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This note explores the extension of D-stability to non-square matrices, applicable to distributed/decentralized controllability analysis. We first present a definition of D-stability for non-square matrices, directly extending from square matrices. We propose sufficient conditions for specific configurations of non-square matrices. Finally, we consider the selection of configurations to ensure the D-stability of a given non-square system., Comment: arXiv admin note: text overlap with arXiv:2401.00367

Brain-Computer Interfaces (BCIs) rely on accurately decoding electroencephalography (EEG) motor imagery (MI) signals for effective device control. Graph Neural Networks (GNNs) outperform Convolutional Neural Networks (CNNs) in this regard, by leveraging the spatial relationships between EEG electrodes through adjacency matrices. The EEG_GLT-Net framework, featuring the state-of-the-art EEG_GLT adjacency matrix method, has notably enhanced EEG MI signal classification, evidenced by an average accuracy of 83.95% across 20 subjects on the PhysioNet dataset. This significantly exceeds the 76.10% accuracy rate achieved using the Pearson Correlation Coefficient (PCC) method within the same framework. In this research, we advance the field by applying a Reinforcement Learning (RL) approach to the classification of EEG MI signals. Our innovative method empowers the RL agent, enabling not only the classification of EEG MI data points with higher accuracy, but effective identification of EEG MI data points that are less distinct. We present the EEG_RL-Net, an enhancement of the EEG_GLT-Net framework, which incorporates the trained EEG GCN Block from EEG_GLT-Net at an adjacency matrix density of 13.39% alongside the RL-centric Dueling Deep Q Network (Dueling DQN) block. The EEG_RL-Net model showcases exceptional classification performance, achieving an unprecedented average accuracy of 96.40% across 20 subjects within 25 milliseconds. This model illustrates the transformative effect of the RL in EEG MI time point classification.

Brain-Computer Interfaces connect the brain to external control devices, necessitating the accurate translation of brain signals such as from electroencephalography (EEG) into executable commands. Graph Neural Networks (GCN) have been increasingly applied for classifying EEG Motor Imagery signals, primarily because they incorporates the spatial relationships among EEG channels, resulting in improved accuracy over traditional convolutional methods. Recent advances by GCNs-Net in real-time EEG MI signal classification utilised Pearson Coefficient Correlation (PCC) for constructing adjacency matrices, yielding significant results on the PhysioNet dataset. Our paper introduces the EEG Graph Lottery Ticket (EEG_GLT) algorithm, an innovative technique for constructing adjacency matrices for EEG channels. It does not require pre-existing knowledge of inter-channel relationships, and it can be tailored to suit both individual subjects and GCN model architectures. Our findings demonstrated that the PCC method outperformed the Geodesic approach by 9.65% in mean accuracy, while our EEG_GLT matrix consistently exceeded the performance of the PCC method by a mean accuracy of 13.39%. Also, we found that the construction of the adjacency matrix significantly influenced accuracy, to a greater extent than GCN model configurations. A basic GCN configuration utilising our EEG_GLT matrix exceeded the performance of even the most complex GCN setup with a PCC matrix in average accuracy. Our EEG_GLT method also reduced MACs by up to 97% compared to the PCC method, while maintaining or enhancing accuracy. In conclusion, the EEG_GLT algorithm marks a breakthrough in the development of optimal adjacency matrices, effectively boosting both computational accuracy and efficiency, making it well-suited for real-time classification of EEG MI signals that demand intensive computational resources.

In this note, we discuss the extension of several important stable square matrices, e.g., D-stable matrices, diagonal dominance matrices, Volterra-Lyapunov stable matrices, to their corresponding non-square matrices. The extension is motivated by some distributed control-related problems, such as decentralized unconditional stability and decentralized integral controllability for non-square processes. We will provide the connections of conditions between these special square matrices and their associated non-square counterparts. Some conjectures for these special matrices are proposed for future research., Comment: 7 pages; no figure

This paper aims to develop a new human-machine interface to improve rehabilitation performance from the perspective of both the user (patient) and the machine (robot) by introducing the co-adaption techniques via model-based reinforcement learning. Previous studies focus more on robot assistance, i.e., to improve the control strategy so as to fulfill the objective of Assist-As-Needed. In this study, we treat the full process of robot-assisted rehabilitation as a co-adaptive or mutual learning process and emphasize the adaptation of the user to the machine. To this end, we proposed a Co-adaptive MDPs (CaMDPs) model to quantify the learning rates based on cooperative multi-agent reinforcement learning (MARL) in the high abstraction layer of the systems. We proposed several approaches to cooperatively adjust the Policy Improvement among the two agents in the framework of Policy Iteration. Based on the proposed co-adaptive MDPs, the simulation study indicates the non-stationary problem can be mitigated using various proposed Policy Improvement approaches., Comment: 11 pages; 4 figures

This paper presents an efficient in-field calibration method tailored for low-cost triaxial MEMS gyroscopes often used in healthcare applications. Traditional calibration techniques are challenging to implement in clinical settings due to the unavailability of high-precision equipment. Unlike the auto-calibration approaches used for triaxial MEMS accelerometers, which rely on local gravity, gyroscopes lack a reliable reference since the Earth's self-rotation speed is insufficient for accurate calibration. To address this limitation, we propose a novel method that uses manual rotation of the MEMS gyroscope to a specific angle (360{\deg}) as the calibration reference. This approach iteratively estimates the sensor's attitude without requiring any external equipment. Numerical simulations and empirical tests validate that the calibration error is low and that parameter estimation is unbiased. The method can be implemented in real-time on a low-energy microcontroller and completed in under 30 seconds. Comparative results demonstrate that the proposed technique outperforms existing state-of-the-art methods, achieving scale factor and bias errors of less than $2.5\times10^{-2}$ for LSM9DS1 and less than $1\times10^{-2}$ for ICM20948.

This note investigates the stability of both linear and nonlinear switched systems with average dwell time. Two new analysis methods are proposed. Different from existing approaches, the proposed methods take into account the sequence in which the subsystems are switched. Depending on the predecessor or successor subsystems to be considered, sequence-based average preceding dwell time (SBAPDT) and sequence-based average subsequence dwell time (SBASDT) approaches are proposed and discussed for both continuous and discrete time systems. These proposed methods, when considering the switch sequence, have the potential to further reduce the conservativeness of the existing approaches. A comparative numerical example is also given to demonstrate the advantages of the proposed approaches.