Pinning observability of competitive neural networks with different time–constants

The new concept called pinning observability is proposed for competitive neural networks with different time-scales and a distributed observer structure, which is determined to estimate the states of this large scale network. This network observer has local distinct sub-observers that process local information at the node level but exchange their state estimates with the neighboring observers and thus reflect the interconnection structure of the neural network. The goal is to employ only a minimum number of measurements at certain nodes within the whole neural network, however to be able to estimate the entire state of the network. This can be interpreted as the dual problem to the longer studied pinning control problem. In this paper, we formulate the proposed approach for the two most common competitive neural networks with different time-scales and derive some decoupled and simple conditions for pinning observability. The sub-observers are driven by only local neuron level information but communicate the estimated local states with the neighboring observers. This exchange of local information is the basis of cortical neural processing. The monitoring of few signals from the network holds important practical application for brain signal processing. Simulation examples are given to illustrate the theoretical concepts.