Self-optimizing control is a strategy for selecting controlled variables. It is distinguished by the fact that an economic objective function is adopted as a selection criterion. The aim is to systematically select the controlled variables such that by controlling them at constant setpoints, the impact of uncertain and varying disturbances on the economic optimality is minimized. If a selection leads to an acceptable economic loss compared to perfectly optimal operation then the chosen control structure is referred to as “self-optimizing”. In this comprehensive survey on methods for finding self-optimizing controlled variables we summarize the progress made during the last fifteen years. In particular, we present brute-force methods, local methods based on linearization, data and regression based methods, and methods for finding nonlinear controlled variables for polynomial systems. We also discuss important related topics such as handling changing active constraints. Finally, we point out open problems and directions for future research

Neural differential equations have recently emerged as a flexible data-driven/hybrid approach to model time-series data. This letter experimentally demonstrates that if the data contains oscillations, then standard fitting of a neural differential equation may result in a “flattened out” trajectory that fails to describe the data. We then introduce the multiple shooting method and present successful demonstrations of this method for the fitting of a neural differential equation to two datasets (synthetic and experimental) that the standard approach fails to fit. Constraints introduced by multiple shooting can be satisfied using a penalty or augmented Lagrangian method.