiclass accuracy and learning time.

In this paper, an adaptive-weight model predictive control (AW-MPC) strategy is proposed to address the trajectory tracking problem of a lower-limb rehabilitation exoskeleton robot. First, based on human motion analysis, the dynamics of the lower-limb rehabilitation exoskeleton are established, and the nonlinear dynamic model is transformed into a linear model. Second, a MPC objective function is formulated to minimize the tracking error, yielding the optimal control input. Then, on the basis of conventional MPC, a weight-tuning scheme is developed: a weighting function is constructed according to the evolution of the tracking error to adaptively adjust the MPC weighting coefficients, and the closed-loop stability of the control system is proven via a Lyapunov-based analysis. Finally, the proposed method is validated on a lower-limb rehabilitation exoskeleton experimental platform, with a PID controller designed as a baseline for comparison. The experimental results demonstrate that, compared with the PID controller, the proposed AW-MPC achieves faster convergence of the tracking error, higher tracking accuracy, and enhanced robustness.

Process data plays a vital role in diagnosing fault sources in chemical production. However, such data contain rich process information and are often sensitive, making direct analysis infeasible due to privacy concerns. Although federated learning mitigates data leakage risks, the conventional averaging strategy falls short in achieving high fault identification accuracy, especially under non-independent and identically distributed (non-IID) client data. To overcome this challenge, we propose a personalized federated learning framework, in which a Takagi–Sugeno (T–S) fuzzy fusion rule is designed. Then, the personalized model is constructed through a structured procedure: fuzzification of model parameter distances, definition of fuzzy rules, fuzzy inference, and defuzzification. Moreover, layer-wise fusion is employed to enhance the precision of aggregation. Evaluations on the Tennessee Eastman (TE) process demonstrate that our method achieves superior fault identification accuracy. The results validate the efficacy of the proposed Fuzzy Rule-Based Federated Layer-wise Fusion (FedFZ) framework in industrial fault diagnosis under heterogeneous data distributions.