On unknown-input functional observability of linear systems

Finding the least possible order of a stable Unknown-Input Functional Observer (UIFO) has always been a challenge in observer design theory. A practical recursive algorithm is proposed in this technical note to design a minimal multi-functional observer for multi-input multi-output (MIMO) linear time-invariant (LTI) systems with unknown-inputs. The concept of unknown-input functional observability is introduced,and it is used as a certificate of the convergence of our algorithm. The proposed procedure looks for a number of additional auxiliary functions to be augmented to the original functions desired for reconstruction. The resulting UIFO is proper, and minimal (of minimum possible order). Moreover, the algorithm does not need the system to be unknown-input observable. A numerical example shows the procedure as well as the effectiveness of the proposed algorithm.

Statistical modelling of artificial neural network for sorting temporally synchronous spikes

Artificial neural network (ANN) models are able to predict future events based on current data. The usefulness of an ANN lies in the capacity of the model to learn and adjust the weights following previous errors during training. In this study, we carefully analyse the existing methods in neuronal spike sorting algorithms. The current methods use clustering as a basis to establish the ground truths, which requires tedious procedures pertaining to feature selection and evaluation of the selected features. Even so, the accuracy of clusters is still questionable. Here, we develop an ANN model to specially address the present drawbacks and major challenges in neuronal spike sorting. New enhancements are introduced into the conventional backpropagation ANN for determining the network weights, input nodes, target node, and error calculation. Coiflet modelling of noise is employed to enhance the spike shape features and overshadow noise. The ANN is used in conjunction with a special spiking event detection technique to prioritize the targets. The proposed enhancements are able to bolster the training concept, and on the whole, contributing to sorting neuronal spikes with close approximations.