This manuscript presents the design of a deep differential neural network (DDNN) for pattern classification. First, we proposed a DDNN topology with three layers, whose learning laws are derived from a Lyapunov analysis, justifying local asymptotic convergence of the classification error and the weights of the DDNN. Then, an extension to include an arbitrary number of hidden layers in the DDNN is analyzed. The learning laws for this general form of the DDNN offer a contribution to the deep learning framework for signal classification with biological nature and dynamic structures. The DDNN is used to classify electroencephalographic signals from volunteers that perform an identification graphical test. The classification results show exponential growth in the signal classification accuracy from 82 with one layer to 100 with three hidden layers. Working with DDNN instead of static deep neural networks (SDNN) represents a set of advantages, such as processing time and training period reduction up to almost 100 times, and the increment of the classification accuracy while working with less hidden layers than working with SDNN, which are highly dependent on their topology and the number of neurons in each layer. The DDNN employed fewer neurons due to the induced feedback characteristic.

The aim of this study was to develop a prototype of an orthotic system that can be used as a support tool in the rehabilitation of the upper limb. The construction of this device was motivated by the increasing number of subjects suffering from full or partial loss of the upper limb function as a consequence of spinal cord injuries, strokes, occupational syndromes and sports injuries. The majority of procedures used in upper limb rehabilitation consist of repetitive movements enforced by physiotherapists; a robotic device executing the same tasks seems to be a plausible solution if the orthosis can be programmed and controlled automatically. This study reports the mechanical design, electronic instrumentation and automatic control of an upper limb orthosis made of plastic polymer that makes the orthosis a wearable and self-carrying device. The orthosis consisted of a mechatronic device with five joints. The pieces made by a three-dimensional plastic printer were used to construct the device leading to a total weight of 2.6 kg. The application of a robust automatic controller based on the sliding-mode theory forces the movement of the arm, while taking into account the constraints in each angular displacement of the orthosis. A set of reference trajectories designed to represent the usual movements of a healthy upper limb served for evaluating the controller execution. The orthosis was tested on 15 volunteers with a maximum experimental steady-state error of 2% in the angular deviation of all articulations with respect to their reference trajectories.