Compact neural network modeling of nonlinear dynamical systems via the standard nonlinear operator form

•The properties are elucidated for a compact dynamic neural network model structure.•The dependency of stability analysis tools on the number of neurons is discussed.•Fewer neurons are needed to model nonlinear dynamics than for other popular models.•Neural network model structures are compared in a multi-stage bioreactor case study.•The model structure captures the nonlinear dynamics with only one or two neurons. Dynamic artificial neural networks (DANNs) have become popular for the data-driven modelling of nonlinear dynamical systems. This article elucidates properties of a compact DANN model structure called the standard normal operator form (SNOF). Sets of nonlinear dynamical systems are characterized for which the SNOF can achieve the same model identification error with fewer neurons than needed by the popular DANN model structures. The results are demonstrated in a case study for a multi-stage bioreactor, which is a highly nonlinear dynamical system in which the cells have a sharp change in dynamics during a change in the feed composition as the bioreactor shifts from growth mode to production mode. The ability of the SNOF to model highly nonlinear dynamical systems with a very small number of neurons suggests its potential for serving as a basis for the design of model-based optimal control systems with theoretical guarantees of closed-loop stability and performance.