Stability and learning of networked systems with application to physics-informed neural networks

This article addresses learning and stability of networked systems. A general methodology is proposed to devise physics-informed data-based networked models by interconnecting multiple submodels according to the networked system topology and jointly training them exploiting input–output data. Since stability properties are crucial in data-based modeling and cannot always be ensured when interconnecting even stable submodels, a novel sufficient condition is proposed guaranteeing incremental input-to-state stability ( δ ISS) of discrete-time networked models. It is shown that this condition can be easily enforced during the training of physics-informed recurrent neural networks, achieving guaranteed stability properties and improved modeling performance compared to standard black-box approaches. Moreover, the enforced δ ISS property enables (i) stable plug-and-play operations on the networked system model, (ii) the development of a convergent decentralized state observer, and (iii) the design of a convergent nonlinear model predictive control regulator. The presented strategies are tested in simulation on a realistic large-scale networked system, i.e., a benchmark chemical plant, showing promising results in both modeling and control design.