Stability analysis of nonlinear singular systems, arising from differential algebraic equations, is addressed in this report, exploiting the fact that it belongs to the class of Positvstellensatz problems. By means of the direct Lyapunov method and a variety of convex descriptor forms, sufficient conditions in terms of linear matrix inequalities are developed. Issues concerning proper initialization and simulation are also considered. Illustrative examples are provided.

Brain-computer interfaces (BCIs) can be used to induce neural plasticity in the human nervous system by pairing motor cortical activity with relevant afferent feedback, which can be used in neurorehabilitation. The aim of this study was to identify the optimal type or combination of afferent feedback modalities to increase cortical excitability in a BCI training intervention. In three experimental sessions, 12 healthy participants imagined a dorsiflexion that was decoded by a BCI which activated relevant afferent feedback: (1) electrical nerve stimulation (ES) (peroneal nerve—innervating tibialis anterior), (2) passive movement (PM) of the ankle joint, or (3) combined electrical stimulation and passive movement (Comb). The cortical excitability was assessed with transcranial magnetic stimulation determining motor evoked potentials (MEPs) in tibialis anterior before, immediately after and 30 min after the BCI training. Linear mixed regression models were used to assess the changes in MEPs. The three interventions led to a significant (p < 0.05) increase in MEP amplitudes immediately and 30 min after the training. The effect sizes of Comb paradigm were larger than ES and PM, although, these differences were not statistically significant (p > 0.05). These results indicate that the timing of movement imagery and afferent feedback is the main determinant of induced cortical plasticity whereas the specific type of feedback has a moderate impact. These findings can be important for the translation of such a BCI protocol to the clinical practice where by combining the BCI with the already available equipment cortical plasticity can be effectively induced. The findings in the current study need to be validated in stroke populations.

Brain-computer interfaces (BCIs) have been proven to be useful for stroke rehabilitation, but there are a number of factors that impede the use of this technology in rehabilitation clinics and in home-use, the major factors including the usability and costs of the BCI system. The aims of this study were to develop a cheap 3D-printed wrist exoskeleton that can be controlled by a cheap open source BCI (OpenViBE), and to determine if training with such a setup could induce neural plasticity. Eleven healthy volunteers imagined wrist extensions, which were detected from single-trial electroencephalography (EEG), and in response to this, the wrist exoskeleton replicated the intended movement. Motor-evoked potentials (MEPs) elicited using transcranial magnetic stimulation were measured before, immediately after, and 30 min after BCI training with the exoskeleton. The BCI system had a true positive rate of 86 ± 12% with 1.20 ± 0.57 false detections per minute. Compared to the measurement before the BCI training, the MEPs increased by 35 ± 60% immediately after and 67 ± 60% 30 min after the BCI training. There was no association between the BCI performance and the induction of plasticity. In conclusion, it is possible to detect imaginary movements using an open-source BCI setup and control a cheap 3D-printed exoskeleton that when combined with the BCI can induce neural plasticity. These findings may promote the availability of BCI technology for rehabilitation clinics and home-use. However, the usability must be improved, and further tests are needed with stroke patients.

This article presents a systematic approach to robustly control a lower-limb exoskeleton in real-time using multimodal sensors. The control adopts two sensor bands that combine an array of force-sensitive resistors (FSR) and an inertial measurement unit (IMU) to measure both force myography (FMG) signals and limb motion. A robust sensor fusion algorithm that combines FMG and IMU signals with artificial neural networks is developed to accurately estimate the wearer’s hip and knee rotation angles. Moreover, a mathematical model of the lower-limb exoskeleton is calibrated and validated with real-time experimental data. Finally, a model-based controller is designed to track position references generated from the network through linear matrix inequalities. The biomimetic control algorithm is tested in simulation and a physical setup to show the effectiveness of the novel control method. Note to Practitioners —This work addresses the challenge of real-time control of lower-limb exoskeletons. Our approach to address the trajectory generation problem involves emulating the movements of a healthy limb. This is achieved through a robust sensor fusion algorithm to integrate data from two multimodal sensors, namely, FMG and IMU sensors, enabling a reliable estimation of the hip and knee’s angular positions. Signals are processed and neural networks are trained with exoskeleton encoder measurements as targets. Physical tests show both the accuracy and robustness of the control method. Potential applications of the new method include real-time gait analysis, control of upper limb exoskeletons, and study of the induction of neural plasticity.