Modeling and predictive control of networked systems via physics-informed neural networks

This article addresses the data-driven modeling and predictive control of networked systems. The main contribution is a novel methodology to develop a physics-informed recurrent neural network (PI-RNN) model with guaranteed stability properties. The idea consists in interconnecting multiple RNNs consistently with the known physical topology of the networked system, and in jointly training them while enforcing conditions guaranteeing the input-to-state stability of the PI-RNN model. The stability properties of the proposed PI-RNN model pave the way for the design of (i) a decentralized state observer and (ii) a Nonlinear Model Predictive Control (NMPC) regulator with convergence guarantees. The presented strategies are tested on a realistic large-scale networked system, i.e., a district heating network, demonstrating promising results from both the modeling and the control design perspective.