Super-twisting-based continuous neural networks modelling of second-order interconnected systems

The aim of this work was to design a non-parametric model of interconnected systems represented by uncertain second-order systems with incomplete information (only the generalized position vector is measurable). Artificial neural networks appeared to be a plausible alternative to get a non-parametric representation of the aforementioned interconnected systems. The modelling strategy used a set of spatial distributed second-order continuous neural networks (CNN). Each node in the interconnected system was represented as a second-order continuous neural network added by the super-twisting discontinuous sliding mode algorithm. The non-parametric modelling problem was reduced to design a feasible expression for the CNN weights in order to reproduce the states (including the generalized derivative of position vector) of all the nodes dynamics together and simultaneously. The adaptive laws for the CNN weights ensured the convergence of the CNN trajectories to the states of the uncertain interconnected system. To investigate the qualitative behaviour of the suggested methodology, two numerical examples were proposed. The first one represents the interconnection of three mass–spring–damper mechanical systems. The second example considers the problem of the non-parametric modelling problem for a wave partial differential equation. A set of three-dimensional graphic representations were used to demonstrate the identification abilities achieved by the CNN designed in this study for the second case.