Passivity-based control of networks of memristors and capacitors

This paper presents a mathematical framework for modelling networks of memristors and capacitors. Using this framework, we analyse the dynamic behaviour of the fluxes at the memristors in the network. In particular, we show that when no external input is applied to the network, the fluxes at the memristors converge towards an asymptotically stable equilibrium. Moreover, by taking inspiration from passivity-based control, we introduce two control strategies that can be used to steer the fluxes at the memristors in the direction of a desired equilibrium. The results presented in this work are particularly of interest to Neuromorphic Computing as that field suggests utilising memristors as the synaptic weights in hardware implementations of ANNs.