To solve online continuous time-varying convex quadratic-programming problems constrained by a time-varying linear-equality, a novel varying-parameter convergent-differential neural network (termed as VP-CDNN) is proposed and analyzed. Different from fixed-parameter convergent-differential neural network (FP-CDNN) like the gradient-based recurrent neural network, the classic Zhang neural network and the finite-time Zhang neural network (FT-ZNN), VP-CDNN is based on monotonically increasing time-varying design-parameters. Theoretical analysis proves that VP-CDNN has super exponential convergence and the residual errors of VP-CDNN converge to zero even under perturbation situations, which are both better than traditional FP-CDNN and FT-ZNN. Computer simulations based on different activation functions are illustrated to verify the super exponential convergence performance and strong robustness characteristics of the proposed VP-CDNN. A robot tracking example is finally presented to verify the effectiveness and availability of the proposed VP-CDNN.

Object: Motor imagery (MI) is a mental process widely utilized as the experimental paradigm for brain-computer interfaces (BCIs) across a broad range of basic science and clinical studies. However, decoding intentions from MI remains challenging due to the inherent complexity of brain patterns relative to the small sample size available for machine learning. Approach: This paper proposes an end-to-end Filter-Bank Multiscale Convolutional Neural Network (FBMSNet) for MI classification. A filter bank is first employed to derive a multiview spectral representation of the EEG data. Mixed depthwise convolution is then applied to extract temporal features at multiple scales, followed by spatial filtering to mitigate volume conduction. Finally, with the joint supervision of cross-entropy and center loss, FBMSNet obtains features that maximize interclass dispersion and intraclass compactness. Main results: We compare FBMSNet with several state-of-the-art EEG decoding methods on two MI datasets: the BCI Competition IV 2a dataset and the OpenBMI dataset. FBMSNet significantly outperforms the benchmark methods by achieving 79.17% and 70.05% for four-class and two-class hold-out classification accuracy, respectively. Significance: These results demonstrate the efficacy of FBMSNet in improving EEG decoding performance toward more robust BCI applications. The FBMSNet source code is available at https://github.com/Want2Vanish/FBMSNet .

In order to solve the joint-angular-drift problems of redundant robot manipulators, a novel varying-parameter convergent-differential neural network (VP-CDNN) is proposed and exploited. To do so, a quadratic program (QP)-based feedback-considered joint-angulardrift-free (FC-JADF) scheme is first designed and presented. The FC-JADF scheme adopted in this paper is composed of an optimization criterion simultaneously optimizing quadratic and linear terms, and a velocity layer kinematic equation with adding feedback. Second, the FC-JADF scheme is formulated as a standard QP. Third, the VP-CDNN is proposed to solve the resultant standard QP problem. The Lyapunov theory proves that the proposed VP-CDNN solver can globally converge to an optimal solution to the standard QP problem corresponding to redundant robot manipulators, and the joint-angular-drift problems are solved. Two computer simulations and physical experiments based on a six-degree-of-freedom Kinova Jaco² robot, i.e., a starfish path and a cardioid path, verify the effectiveness, accuracy, safety, and practicability of the QP-based FC-JADF scheme and the VP-CDNN solver for solving the joint-angular-drift problems of redundant robot manipulators.

Motor imagery (MI) decoding is an important part of brain-computer interface (BCI) research, which translates the subject’s intentions into commands that external devices can execute. The traditional methods for discriminative feature extraction, such as common spatial pattern (CSP) and filter bank common spatial pattern (FBCSP), have only focused on the energy features of the electroencephalography (EEG) and thus ignored the further exploration of temporal information. However, the temporal information of spatially filtered EEG may be critical to the performance improvement of MI decoding. In this paper, we proposed a deep learning approach termed filter-bank spatial filtering and temporal-spatial convolutional neural network (FBSF-TSCNN) for MI decoding, where the FBSF block transforms the raw EEG signals into an appropriate intermediate EEG presentation, and then the TSCNN block decodes the intermediate EEG signals. Moreover, a novel stage-wise training strategy is proposed to mitigate the difficult optimization problem of the TSCNN block in the case of insufficient training samples. Firstly, the feature extraction layers are trained by optimization of the triplet loss. Then, the classification layers are trained by optimization of the cross-entropy loss. Finally, the entire network (TSCNN) is fine-tuned by the back-propagation (BP) algorithm. Experimental evaluations on the BCI IV 2a and SMR-BCI datasets reveal that the proposed stage-wise training strategy yields significant performance improvement compared with the conventional end-to-end training strategy, and the proposed approach is comparable with the state-of-the-art method.

Varying-parameter recurrent neural network, being a special kind of neural-dynamic methodology, has revealed powerful abilities to handle various time-varying problems, such as quadratic minimization (QM) and quadratic programming (QP) problems. In this paper, a novel power-type varying-parameter recurrent neural network (PT-VP-RNN) is proposed to solve the perturbed time-varying QM and QP problems. First, based on the generalization of time-varying QM and QP problems, the design process of the PT-VP-RNN is presented in detail. Second, the robustness performance of the proposed PT-VP-RNN is theoretically analyzed and proved. What is more, two numerical examples are simulated to illustrate the robustness convergence performance of PT-VP-RNN even in a large disturbance condition. Finally, two practical application examples (i.e., a robot tracking example and a venture investment example) further verify the effectiveness, accuracy, and widespread applicability of the proposed PT-VP-RNN.

Decoding brain activity from non-invasive electroencephalography (EEG) is crucial for brain-computer interfaces (BCIs) and the study of brain disorders. Notably, end-to-end EEG decoding has gained widespread popularity in recent years owing to the remarkable advances in deep learning research. However, many EEG studies suffer from limited sample sizes, making it difficult for existing deep learning models to effectively generalize to highly noisy EEG data. To address this fundamental limitation, this paper proposes a novel end-to-end EEG decoding algorithm that utilizes a low-rank weight matrix to encode both spatio-temporal filters and the classifier, all optimized under a principled sparse Bayesian learning (SBL) framework. Importantly, this SBL framework also enables us to learn hyperparameters that optimally penalize the model in a Bayesian fashion. The proposed decoding algorithm is systematically benchmarked on five motor imagery BCI EEG datasets ( $N=192$ ) and an emotion recognition EEG dataset ( $N=45$ ), in comparison with several contemporary algorithms, including end-to-end deep-learning-based EEG decoding algorithms. The classification results demonstrate that our algorithm significantly outperforms the competing algorithms while yielding neurophysiologically meaningful spatio-temporal patterns. Our algorithm therefore advances the state-of-the-art by providing a novel EEG-tailored machine learning tool for decoding brain activity.